What affects plant growth?
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Table of Contents
Custom Lab Manual for Physical Science NSCI 101/103 Lab 1: Introduc on to Science Lab 2: Types of Forces Lab 3: Newton’s Laws Lab 4: Acids & Bases Lab 5: Chemical Processes Lab 6: Light Lab 7: Radioac vity
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Time and Addi onal Materials Required
Time and Addi onal Materials Required for Each Lab
Lab 1: Introduc on to Science o Time Required: 60 minutes o Addi onal Materials Needed: None Lab 2: Types of Forces o Time Required: 60 minutes o Addi onal Materials Needed: None Lab 3: Newton’s Laws o Time Required: 60 minutes o Addi onal Materials Needed: A deep dish, water, 2 chairs (for supports)
Lab 4: Acids and Bases
o Time: 60 min. o Materials needed: Tomato juice, dis lled water, milk
Lab 5: Chemical Processes
o Time: 60 min. o Materials needed: none Lab 6: Light o Time Required: 45‐60 minutes o Addi onal Materials Needed: White paper Lab 7: Radioac vity o Time Required: 45‐60 minutes o Addi onal Materials Needed: None
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Lab Safety
Lab Safety Always follow the instruc ons in your laboratory manual and these general rules:
Lab prepara on
Please thoroughly read the lab exercise before star ng!
If you have any doubt as to what you are supposed to be doing and how to do it safely, please STOP and then:
Double‐check the manual instruc ons.
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Contact us for technical support by phone at 1‐888‐ESL‐Kits (1‐888‐375‐5487) or by email at Help@esciencelabs.com.
Read and understand all labels on chemicals.
If you have any ques ons or concerns, refer to the Material Safely Data Sheets (MSDS) available at www.esciencelabs.com. The MSDS lists the dangers, storage requirements, exposure treatment and disposal instruc ons for each chemical.
Consult your physician if you are pregnant, allergic to chemicals, or have other medical condi ons that may require addi onal protec ve measures.
Proper lab a re
Remove all loose clothing (jackets, sweatshirts, etc.) and always wear closed‐toe shoes.
Long hair should be pulled back and secured and all jewelry (rings, watches, necklaces, earrings, bracelets, etc.), should be removed.
Safety glasses or goggles should be worn at all mes. In addi on, wearing so contact lenses while conduc ng experiments is discouraged, as they can absorb poten ally harmful chemicals.
eScience Labs, LLC designs every kit with safety as our top priority. Nonetheless, these are science kits and contain items which must be
handled with care. Safety in the laboratory always comes first!
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Lab Safety
When handling chemicals, always wear the protec ve goggles, gloves, and apron provided.
Performing the experiment
Do not eat, drink, chew gum, apply cosme cs or smoke while conduc ng an experi‐ ment.
Work in a well ven lated area and monitor experiments at all mes, unless instructed otherwise.
When working with chemicals:
Never return unused chemicals to their original container or place chemicals in an unmarked container.
Always put lids back onto chemicals immediately a er use.
Never ingest chemicals. If this occurs, seek immediate help.
Call 911 or “Poison Control” 1‐800‐222‐1222
Never pipe e anything by mouth.
Never leave a heat source una ended.
If there is a fire, evacuate the room immediately and dial 911.
Lab Clean‐up and Disposal
If a spill occurs, consult the MSDS to determine how to clean it up.
Never pick up broken glassware with your hands. Use a broom and a dustpan and dis‐ card in a safe area.
Do not use any part of the lab kit as a container for food.
Safely dispose of chemicals. If there are any special requirements for disposal, it will be noted in the lab manual.
When finished, wash hands and lab equipment thoroughly with soap and water.
Above all, USE COMMON SENSE!
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Student Portal
Introduc on o Safety Video o Scien fic Method Video
Newtonian Mechanics
o The Science of Sailing Video o The Moving Man o Slam Dunk Science o The Science of Skateboarding o Projec le Mo on o Ladybug Revolu on o Energy Skate Park
Chemistry and Light
o Acid base reac ons o Geometric Op cs
Log on to the Student Portal using these easy steps:
Visit our website, www.esciencelabs.com, and click on the green bu on (says
“Register or Login”) on the top right side of the page. From here, you will be taken to a login page. If you are registering your kit code for the first me, click the “create an account” hyperlink. Locate the kitcode, located on a label on the inside of the kit box lid. Enter this, along with other re‐
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Student Portal. Have fun!
Student Portal Content
Lab 1: Introduc on to Science
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Lab 1: Introduc on to Science
What is science? You have likely taken several classes throughout your career as a student, and know that it is more than just chapters in a book. Science is a process. It uses evidence to understand the history of the natural world and how it works. Scien fic knowledge is constantly evolving as we understand more about the natural world. Science begins with observa ons that can be measured in some way, and o en concludes with observa ons from analyzed data.
Following the scien fic method helps to minimize bias when tes ng a theory. It helps scien sts collect and organize informa on in a useful way so that pa erns and data can be analyzed in a meaningful way. As a sci‐ en st, you should use the scien fic method as you conduct the experiments throughout this manual.
Concepts to explore: The Scien fic Method
Observa ons
Hypothesis
Variables
Controls
Data Analysis
Unit Conversions
Scien fic Nota on
Significant Digits
Data Collec on
Tables
Graphs
Percent Error
Scien fic Reasoning
Wri ng a Lab Report
Figure 1: The process of the scien fic method
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Lab 1: Introduc on to Science
The process of the scien fic method begins with an observa on. For ex‐ ample, suppose you observe a plant growing towards a window. This ob‐ serva on could be the first step in designing an experiment. Remember that observa ons are used to begin the scien fic method, but they may also be used to help analyze data.
Observa ons can be quan ta ve (measurable), or qualita ve (immeasurable; observa onal). Quan ta ve observa ons allow us to rec‐ ord findings as data, and leave li le room for subjec ve error. Qualita ve observa ons cannot be measured. They rely on sensory percep ons. The nature of these observa ons makes them more subjec ve and suscep ble to human error.
Let’s review this with an example. Suppose you have a handful of pennies. You can make quan ta ve observa‐ ons that there are 15 pennies, and each is 1.9 cm in diameter. Both the quan ty, and the diameter, can be pre‐
cisely measured. You can also make qualita ve observa ons that they are brown, shiny, or smooth. The color and texture are not numerically measured, and may vary based on the individual’s percep on or background.
Quan ta ve observa ons are generally preferred in science because they involve “hard” data. Because of this, many sci‐ en fic instruments, such as microscopes and scales, have been developed to alleviate the need for qualita ve observa‐ ons. Rather than observing that an object is large, we can
now iden fy specific mass, shapes, structures, etc.
There are s ll many situa ons, as you will encounter throughout this lab manual, in which qualita ve observa‐ ons provide useful data. No cing the color change of a leaf or the change in smell of a compound, for example,
are important observa ons and can provide a great deal of prac cal informa on.
Once an observa on has been made, the next step is to develop a hypothesis. A hypothesis is a statement de‐ scribing what the scien st thinks will happen in the experiment. A hypothesis is a proposed explana on for an event based on observa on(s). A null hypothesis is a testable statement that if proven true, means the hypothe‐ sis was incorrect. Both a hypothesis and a null hypothesis statement must be testable, but only one can be true. Hypotheses are typically wri en in an if/then format. For example:
Hypothesis:
If plants are grown in soil with added nutrients, then they will grow faster than plants grown without added nutrients.
If plants grow quicker when nutrients are added, then the hypothesis is accepted and the null
hypothesis is rejected.
Figure 2: What affects plant growth?
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Lab 1: Introduc on to Science
Null hypothesis:
If plants are grown in soil with added nutri‐ ents, then they will grow at the same rate as plants grown in soil without nutrients.
There are o en many ways to test a hypothesis. However, three rules must always be followed for re‐ sults to be valid.
The experiment must be replicable.
Only test one variable at a me.
Always include a control.
Experiments must be replicable to create valid theories. In other words, an experiment must provide precise results over mul ple trials Precise results are those which have very similar values (e.g., 85, 86, and 86.5) over mul ‐ ple trials. By contrast, accurate results are those which demonstrate what you expected to happen (e.g., you expect the test results of three students tests to be 80%, 67%, and 100%). The following example demonstrates the significance of experimental repeatability. Suppose you conduct an experi‐ ment and conclude that ice melts in 30 seconds when placed on a burner,
but you do not record your procedure or define the precise variables included. The conclusion that you draw will not be recognized in the scien‐ fic community because other scien sts cannot
repeat your experiment and find the same results. What if another scien st tries to repeat your ice experiment, but does not turn on the burner; or, us‐ es a larger ice chunk. The results will not be the same, because the experi‐ ment was not repeated using the same procedure. This makes the results invalid, and demonstrates why it is important for an experiment to be repli‐ cable.
Variables are defined, measurable components of an experiment. Controlling variables in an experi‐ ment allows the scien st to quan fy changes that occur. This allows for focused results to be meas‐ ured; and, for refined conclusions to be drawn. There are two types of variables, independent variables and dependent variables.
Independent variables are variables that scien sts select to change. For example, the me of day, amount of substrate, etc. Independent variables are used by scien sts to test hypotheses. There can
If plants grow quicker when nutrients are added, then the hypothesis is accepted and the null
hypothesis is rejected.
Accurate results all hit the bulls‐eye on a target.
Precise results may not hit the bulls‐eye, but they all
hit the same region.
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Lab 1: Introduc on to Science
only be one independent variable in each experiment. This is because if a change occurs, scien sts need to be able to pinpoint the cause of the change. Independent variables are always placed on the x‐ axis of a chart or graph.
Dependent variables are variables that scien sts observe in rela onship to the independent variable. Common examples of this are rate of reac on, color change, etc. Any changes observed in the depend‐ ent variable are caused by the changes in the independent variable. In other words, they depend on the independent variable. There can be more than one dependent variable in an experiment. Depend‐ ent variables are placed on the y‐axis of a chart or graph.
A control is a sample of data collected in an experiment that is not exposed to the independent varia‐ ble. The control sample reflects the factors that could influence the results of the experiment, but do not reflect the planned changes that might result from manipula ng the independent variable. Con‐ trols must be iden fied to eliminate compounding changes that could influence results. O en, the hardest part of designing an experiment is determining how to isolate the independent variable and control all other possible variables. Scien sts must be careful not to eliminate or create a factor that could skew the results. For this reason, taking notes to account for uniden fied variables is important. This might include factors such as temperature, humidity, me of day, or other environmental condi‐ ons that may impact results.
There are two types of controls, posi ve and nega ve. Nega ve controls are data samples in which you expect no change to occur. They help scien sts determine that the experimental results are due to the independent variable, rather than an uniden fied or unaccounted variable. For example, suppose you need to culture bacteria and want to include a nega ve control. You could create this by streaking a sterile loop across an agar plate. Sterile loops should not create any microbial growth; therefore, you expect no change to occur on the agar plate. If no growth occurs, you can assume the equipment used was sterile. However, if microbial growth does occur, you must assume that the equipment was con‐ taminated prior to the experiment and must redo the experiment with new materials.
Alterna vely, posi ve controls are data samples in which you do expect a change. Let’s return to the growth example, but now you need to create a posi ve control. To do this, you now use a loop to streak a plate with a sample that you know grows well on agar (such as E. coli). If the bacteria grow, you can assume that the bacteria sample and agar are both suitable for the experiment. However, if the bacteria do not grow, you must assume that the agar or bacteria has been compromised and you must re‐do the experiment with new materials.
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Lab 1: Introduc on to Science
The scien fic method also requires data collec on. This may reflect what occurred before, during, or a er an experiment. Collected results help reveal experimental results. Results should include all rele‐ vant observa ons, both quan ta ve and qualita ve.
A er results are collected, they can be analyzed. Data analysis o en involves a variety of calcula ons, conversions, graphs, tables etc. The most common task a scien st faces is unit conversion. Units of me are a common increment that must be converted. For example, suppose half of your data is meas‐
ured in seconds, but the other half is measured in minutes. It will be difficult to understand the rela‐ onship between the data if the units are not equivalent.
When calcula ng a unit conversion, significant digits must be accounted for. Significant digits are the digits in a number or answer that describe how precise the value actually is. Consider the following rules:
Addi on and subtrac on problems should result in an answer that has the same number of significant decimal places as the least precise number in the calcula on. Mul plica on and division problems should keep the same total number of significant digits as the least precise number in the calcula on. For example:
Addi on Problem: 12.689 + 5.2 = 17.889 → round to 18
Mul plica on Problem: 28.8 x 54.76 = 1577.088 → round to 1580 (3 sig. digits)
Rule Example
Any non‐zero number (1‐9) is always significant 45 has two significant digits
3.99 has three significant digits 248678 has six significant digits
Any me a zero appears between significant num‐ bers, the zero is significant
4005 has four significant digits 0.34000000009 has eleven significant digits
Zeros that are ending numbers a er a decimal point or zeros that are a er significant numbers
before a decimal point are significant
45.00 has four significant digits 15000.00 has seven significant digits
Zeros that are used as placeholders are NOT sig‐ nificant digits
62000000 has only two significant digits .0000000897 has only three significant digits
A zero at the end of a number with no decimal can be a significant digit
50 cm exactly has two significant digits (not rounded)
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Lab 1: Introduc on to Science
Scien fic nota on is another common method used to transform a number. Scien fic data is o en very large (e.g., the speed of light) or very small (e.g., the diameter of a cell). Scien fic nota on provides an abbreviated expression of a number, so that scien sts don’t get caught up coun ng a long series of zeroes.
There are three parts to scien fic nota on: the base, the coefficient and the exponent. Base 10 is al‐ most always used and makes the nota on easy to translate. The coefficient is always a number be‐ tween 1 and 10, and uses the significant digits of the original number. The exponent tells us whether the number is greater or less than 1, and can be used to “count” the number of digits the decimal must be moved to translate the number to regular nota on. A nega ve exponent tells you to move the deci‐ mal to the le , while a posi ve one tells you to move it to the right.
For example, the number 5,600,000 can be wri en as 5.6 x 106. If you mul ply 5.6 by 10 six mes, you will arrive at 5,600,000. Note the exponent, six, is posi ve because the number is larger than one. Al‐ terna ve, the number 0.00045 must be wri en using a nega ve exponent. To write this number in sci‐ en fic nota on, determine the coefficient. Remember that the coefficient must be between 1 and 10. The significant digits are 4 and 5. Therefore, 4.5 is the coefficient. To determine the exponent, count how many places you must move the decimal over to create the original number. Moving to the le , we have 0.45, 0.045, 0.0045, and finally 0.00045. Since we move the decimal 4 places to the le , our exponent is ‐4. Wri en in scien fic nota on, we have 4.5 x 10‐4
Although these calcula ons may feel laborious, a well‐calculated presenta on can transform data into a format that scien sts can more easily understand and learn from. Some of the most common meth‐ ods of data presenta on are:
Table: A well‐organized summary of data collected. Tables should display any informa on relevant to the hypothesis. Always include a clearly stated tle, labeled columns and rows, and measurement units.
Variable Height Wk. 1 (mm) Height Wk. 2 (mm) Height Wk. 3 (mm) Height Wk. 4 (mm)
Control (without nutrients) 3.4 3.6 3.7
4.0
Independent (with nutrients)
3.5 3.7 4.1 4.6
Table Example: Plant Growth With and Without Added Nutrients
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Lab 1: Introduc on to Science
Graph: A visual representa on of the rela onship between the independent and dependent variable. They are typically created by using data from a table. Graphs are useful in iden fying trends and illus‐ tra ng findings. When construc ng a graph, it is important to use appropriate, consistent numerical intervals. Titles and axes labels should also reflect the data table informa on. There are several differ‐ ent types of graphs, and each type serves a different purpose. Examples include line graphs or bar graphs. Line graphs show the rela onship between variables using plo ed points that are connected with a line. There must be a direct rela onship and dependence between each point connected. More than one set of data can be presented on a line graph. By comparison, bar graphs: compare results that are independent from each other, as opposed to a con nuous series.
Speed (kph)
Figure 4: Top speed for Cars A, B, C, and D
Figure 3: Plant growth, with and without nutrients, over me
Height (mm)
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Lab 1: Introduc on to Science
A er compiling the data, scien sts analyze the data to determine if the experiment supports or re‐ futes the hypothesis. If the hypothesis is supported, you may want to consider addi onal variables that should be examined. If your data does not provide clear results, you may want to consider run‐ ning addi onal trials or revising the procedure to create a more precise outcome.
One way to analyze data is to calculate percent error. Many experiments perform trials which calcu‐ late known value. When this happens, you can compare experimental results to known values and cal‐ culate percent error. Low percent error indicates that results are accurate, and high percent error indi‐ cates that results are inaccurate. The formula for percent error is:
Note that the brackets in the numerator indicate “absolute value”. This means that the number in the equa on is always posi ve.
Suppose your experiment involves gravity. Your experimental results indicate that the speed of gravity is 10.1 m/s2, but the known value for gravity is 9.8 m/s2. We can calculate the percent error through the following steps:
The scien fic method gives us a great founda on to conduct scien fic reasoning. The more data and observa ons we are able to make, the more we are able to accurately reason through the natural phe‐ nomena which occur in our daily lives. Scien fic reasoning does not always include a structured lab report, but it always helps society to think through difficult concepts and determine solu ons. For ex‐ ample, scien fic reasoning can be used to create a response to the changing global climate, develop medical solu ons to health concerns, or even learn about subatomic par cles and tendencies.
Although the scien fic method and scien fic reasoning can guide society through cri cal or abstract thinking, the scien fic industry typically promotes lab reports as a universal method of data analysis and presenta on. In general terms, a lab report is a scien fic paper describing the premise of an ex‐ periment, the procedures taken, and the results of the study. They provide a wri en record of what
Percent Error = |(Experimental—Actual)| x 100% Actual
Percent Error = |(10.1 m/s2 ‐ 9.8 m/s2)| x 100% (9.8 m/s2)
Percent Error = |0.3 | x 100% (Note the units cancel each other out) (9.8 )
Percent Error = 0.0306 x 100% = 3.1% (Remember the significant digits)
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Lab 1: Introduc on to Science
took place to help others learn and expedite future experimental pro‐ cesses. Though most lab reports go unpublished, it is important to write a report that accurately characterizes the experiment per‐ formed.
Title A short statement summarizing the topic
Abstract A brief summary of the methods, results and conclusions. It should not exceed 200 words and should be the last part wri en.
Introduc on
An overview of why the experiment was conducted. It should include: Background ‐ Provide an overview of what is already known and what ques ons re‐
main unresolved. Be sure the reader is given enough informa on to know why and how the experiment was performed.
Objec ve ‐ Explain the purpose of the experiment (i.e. “I want to determine if taking baby aspirin every day prevents second heart a acks.”)
Hypothesis ‐ This is your “guess” as to what will happen when you do the experiment.
Materials and Methods A detailed descrip on of what was used to conduct the experiment, what was actually done (step by step) and how it was done. The descrip on should be exact enough that someone reading the report can replicate the experiment.
Results Data and observa ons obtained during the experiment. This sec on should be clear and concise. Tables and graphs are o en appropriate in this sec on. Interpreta ons should not be included here.
Discussion
Data interpreta ons and experimental conclusions. Discuss the meaning of your findings. Look for common themes, rela onships and
points that perhaps generate more ques ons. When appropriate, discuss outside factors (i.e. temperature, me of day, etc.) that
may have played a role in the experiment. Iden fy what could be done to control for these factors in future experiments.
Conclusion A short, concise summary that states what has been learned.
References Any ar cles, books, magazines, interviews, newspapers, etc. that were used to support your background, experimental protocols, discussions and conclusions.
Part of the Lab Report Purpose
Figure 5: Lab reports are an important part of science, providing a way to
report conclusions and ideas.
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Lab 1: Introduc on to Science
Exercise 1: Data Interpreta on
Dissolved oxygen is oxygen that is trapped in a fluid, such as water. Since virtually every living organ‐ ism requires oxygen to survive, it is a necessary component of water systems such as streams, lakes and rivers in order to support aqua c life. The dissolved oxygen is measured in units of ppm—or parts per million. Examine the data in Table 2 showing the amount of dissolved oxygen present and the number of fish observed in the body of water the sample was taken from; finally, answer the ques‐ ons below.
Ques ons 1. What pa erns do you observe based on the informa on in Table 2?
2. Develop a hypothesis rela ng to the amount of dissolved oxygen measured in the water sample and the number of fish observed in the body of water.
3. What would your experimental approach be to test this hypothesis?
4. What would be the independent and dependent variables?
5. What would be your controls?
Dissolved Oxygen (ppm) 0 2 4 6
Number of Fish Observed 0 1 3 10
8
12
10
13
12
15
14
10
16
12
18
13
Table 2: Water Quality vs. Fish Popula on
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Lab 1: Introduc on to Science
6. What type of graph would be appropriate for this data set? Why?
7. Graph the data from Table 2: Water Quality vs. Fish Popula on (found at the beginning of this experiment).
8. Interpret the data from the graph made in Ques on 7.
Exercise 2: Testable Observa ons Determine which of the following observa ons are testable. For those that are testable:
Determine if the observa on is qualita ve or quan ta ve Write a hypothesis and null hypothesis What would be your experimental approach? What are the dependent and independent variables? What are your controls ‐ both posi ve and nega ve? How will you collect your data? How will you present your data (charts, graphs, types)? How will you analyze your data?
Observa ons 1. When a plant is placed on a window sill, it grows 3 inches faster per day than when it is placed on
a coffee table in the middle of the living room. Quan ta ve
2. The teller at the bank with brown hair and brown eyes is taller than the other tellers.
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Lab 1: Introduc on to Science
3. When Sally eats healthy foods and exercises regularly, her blood pressure is 10 points lower than when she does not exercise and eats fa y foods.
4. The Italian restaurant across the street closes at 9 pm but the one two blocks away closes at 10 pm.
5. For the past two days, the clouds have come out at 3 pm and it has started raining at 3:15 pm.
6. George did not sleep at all the night following the start of daylight savings.
Exercise 3: Conversion
For each of the following, convert each value into the designated units.
1. 46,756,790 mg = _______ kg
2. 5.6 hours = ________ seconds
3. 13.5 cm = ________ inches
4. 47 °C = _______ °F
Exercise 4: Accuracy and Precision
For the following, determine whether the informa on is accurate, precise, both or neither.
1. During gym class, four students decided to see if they could beat the norm of 45 sit‐ups in a mi‐ nute. The first student did 64 sit‐ups, the second did 69, the third did 65, and the fourth did 67.
2. The average score for the 5th grade math test is 89.5. The top 4th graders took the test and
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Lab 1: Introduc on to Science
scored 89, 93, 91 and 87.
3. Yesterday the temperature was 89 °F, tomorrow it’s supposed to be 88°F and the next day it’s supposed to be 90°F, even though the average for September is only 75°F degrees!
4. Four friends decided to go out and play horseshoes. They took a picture of their results shown to the right:
5. A local grocery store was holding a contest to see who could most closely guess the number of pennies that they had inside a large jar. The first six people guessed the numbers 735, 209, 390, 300, 1005 and 689. The gro‐ cery clerk said the jar actually contains 568 pennies.
Exercise 5: Significant Digits and Scien fic Nota on
Part 1: Determine the number of significant digits in each number and write out the specific signifi‐ cant digits.
1. 405000
2. 0.0098
3. 39.999999
4. 13.00
5. 80,000,089
6. 55,430.00
7. 0.000033
8. 620.03080
Part 2: Write the numbers below in scien fic nota on, incorpora ng what you know about signifi‐ cant digits.
1. 70,000,000,000
2. 0.000000048
3. 67,890,000
4. 70,500
5. 450,900,800
6. 0.009045
7. 0.023
Lab 2: Types of Forces
27
Lab 2: Types of Forces
Mo on is an elementary concept of physics. It is what happens when an object changes posi on and is produced by a force (a push or pull on the object). Kinema cs is the study of how things move. Be‐ cause we deal so much with moving objects in the world, kinema cs is one of the most important and visual areas in physics. It is important to remember that mo on is rela ve. Even when we stand s ll, we are s ll moving. The Earth that we stand on is rota ng and thus we are s ll moving. Nonetheless, it is of great value to measure how things move. Velocity is a measure of how fast something is moving in a specific direc on (velocity is commonly called speed, but the two terms have an important difference). Expressed as a ra o, velocity is the distance an object covers over an elapsed me. Since we don’t know how much the object has accelerated or decelerated in between measurements, this ra o will give us an average velocity:
Figure 1: Surprisingly, light and heavy objects fall at the same rate when there is no air resistance. If these two objects were dropped in a vacuum, both would hit the
ground at the same me.
Concepts to explore: Kinema cs Types of forces Velocity Accelera on Balanced/unbalanced forces Free body diagrams
Net force Equilibrium
v = Δx Δt
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Lab 2: Types of Forces
Here, the value Δx is called the displacement, which is another word for the total change in posi on measured in a straight line from an object’s star ng point to its ending point. (Note: Δ is the Greek symbol for ‘change’ and represents a calcula on of the final measurement subtracted by the ini al measurement). Velocity can be measured as an average over me—as above—or at a single moment (instantaneous velocity). Velocity differs from our normal understanding of speed in that it requires a known direc on. For example, if a car is driving 30 mph at a moment in me we know its speed; but, if we say it is going 30 mph west, we know the velocity at that point. Constant velocity requires both constant speed and constant direc on. Accelera on occurs when an object undergoes a change in velocity. Therefore, accelera on occurs when an object’s speed, direc‐ on of travel, or both change :
When you press the gas pedal in your car while driving on a straight road, you will experience linear accelera on. The force of the seat pressing against your back indicates this change in velocity. If you are driving around a turn, your speed may be constant but your direc on is changing. Fric on between the road and your res is causing you to accelerate into a new direc on of mo on. All accelera ons are caused by forces—more specifically, unbalanced forces. There are many types of forces that can act on an object, characterized by the type of interac on between objects.
Applied force is the force exerted on the object by a person or another object. Gravita onal force is a force of a rac on between two masses. The size of the gravita on‐
al force depends on the size of the masses and the distance between them (Fgravity=m ·g). Gravity is a long‐range force which is rela vely weak, but it can have great effects when objects are very massive—such as planets!
An electromagne c force is a force that occurs between charged objects. Like gravity, elec‐ tromagne c forces can act at long ranges. These forces are very powerful even if the par ‐ cles involved do not have much mass. Atomic nuclei are held together by electromagne c forces.
The normal force is the support force exerted on an object when it is in contact with an‐ other sta onary object. The normal force is the force exerted upward by the ground on your feet (or whatever you are standing on) that keeps you from falling through the sur‐ face.
Fric onal forces act to oppose the mo on of an object. No surface is perfectly smooth at a microscopic scale. Fric on occurs when two surfaces are pressed together and molecules
Figure 2: Scalar quan es express magnitudes, while vector quan es ex‐ press magnitude and direc on.
Scalar: Average Speed = 10 m/s
Vector: Velocity = 10 m/s at 30°
a = Δv Δt
29
Lab 2: Types of Forces
on each surface collide, impeding each other’s mo on. A specialized fric on force when an object is in free fall is air resistance, which is affected by the speed of an object and its cross‐sec onal area. Though it can never cause an object to move, it can check or stop mo‐ on. As resistance, fric on wastes power, creates heat and causes wear. It has been shown
that the force required to slide one object over another is propor onal to the normal force pressing the surfaces together, expressed by the equa on shown below: Ff = μFN where μ is called the coefficient of fric on and represents the roughness of the surfaces in contact. There are two types of fric on, sta c (not moving) fric on and kine c (moving) fric on. They have unique coefficients of fric on, μs and μk, respec vely. In general, μs ≥ μk.
Tensile forces are transmi ed through an object when opposing forces pull at op‐ posite ends. The tension force pulls equally on the object from the opposite ends.
Spring forces are exerted on an object by a compressed or stretched spring. The spring acts to restore its original or equi‐ librium posi on. For most springs, the magnitude of the force is directly propor‐ onal to the stretch or compression of
the spring, expressed by the equa on below:
Fs=‐k∆x The SI unit for force is the Newton (N), where 1 N = 1 kg·m/s2 (the lb is the English unit). In other words, it takes 1 N of force to accelerate a 1 kg mass by 1 m/s2. If you are given a mass in kilograms, all you need to do to find the force (N) is to mul ply the mass by the accelera on due to gravity, g = 9.8 m/s2. Take a look at Figure 5 for an example. Another measurement of force you are familiar with is the pound (lb), but scien sts usually s ck with the SI units of measurement. When a number of forces act on an object at once, it is helpful to draw a free body diagram (FBD). Free body diagrams show all the forces ac ng on an object as arrows. For now, we will only talk about forc‐ es that point in the horizontal or ver cal direc ons. Since forces are vector quan es, when they add together we must take into account both magnitude and direc on. For example, if a 5 N force acts to the le on an object, and at the same me an 8 N force acts to the right, the total force or net force would be 3 N to the right. Using FBDs, you can visualize which forces will cancel others out. When you draw a FBD, each object of interest is drawn (you can draw the object, or even a box or point to represent the object), and each force is represented by an arrow. The length of the arrow rep‐ resents that magnitude of the force, and the direc on of the arrow indicates the direc on the force is ac ng upon the object. This way, you can visualize which forces will cancel out others, leaving a total net force in one direc on. If all the forces cancel each other out (for instance, equal but opposite forc‐ es in the ver cal and horizontal direc ons) the object is said to be in sta c equilibrium—the net force is equal to zero, even though there are many forces ac ng at once.
Figure 3: Despite gravity’s weakness as a force, it is responsible for the ball shape of planets and stars, and for the shape of galaxies. Masses within these structures a ract every other bit of mass within
the object, which creates their ball shape.
30
Lab 2: Types of Forces
Consider a book si ng on a table. If you apply a force to slide it across the table to your study partner, there are actually four forces involved in the mo on. The FBD would involve the normal force, gravity, the applied force and fric on, and the diagram is shown in Figure 4. The normal force arrow is drawn perpendicular to the surface, directly opposite the force of gravity in this case. We know the object is not moving in the ver cal direc on, so the ver cal forces are equal but in opposite direc ons and can‐ cel out on the net force diagram. Since enough force was applied to overcome fric on and move the book, we draw the applied force arrow longer than the fric onal force arrow that acts to resist mo on. The applied force is greater than the fric on force, so the net force is in the direc on of the applied force. This object will accelerate to the right. When an object is not moving in the horizontal or ver cal direc on, the sum of the forces must equal zero in that direc on (∑F=0).
Figure 4: The le figure is an example of a typical free body diagram (FBD) with a variety of forces labeled. The normal force (Fnorm) and the force due to gravity (Fgrav) must be equal and opposite because the object is not falling into the surfaces or accelera ng into the air. The applied force Fapp is larger than the force due to fric‐ on, so the net overall force Fnet points to the right‐‐shown on the reduced FBD on the right. The normal force
is not always directly opposite the force of gravity, as with an object res ng on an incline.
Figure 5: The 1 kg mass on the le is supported by a rope drawn around a pulley and anchored to a flat sur‐ face. The free body diagram on the right shows the case of sta c equilibrium: the force of gravity is balanced out
by the tension in the string. In FBDs only the forces ac ng direc onally on the object of interest ma er!
Figure 6: The two masses (weights labeled) are sus‐ pended by a single rope through a pulley wheel. The right side is a free body diagram for each mass; note that the tension in the string is the same on each side (in other words, the string does not stretch). The net force is upward on the 5 N mass and downward on the
8 N mass—which way will the assembly move?
31
Lab 2: Types of Forces
The following experiments will demonstrate the effects of balanced and unbalanced forces. You will draw Free Body Diagrams to analyze the balance of forces and use simple kinema c equa ons to calcu‐ late velocity and accelera on. Experiment 1: Fric on When two materials are in contact with each other, the fric on between them acts to impede mo on. Fric on is always a reac on force, meaning fric on never causes an object to move by itself. Instead, fric on acts to oppose applied forces. The equa on used to calculate the force of fric on is:
Ff = μFN
where Ff is the force of fric on, μ is the coefficient of fric on which represents the roughness of the surface, and FN is the normal force. On a horizontal surface, FN = ‐mg, and the equa on becomes:
Ff = ‐μmg
In this lab you will demonstrate this rela onship between the normal force, FN, and the force of fric‐ on, Ff.
Figure 7: Since the force that team 1 exerts on team 2 is equal and opposite to the reac on force that team 2 exerts on team 1, how can anyone ever win a tug of war? If no accelera on is occurring, the
game is in a state of equilibrium.
32
Lab 2: Types of Forces
Procedure 1. Use Steps 2 ‐ 5 to complete the experiment with the plas c, Styrofoam, and paper cups. Begin with
the plas c cup, then use the Styrofoam cup, and conclude with the paper cup. Record the force readings on the spring scale for each trial in Table 1.
NOTE: For the paper cup, use smaller amounts of water as indicated in Table 1
2. Tie the string around the outside edge of the cup, leaving some slack. Tie a loop at the end of the string.
3. Fill the cup with 300 mL of water (1 mL water = 1 g water). Place the materials on a smooth, flat surface (be sure to use the same surface for each trial). Record a descrip on of the surface in Table 1.
4. Hook the spring scale to the string. Pull on the scale gradually un l the cup starts to slide at a con‐ stant speed. Record the value of the force (Fapp) as the cup starts to move in Table 1. Repeat four more mes.
5. Using the same cup, empty the cup and fill it back up with 150 mL of water. Measure the force re‐ quired to slide the cup. Repeat the process four more mes (as done in Step 4 with the 300 mL of water).
6. Average the data for the Force Applied (spring scale readings) columns and record your results in Table 1.
Materials Styrofoam cup Plas c cup Paper cup String Spring Scale
33
Lab 2: Types of Forces
Please submit your table data and answers for this experiment on the Word document provided to you.
Cup Material Force Applied F1 m1 = 300 g water Force Applied F2 m2 = 150 g water
F1 / FN1 F2 / FN2
Plas c
Avg: Avg: Avg: Avg:
Styrofoam
Avg: Avg: Avg: Avg:
Paper
F1 m1 = 150 g water
F2 m1 = 100 g water
F1 / FN1 F2 / FN2
Avg: Avg: Avg: Avg:
Surface Descrip on
Table 1: Applied force required to slide cup
34
Lab 2: Types of Forces
Ques ons 1. What happened to your applied force Fapp as you decreased the amount of water in the cup? 2. Assume the mass to be exactly equal to the mass of water. Calculate the normal force (FN) for 300
g, 150 g, and 100 g. Use these values to compute the ra o of the Applied Force (Fapp) to the Nor‐ mal Force (Fn). Place these values in the rightmost column of Table 1.
What do these last two columns represent? What is the ra o of the normal forces F1 / F300? Com‐ pare this to your values for F2/ F150, and F3/F100. What can you conclude about the ra o between the Force Normal and the Force Fric on? FN= mg FN (300 g) = _________kg × 9.8 m/s2 = ___________ FN (150 g) = _________kg × 9.8 m/s2 = ___________ FN (100 g) = _________kg × 9.8 m/s2 = ___________
3. Why doesn’t the normal force (FN) depend on the cup material? 4. Right as the cup begins to slide the applied force is equal to the Force Fric on (Ff)‐ draw a free body
diagram sliding each type of cup (a total of three diagrams). Label the Force Gravity (=mg), the Nor‐ mal Force (FN), and the Fric on Force (Ff), but don’t use any specific numbers. What makes this a state of equilibrium?
5. Does it take more force to slide an object across a surface if there is a high value of μ or a low one? Explain your answer
35
Lab 2: Types of Forces
Experiment 2: Velocity and Air‐resistance In a vacuum, all objects accelerate due to gravity at the same rate: 9.8 m/s2. In actuality, fric on from air resistance prevents this from happening. A falling object will accelerate un l the force of air re‐ sistance matches the force on it due to gravity (mg). When these forces are equal, the object is said to have reached terminal velocity, and will con nue to fall at a constant rate indefinitely. In this experiment you will see how the air resistance of an object can work against the force of gravity for an object of low weight and a large air resistance. If the object is light enough, air resistance can cancel out the force of gravity, resul ng in a constant velocity.
Procedure 1 1. Measure the height of a table and record the value in Table 2. 2. Push one coffee filter off the edge of the table and start the stopwatch. In Table 2, record how
long it takes for the filter to hit the ground in Table 2. Repeat four mes and average your results. 3. Using the average me calculated from Step 2, find the average speed of the falling filter using the
measured height of the table. 4. Repeat Steps 2‐3 with two coffee filters stuck together. Procedure 2 1. Find a higher table, or get a friend to help you drop the filter from a higher spot. Measure the actu‐
al height. 2. Push one coffee filter off the edge of the table and start the stopwatch. In Table 2, record how
long it takes for the filter to hit the ground in Table 2. Repeat four mes and average your results in Table 2.
3. Using the average me calculated from Step 2, find the average speed of the falling filter using the measured height of the table.
4. Repeat Steps 2‐3 with two coffee filters stuck together.
Materials Tape measure Stopwatch Coffee filters (re‐shape to how they would sit in a coffee pot)
36
Lab 2: Types of Forces
Please submit your table data and answers for this experiment on the Word document provided to you. Ques ons 1. Draw a FBD for the falling coffee filter. What is the net force?
Table 2: Coffee Filter Data
Procedure 1
1 Coffee Filter 2 Coffee Filters
Height of table (m)
Total Time (s) ‐ Trial 1
Total Time (s) ‐ Trial 2
Total Time (s) ‐ Trial 3
Total Time (s) ‐ Trial 4
Total Time (s) ‐ Trial 5
Calculated average speed (m/s)
Procedure 2
Measured height (m)
Calculated average speed (m/s)
Total Time (s) ‐ Trial 5
Total Time (s) ‐ Trial 1
Total Time (s) ‐ Trial 4
Total Time (s) ‐ Trial 2
Total Time (s) ‐ Trial 3
37
Lab 2: Types of Forces
2. What are we assuming by using the average velocity from Procedure 1 to es mate the height of the fall in Procedure 2?
3. Is the object actually traveling at the average speed over the dura on of its fall? Where does the accelera on occur?
4. Draw the FBD for the 2‐filter combina on, assuming constant velocity. What is the net force?
5. How do your measured and calculated values for the height in Procedure 2 compare? If they are significantly different, explain what you think caused the difference.
6. Why do two coffee filters reach a higher velocity in free fall than one coffee filter?
7. How would the FBD differ for a round rubber ball dropped from the same height?
Lab 3: Newton’s Laws
41
Lab 3: Newton’s Laws
Forces can produce or prevent mo on. The laws used today to describe all aspects of mo on date back to the 1700s, when Sir Isaac Newton proposed a set of rules to describe how all objects move. New‐ ton’s First Law of Mo on states that an object will remain at rest, or in uniform mo on, unless acted on by an unbalanced force. In other words, objects have the tendency to resist changes in mo on. The concept that force can change the velocity of a mass is very important. Nothing would change without forces. Newton’s First Law is also called the Law of Iner a. Iner a is an object’s tendency to resist changes in state of mo on (speed or direc on). Ma er has this property whether it is at rest or in mo on. The First Law states that an object will con nue at a constant velocity in one direc on unless acted on by a net force. When a net force on an object is applied, the object will accelerate in the direc on of that
Figure 1: Newton’s First Law of Mo on in ac on ‐ billiard balls remain at rest un l an external force (the cue ball) causes them to move.
Concepts to explore: Newton’s First Law Weight vs. Mass Iner a Newton’s Second Law Newton’s Third Law
42
Lab 3: Newton’s Laws
force. The movement of planets around the Sun is an example of in‐ er a. Planets have a lot of mass, and therefore a great amount of iner a—it takes a huge force to accelerate a planet in a new direc‐ on. The pull of gravity from the Sun keeps the planets in orbit—if
the Sun were to suddenly disappear, the planets would con nue at a constant speed in a straight line, shoo ng off into space! Newton also observed a special rela onship between mass and iner‐ a. Mass is o en confused with weight, but the difference is crucial in
physics. While mass is the measure of how much ma er is in an ob‐ ject (how much stuff is there), weight is a measure of the force expe‐ rienced by an object due to gravity. Thus, weight is rela ve to your loca on – your weight would differ at the Earth’s core, at the summit of Mount Everest, and especially in outer space, when compared to the surface. On the other hand, mass remains constant in all these loca ons. Mathema cally, weight is the mass of an object mul plied by its accelera on due to gravity:
w = mg
where w is weight, m is mass and g is gravity. Sir Isaac Newton noted that the greater an object’s mass, the more it resisted changes in mo on. Therefore, he concluded that mass and iner a are directly propor onal (↑mass = ↑iner a). This predic on produced Newton’s Second Law of Mo on, an expression for how an object will accelerate based on its mass and the net force applied to the object. This law can be summarized by the equa on:
ΣF = ma where ΣF is the sum of all forces ac ng on the object, m is its mass and a is its accelera on. The stand‐ ard measurement for mass is the kilogram (kg), and for accelera on is the meter/sec/sec, or m/s2. The standard measurement for force is the Newton, where 1 N = 1 kg·m/s2. Comparing this equa on to the first one helps reinforce the difference between mass and force (such as weight). Newton’s Third Law of Mo on states that for every ac on there is an equal, but opposite reac on. When you hold up a heavy object, the force of gravity is pulling the object down against your hands. In order to keep the object from falling to the floor, your hands and arms supply an equal and opposite force upward against the ball. Thus, single forces do not exist, only pairs of forces (the ac on force and the reac on force). You might not think about it, but you do not directly feel the force of gravity when you stand on the ground; what you’re really feeling is the opposing force exerted by the ground that keeps you from falling toward the center of the earth! Even when you walk, you push against the ground, and it pushes right back! Newton’s three laws of mo on govern the rela onship of forces and accelera on. There are many ap‐ plica ons of Newton’s Laws in your everyday life. To get that last bit of ketchup from the bo le, you
Figure 2: When this player leaps to the bas‐ ket you are seeing the Third Law in ac on: the player’s downward push receives an equal and opposite force upward from the ground. Without this reac on force, he
would have no way to accelerate upward to the rim.
43
Lab 3: Newton’s Laws
shake the bo le upside‐down, and quickly stop it (with the lid). Consider riding in a car. Have you ever experienced iner a while rapidly accelera ng or decelera ng? Thousands of lives are saved every year by seatbelts, which are safety restraints that protect against the iner a that propels a person forward when a car comes to a quick stop. Experiment 1: Newton’s First Law
Procedure 1. Fill the container with about 4 inches of water. 2. Find an open space outside to walk around in with the container of water in your hands. 3. Perform the following ac vi es:
a. Start with the water at rest (i.e., on top of a table). Grab the container and quickly acceler‐ ate.
b. Walk with constant speed in a straight line for 15 feet. c. A er walking a straight line at constant speed, make an abrupt right‐hand turn. Repeat with
a le ‐hand turn. d. A er walking a straight line at constant speed, stop abruptly.
4. Record your observa ons for each type of mo on from Step 3 in the space below. Comment on where the water tended to move. If it spilled, note if it spilled right, le , away from you, or toward you.
a. b. c. d.
Materials Deep bowl or pitcher* Water* * You must provide
44
Lab 3: Newton’s Laws
Ques ons Please submit your answers for this experiment on the Word document provided to you. 1. Explain how your observa ons of the water demonstrate Newton’s law of iner a.
2. Draw a free body diagram of your containers of water from the situa on in Step 3, Part d. Draw arrows for the force of gravity, the normal force (your hand pushing up on the container), and the stopping force (your hand decelera ng the container as you stop.) What is the direc on of the water’s accelera on?
*Note, free body diagrams are discussed in depth in Lab 2: Types of Forces. See Figure 3 for a sample diagram. Remember, the ob‐ ject is usually indicated as a box, and each force that acts upon the box is indicated with an arrow. The size of the arrow indicates the magnitude of the force, and the direc on of the arrow indi‐ cates the direc on which the force is ac ng. Each arrow should be labeled to iden fy the type of force. Note, not all objects have four forces ac ng upon them.
3. Can you think of any instances when your are driving or riding a car that are similar to this experi‐ ment? Describe two instances where you feel forces in a car in terms of iner a.
Experiment 2: Unbalanced Forces – Newton’s Second Law This experiment will demonstrate the mechanical laws of mo on using a simple assembly similar to that used by Rev. George Atwood in 1784 to verify Newton’s Second Law, named the Atwood machine.
Materials Pulley String Tape measure Stop watch 2 Paperclips 15 Washers Masking tape
Ffric on Fapp
Fnormal
Fgravity
Figure 3
45
Lab 3: Newton’s Laws
Procedure 1 1. Support the pulley so that objects hanging from it can descend
to the floor. (i.e., Tape a pencil to the top of a table, door, etc.) Remember that higher support will produce longer me inter‐ vals which are easier to measure. See
2. Thread a piece of string through the pulley so that you can a ach washers to both ends of the string. The string should be long enough for one set of washers to touch the ground with the other set near the pulley. (You may a ach the washers using a paperclip or by tying them on.)
3. Count out 15 washers 4. A ach seven washers to each end of the string. 5. Observe how the washers on one side behave when you pull
on the washers on the other side. Answer ques on 1 based on your observa ons.
6. Add the remaining washer to one end of the string so one side of the string has seven washers (M1), and the other has 8 washers a ached to it (M2).
7. Place M1 on the floor. Measure the height of M2 when sus‐ pended while M1 is on the floor. Measure the distance M2 falls when you release the light set when it is in contact with the floor, and record it in Table 1.
8. Time how long it takes for M2 to reach the floor. 9. Repeat Steps 7 ‐ 8 four more mes (for a total of five mes),
recording the values in Table 1. Calculate the average me. 10. Calculate the accelera on (assuming it is constant) from the
average me and the distance the washers moved. Refer to the “Hint” below Table 1 for help.
Procedure 2 1. Transfer one washer, so that there are six on one end of the
string (M1) and nine on the other (M2). 2. Place the M1 on the floor. Measure the height that M2 is sus‐
pended at while M1 is on the floor. Measure the distance M2 will fall if you release the light set when it is in contact with the floor.
3. Time how long it takes for the heavy set of washers to reach the floor.
4. Repeat Steps 2 ‐ 3 four more mes (for a total of five mes), recording the values in a table and then calculate the average me.
5. Calculate the accelera on (assuming it is constant) from the average me and the distance the washers moved.
Figure 5: Atwood machine. The tension force is directed up for both M1 and M2. M1 accelerates upward, and M2 acceler‐ ates downward. Do you know what causes the downward force?
M2
M1 Tension force
Tension force
Figure 4: Sample experimental set‐up. This set‐up hangs the pulley from a pencil that has been taped to a table. Although, any level surface (such as a counter‐top or door) will suffice. Metal washers will also be ed to both ends of the string for this experiment. Do not e the string in a knot you cannot un e!
46
Lab 3: Newton’s Laws
Please submit the table data and answers for this experiment on the Word document provided to you. Table 1: Mo on Data for Experiment 2
Trial M1 M2 Δd of M2 Time (s) Accelera on
Procedure 1
1
2
3
4
5
Average
Procedure 2
1
2
3
4
5
Average
Hint: You need to rearrange the formula d = 1/2 at2 to calculate the accelera on. In this equa on, d = distance, a = accelera on, and t = me. Example: Suppose you set up an Atwood Machine. The M2 weight accelerates downward a distance of 1.30 me‐ ters in 1.50 seconds. What was the accelera on rate? Given: d = 1.30 meters t = 1.50 seconds The goal is to rearrange the formula to end with “a” by itself on one side of the equa on. To do this… 1. Set up your equa on, and square the value for t; 1.30 meters = 1/2 · (a · (1.50 seconds)2) 2. Remove the “1/2” by mul plying each side of the equa on by 2; (2) · 1.30 meters = 1/2 · (a · 2.25 seconds) · (2) 3. Remove the 2.25 seconds by dividing each side of the equa on by 2.25 seconds; 2.60 meters/2.25 seconds = a Answer: The accelera on for M2 = 1.15 meters per second.
47
Lab 3: Newton’s Laws
Ques ons 1. When you give one set of washers a downward push, does it move as easily as the other set? Does
it stop before it reaches the floor. How do you explain this behavior?
2. Draw a FBD for M1 and M2 in each procedure (Procedure 1 and Procedure 2). Draw force arrows for
the force due to gravity ac ng on both masses (Fg1 and Fg2) and the force of tension (FT). Also draw
arrows indica on the direc on of accelera on, a.
Experiment 3: Newton’s Third Law
Procedure 1. Tie one end of the fishing line to a chair. Space the second chair about 10 feet away. 2. String the other end of the fishing line through the straw. 3. Tie the loose end of the fishing line to the second chair. 4. Inflate a balloon. Hold it closed with your fingers, and tape it to the straw. 5. Slide the straw/balloon back so that the mouth of the balloon is facing the nearest chair. 6. Let go of the balloon and observe what happens.
Materials Fishing line Balloon Plas c straw Masking tape 2 Chairs* *You must provide
48
Lab 3: Newton’s Laws
Ques ons Please submit your answers for this experiment on the Word document provided to you. 1. Explain what caused the balloon to move in terms of Newton’s Third Law.
2. What is the force pair in this experiment? Draw a Free Body Diagram (FBD) to represent the (unbalanced) forces on the balloon/straw combina on.
3. Add some mass to the straw by taping some metal washers to the bo om and repeat the experi‐ ment. How does this change the mo on of the assembly? How does this change the FBD?
4. If the recoil of the rifle has the same magnitude force on the shooter as rifle has on the bullet, why does the shooter not fly backwards with a high velocity?
Lab 4: Acids & Bases
51
Lab 4: Acids & Bases
Introduc on
Have you ever had a drink of orange juice a er brushing your teeth? What do you taste when you brush your teeth and drink orange juice a erwards? Yuck! It leaves a really bad taste in your mouth. But why? Orange juice and toothpaste by them‐ selves taste good. The terrible taste is the result of an acid/base reac on that occurs in your mouth. Orange juice is a weak acid and the toothpaste is a weak base. When they are placed together they neutralize each other and produce a product that is unpleasant to taste. In this lab we will discover how to dis nguish between acids and bases.
Two very important classes of compounds are acids and bases. But what exactly makes them different? Acids and bases have physical and chemical differences that you can ob‐ serve and test. According to the Arrhenius defini on, acids ionize in water to produce a hydronium ion (H3O+), and bases dissociate in water to produce hydroxide ion (OH‐).
Physical differences between acids and bases can be detected by the senses, including taste and touch. Acids have a sour or tart taste and can produce a s nging sensa on to broken skin. For example, if you have ever tasted a lemon, it can o en result in a sour face. Bases have a bi er taste and a slippery feel. Soap and many cleaning products are bases. Have you accidentally tasted soap or had it slip out of your hands?
Reac ons with acids and bases vary depending on the par cular reactants, and acids and bases each react differently with other substances. For example, bases do not react with most metals, but acids will react readily with certain metals to pro‐ duce hydrogen gas and an ionic compound—which is referred to as a salt. An example of this type of reac on occurs when magnesium metal reacts with hydrochloric acid. In this reac on, magnesium chloride (a salt) and hydrogen gas are formed.
Mg (s) + 2 HCl (aq) → MgCl2 (aq) + H2(g)
metal + acid → a salt + hydrogen gas
Acids may also react with a carbonate or bicarbonate to form carbon dioxide gas and water. The general reac on equa on for a reac on between an acid and a carbonate can be represented in this manner:
CO32-(aq) + 2 H3O+(aq) → CO2 (g) + 3 H2O (l)
carbonate + acid → carbon dioxide + water
The general equa on for a reac on between an acid and a bicarbonate is similar and can be represented in this manner:
Figure 1: Orange juice has a pH of around 3.5. Dairy milk, by comparison, is much less acid‐ ic, with a pH of around 6.5.
Concepts to explore: Understand the proper es and reac ons of acids and bases Relate these proper es to common household products
52
Lab 4: Acids & Bases
HCO3- (aq) + H3O+ (aq) → CO2 (g) + 2 H2O (l)
Acids and bases can also react with each other. In this case, the two opposites cancel each other out so that the product formed has neither acidic nor basic (also called alkaline) proper es. This type of reac on is called a neutraliza on reac on. The general equa on for the reac on between an acid and a base is represented in this manner:
H3O+ + OH – → 2 H2O
An example of a neutraliza on reac on is when an aqueous solu on of HCl, a strong acid, is mixed with an aqueous solu on of NaOH, a strong base. HCl, when dissolved in water, forms H3O+ and Cl‐. NaOH in water forms Na+ and OH‐. When the two solu ons are mixed together the products are water and common table salt (NaCl). Neither water nor table salt has acid or base proper es. Generally this reac on is wri en without the water solvent shown as a reactant:
HCl + NaOH → H2O + NaCl
There is another group of acids called organic acids. Ace c acid found in vinegar and citric acid found in citrus fruit are examples of organic acids. These acids are all much weaker than HCl. Organic acids have at least one –CO2H group in their molecular formula. When a base is added, the –H of the –CO2H group is replaced just like the –H in HCl. In this lab you will use citric acid as the acid and sodium bicarbonate as the base. Citric acid has three –CO2H groups and only each of the H’s on these groups react with a sodium bicarbonate. The other H’s in the formula do not react. This reac on can be represented in this manner:
HOC(CO2H)(CH2CO2H)2 + 3 NaHCO3 → HOC(CO2‐Na+)(CH2CO2‐Na+ )2 + 3 CO2 + 3 H2O
Acids and bases are measured on a scale called pH. The pH of a substance is defined as the nega ve log of its hydronium ion concentra on. An aqueous (water) solu on that has a lot of hydronium ions but very few hy‐ droxide ions is considered to be very acidic, while a solu on that contains many hydroxide ions but very few hydronium ions is considered to be very basic.
pH = ‐ log [H3O+]
pH values range from less than 1 to 14, and are measured on a logarithmic scale (equa on above). This means that a substance with a pH of 2 is 10‐ mes (101) more acidic than a substance with a pH of 3. Similarly, a pH of 7 is 100‐ mes (102)more basic than a pH of 5. This scale lets us quickly tell if something is very acidic, a li le
bicarbonate + acid → carbon dioxide + water
Table 1: Approximate pH of various common foods.
Food pH Range
Lime 1.8 ‐ 2.0
So Drinks 2.0 ‐ 4.0
Apple 3.3 ‐ 3.9
Tomato 4.3 ‐ 4.9
Cheese 4.8 ‐ 6.4
Potato 5.6 ‐ 6.0
Drinking Water 6.5 ‐ 8.0
Tea 7.2
Eggs 7.6 ‐ 8.0
Acid + Base → Water
53
Lab 4: Acids & Bases
acidic, neutral (neither acidic nor basic), a li le basic, or very basic. A pH of 1 is highly acidic, a pH of 14 is highly basic, and a pH of 7 is neutral.
pH indicators, which change color under a certain pH level, can be used to determine whether a solu on is acidic or basic. Litmus paper is made by coa ng a piece of paper with litmus, which changes color at around a pH of 7. Either red or blue litmus paper can be purchased depending on the experimental needs. Blue lit‐ mus paper remains blue when dipped in a base, but turns red when dipped in an acid, while red litmus paper stays red when dipped in an acid, but turns blue when in contact with a base.
A more precise way to determine acidity or basicity is with pH paper. When a substance is placed on pH pa‐ per a color appears, and this color can be matched to a color chart that shows a wide range of pH values. In this way, pH paper allows us to determine to what degree a substance is acidic or basic and can provide an approximate pH value.
Pre‐lab Ques ons
1. What is a neutraliza on reac on?
2. Hydrochloric acid (HCl) is a strong acid. About what pH would you expect it to be?
3. Sodium hydroxide (NaOH) is a strong base. About what pH would you expect it to be?
54
Lab 4: Acids & Bases
Experiment: Acidity of Common Household Products
In this experiment, we will observe the neutraliza on of acids and bases using grape juice as an indicator. We will also test common household products for their acidity or alkalinity.
Procedure
Part 1: Acid‐Base Neutraliza on
1. Label three test tubes 1, 2, and Standard.
2. Prepare 50 mL of a 10% grape juice solu on by first pouring 5 mL of grape Juice into a 100 mL graduated cylinder. Add dis lled water un l the total volume of liquid is 50 mL. Mix well by s rring the solu on with a s rring rod.
3. Pour 10 mL of the dilute grape juice solu on into each test tube.
4. Note the color of the juice in the test tube labeled Standard in Table 2.
5. Using a pipe e, add 15 drops of saturated citric acid solu on into test tube 1. Record your observa ons concerning the color change in Ta‐ ble 2 of the Data sec on. Use the juice in the test tube labeled Standard for comparison.
6. Using a pipe e, add 15 drops of saturated sodium bicarbonate solu on into test tube 2. Record your observa ons concerning the color change in Table 2 of the Data sec on. Use the juice in the test tube labeled Standard for comparison.
7. Use pH paper to determine the pH of the solu on in each of the 3 test tubes. Record the pH val‐ ues in Table 2.
8. Using a pipe e, add drops of saturated sodium bicarbonate solu on to test tube 1 un l it re‐ turns to its original color. Record your observa ons in Table 3.
Materials Safety Equipment: Safety goggles, gloves Vinegar Household ammonia **Grape Juice 3 test tubes pH strips Saturated citric acid solu on (60% Test tube rack Neutral litmus paper
Saturated sodium bicarbonate solu‐ on (15%)
(2) 50 mL beakers Tomato juice Sodium bicarbonate 12‐well plate Powdered milk Lemon juice 10 Droppers (pipe es) Baking soda Dishwashing liquid
S rring rod 100 mL Graduated cylinder *Dis lled water *You must provide **Used in the next lab— refrigerate a er opening
HINT: If the grape juice is not dilute enough or
the base is not as strong as needed, you may con nue adding
drops of base.
55
Lab 4: Acids & Bases
9. Using a pipe e, add drops of saturated citric acid solu on to test tube 2 un l it returns to its original col‐ or. Record your observa ons in Table 3.
10. Use pH paper to test the pH of the three solu ons. Record the pH values in Table 3.
Part 2: Tes ng acidity and basicity of common household products
1. Use the pipe es to place into different wells of your 12‐well plate a couple of drops of each of the fol‐ lowing items: tomato juice, household ammonia, milk (mix powdered milk with 50mL water un l dis‐ solved), vinegar, lemon juice, and diluted dishwashing liquid (mix 1mL dishwashing liquid with 5mL wa‐ ter). Be sure to label or write down where each item is located in the 12‐well plate. CAUTION: Do not contaminate the items being tested. Be sure to use only a clean pipe e for each item.
2. Guess the pH of each of the items before you find the experimental value and record your guess in Table 4.
3. Test each item with litmus paper and pH paper. Record your results in Table 4.
4. To clean up rinse all chemicals into a waste beaker. Neutralize the waste to a pH between 4 and 8 using either baking soda or vinegar. Wash the waste solu on down the drain.
Data
Please submit your table data and answers for this experiment on the Word document provided to you.
Table 2: Acid‐Base Neutraliza on for Part 1, Steps 5 & 6 Table 3: Acid‐Base Neutraliza on for Part 1, Steps 8 & 9
Test tube 1 Test tube 2 Standard
Step 1 Add acid Add base Neutral
Color
pH value
Test tube 1 Test tube 2 Standard
Step 1 Add base Add acid Neutral
Color
pH value
Table 4: Acidity and basicity tes ng for household products data
Product Hypothesized pH Color of Litmus Paper Color of pH Paper Actual pH
56
Lab 4: Acids & Bases
Ques ons
1. Why did the grape juice change color when an acid or base was added?
2. You added a base, sodium bicarbonate, to test tube 1 that contained citric acid and an acid to test tube 2 that contained base. Why did the grape juice return to its original color?
3. Name two acids and two bases you o en use.
Lab 5: Chemical Processes
59
Lab 5: Chemical Processes
Introduc on
Have you ever needed to place a cold pack on a sprained muscle? It’s the final seconds of the community league champion‐ ship basketball game, and your team is behind by one point. One of your team’s players takes a shot and scores. The game is over, and your team won! But something is wrong: the player is si ng on the floor, and appears to be in a lot of pain. The coach quickly brings a cold pack to the player, squeezes it, and places it on the swelling ankle. The bag immediately becomes cold—but how?
Though we o en use them interchangeably, heat and tem‐ perature have different defini ons—though they are close‐ ly related in the study of thermodynamics. Heat is the transfer of energy from one object to another due to a difference in temperature. Temperature, on the other hand, describes how much energy the atoms and molecules in a sub‐ stance have. This energy, o en called internal energy, describes how quickly the atoms or molecules in a substance move or vibrate around. When an object gains heat its molecules vibrate with more energy, which we can sense or measure as an increase in temperature. When you touch a hot object, it feels hot because a heat moves from the hot object (higher energy) to your skin (lower energy). Similarly, an object feels cold when heat is lost by your hand and gained by the cold object. Heat always transfers in the direc on of high temperature to low temperature—high energy to low energy.
Both physical processes and chemical reac ons can release or absorb energy in the form of heat. When a reac on or phys‐ ical change gives off energy it is called an exothermic process. To remember exothermic, think of ‘exi ng’ as in leaving or going out. An endothermic process does just the opposite—it takes in energy from its surroundings. The generalized chemical equa ons for exothermic and endothermic reac ons are:
The direc on energy moves determines whether the process is considered endothermic or exothermic, and tells you how the temperature of a system changes. In an endothermic reac on or physical change, energy is absorbed and the overall temperature of the system decreases. Some examples of endothermic processes include the mel ng of water in a so drink or the evapora on of a liquid. Similarly, an endothermic reac on takes in energy for chemical changes to occur. One example is what occurs in an instant cold pack like the ones used to decrease the swelling caused from a sports injury. The‐
exothermic:
endothermic:
reactants → products + energy
reactants + energy → products
Figure 1: The combus on of fuel, such as wood or coal, is a com‐ mon example of an exothermic reac on. Under the right condi‐ ons (usually the applica on of enough heat), a chemical reac‐ on occurs between wood and the oxygen in air. Fire is the re‐
Concepts to explore: Understand the difference between endothermic and exothermic
processes Understand the concept of enthalpy
60
Lab 5: Chemical Processes
se types of cold packs u lize the chemical process of ammonium nitrate (NH4NO3 ) dissolving in water. The ammonium nitrate needs to absorb heat from the surrounding water to dissolve, so the overall temperature of the mixture de‐ creases as the reac on occurs.
In contrast, energy is released in an exothermic process. An example of an exothermic reac on is what occurs in com‐ mon hand warmers. The increase in temperature is the result of the chemical reac on of rus ng iron:
4 Fe(s) + 3 O2(g) 2 Fe2O3(s) + energy
Iron usually rusts fairly slowly so that any heat transfer is not easily no ced. In the case of hand warmers, common table salt is added to iron filings as a catalyst to speed up the rate of the reac on. Hand warmers also have a permea‐ ble plas c bag that regulates the flow of air into the bag, which allows just the right amount of oxygen in so that the desired temperature is maintained for a long period of me. Other ingredients that are found in hand warmers include a cellulose filler, carbon to disperse the heat, and vermiculite to insulate and retain the heat.
Enthalpy is a quan ty of energy contained in a chemical process. In the cases we will be dealing with, the energy re‐ leased or absorbed in a reac on is in the form of heat. Enthalpy by itself does not have an absolute quan ty, but changes in enthalpy can be observed and recorded. For example, if you s ck your finger into a glass of cold tap water, it probably feels pre y cold. However, a er being outside on a freezing winter day for a long period of me, the same glass of water might actually feel warm to touch. It would be difficult to measure the absolute quan ty of energy in the water in either case, but it is rela vely easy to no ce the movement of energy from one object to another. In exother‐ mic reac ons, heat energy is released and the change in enthalpy is nega ve, while in endothermic reac ons, energy is absorbed and the change in enthalpy is posi ve.
Pre‐lab Ques ons
1. Define enthalpy:
2. What is the rela onship between the enthalpy of a reac on and its classifica on as endothermic or exo‐ thermic?
3. With instant hot compresses, calcium chloride dissolves in water and the temperature of the mixture in‐ creases. Is this an endothermic or exothermic process?
Note: the energy term on the right side shows that the reac on is exothermic, but is not required.
61
Lab 5: Chemical Processes
Experiment: Cold Packs vs. Hand Warmers
In this lab you will observe the temperature changes for cold packs and hand warmers. Since temperature is defined as the average kine c energy of the molecules, changes in temperature indicate changes in energy. You will use simply a Styrofoam cup as a calorimeter to capture the energy. The customary lid will not be placed on the cup since ample oxy‐ gen from the air is needed for the hand warmer ingredients to react within a reasonable amount of me.
Procedure
Part 1: Cold Pack
1. Measure 10 mL of dis lled water into a 10 mL graduated cylinder.
2. Place about 1/4 of the ammonium nitrate crystals found in the solid inner contents of a cold pack into a Styrofoam cup. The Styrofoam cup is used as a simple calorimeter.
3. Place a thermometer and a s rring rod into the calorimeter (Styrofoam cup). CAUTION: Hold or secure the calorimeter AND the thermometer to prevent breakage.
4. Pour the 10 mL of water into the calorimeter containing the ammonium nitrate, (NH4NO3) taken from the cold pack.
5. Immediately record the temperature and the me.
6. Quickly begin s rring the contents in the calorimeter.
7. Con nue s rring and record the temperature at thirty second intervals in Table 1. You will need to s r the reac on the en re me you are recording data.
8. Collect data for at least five minutes and un l a er the temperature reaches its minimum and then begins to rise. This should take approximately 5 to 7 minutes.
9. Record the overall minimum temperature in the appropriate place on the data table.
Materials Safety Equipment: Safety goggles, gloves En re contents of a hand warmer S r rod 1/4 contents of a cold pack Spatula Calorimeters (2 Styrofoam cups)
Stopwatch Thermometer (digital) *Dis lled water 10mL Graduated cylinder *You must provide
62
Lab 5: Chemical Processes
Part 2: Hand Warmer
1. Wash and dry the thermometer. HINT: Remember to rinse it with dis lled water before drying.
2. Carefully place and hold the thermometer in another Styrofoam cup.
3. Cut open the inner package of a hand warmer and quickly transfer all of its contents into the calorimeter. Immediately record the ini al temperature of the contents and being ming the reac on. HINT: Data collec‐ on should start quickly a er the package is opened because the reac on will be ac vated as soon as it is
exposed to air.
4. Quickly insert the s rring rod into the cup and begin s rring the contents in the calorimeter.
5. Con nue s rring and record the temperature at thirty second intervals in Table 2. You will need to s r the reac on the en re me you are recording data.
6. Let the reac on con nue for at least five minutes and un l the temperature has reached its maximum and then fallen a few degrees. This should take approximately 5 to 7 minutes.
7. Record the overall maximum temperature in the appropriate place in the data table.
Data
Please submit your table data and answers for this experiment on the Word document provided to you.
Table 1: Cold pack data
Time (sec) Temp. (0C) Time (sec) Temp. in (0C)
Ini al 240
30 270
60 * 300
90 330
120 360
150 390
180 420
210 450
Minimum Temperature (0C) : __________
63
Lab 5: Chemical Processes
Table 2: Hand warmer data
Time (sec) Temp. (0C) Time (sec) Temp. in (0C)
Ini al 240
30 270
60 * 300
90 330
120 360
150 390
180 420
210 450
Maximum Temperature (°C) : __________
64
Lab 5: Chemical Processes
Graph your data from the tables on the Word document provided to you. You may create the graph on any program, but make sure it can be integrated into the Word document.
Ques ons 1. Calculate the overall temperature change (referred to as ΔT) for the cold and hot pack substance. HINT:
This is the difference in the maximum temperature and minimum temperature of each.
Cold pack ΔT:
Hand warmer ΔT:
2. Which pack works by an exothermic process? Use experimental data to support your answer.
3. Which pack works by an endothermic process? Use experimental data to support your answer.
4. Which pack had the greatest change in enthalpy? How do you know?
Lab 6: Light
67
Lab 6: Light
For centuries, scien sts have used op cal equipment such as lenses and mirrors to study the nature of light. Telescopes and microscopes take advantage of the proper es of light to create images from stars across the galaxy and to magnify objects hardly visible to the naked eye. In the late 19th century, James Maxwell proposed a series of equa ons that unify what we know about electricity and magne sm—it turns out that what we see as light is really electromagne c waves in wavelengths ranging from radio waves to gamma rays. Whenever subatomic par cles interact, they release or absorb energy in the form of electromagne c radia on, which travels through space in the form of electromagne c waves! Many mes, this electromagne c radia on can be detected by the human eye as visible light, but other kinds of light such as infrared radia on require special equipment to view.
Figure 1: This camera uses a series of op cal lenses so that the user can adjust for the intended focal point (f‐stop) and magnifica on of the
desired image.
Concepts to explore: Electromagne c waves Speed of light Reflec on and refrac on Mirrors and lenses
68
Lab 6: Light
Electromagne c waves travel fast—so fast that it took scien sts many years to confirm that light does not travel at an infinite speed. Over the past half century there have been a number of experiments con‐ ducted to measure the precise speed of light. Modern experiments confirm the speed of light to be about 2.998×108 m/s, usually rounded off as:
c = 3.00×108 m/s
Just as sound travels at different speeds through different materials, the speed of light also changes depending on the medium it travels in. You can calculate how fast light travels in a material by using the equa‐ on
where n is equal to the index of refrac on for the material. The value of n for all sorts of materials has been found experimentally; some of these materials are listed in Table 1. This number tells us a lot about how light will behave within a material or as it crosses from one medium to another. Because electromagne c waves are so small and fluctuate so quickly, we can divide the light up into idealized lines called rays. You can imagine a ray as a straight beam of light, but in reality light is emi ed from a source in all direc ons. Reflec on occurs when a beam of light bounces off of a material. If the surface is smooth, the reflected beam leaves the surface at the same angle at which it approached. Thus we say that the angle of inci‐ dence equals the angle of reflec on, or θi=θr. You can see your reflec on in a mirror because rays of light from different points on your body reflect in this uniform manner. When a beam of light transmits from one medium to another, refrac on occurs. The direc on of light bends one direc on or another depending on the refrac ve index of each material. In general, when light travels from a material with smaller n to larger n, the ray will bend toward the normal (θ1 > θ2); if it goes from larger n to smaller n, it bends away from the normal. See Figure 2 for a diagram.
Table 1: Sample indices of refrac‐ on for several materials.
Material n
Vacuum 1 (exact)
Air 1.00
Water 1.33
Glass (Crown) 1.52
Diamond 2.15
Figure 2: Reflec on (le ) and Refrac on (right). No ce the direc on the ray of light bends as it moves from a material with larger index of refrac on to a smaller one, and vice versa.
V = c n
69
Lab 6: Light
Mirrors and lenses are devices that u lize the phenomena of reflec on and refrac on to create a num‐ ber of useful results for scien sts and engineers. A mirror is usually a polished metal surface that re‐ flects almost all of the light that lands on it. While it is easy to predict how a ray will bounce off of a plane mirror, such as the one in your bathroom, curved mirrors can produce some very interes ng re‐ sults. The following diagrams show how incident rays will reflect off of different spherical mirrors.
Figure 3: Rays incident on a convex (le ) and concave (right) mirror reflect outward or inward as shown above. Images form where the rays converge (real image) or where they appear to emanate from (virtual image).
● F
Figure 4: Rays incident on a convex (le ) and concave (right) lens reflect outward or inward as shown above. Convex lenses (le ) focus parallel incident rays through a single point, called the focus point. For this reason, they are some mes referred to as convergent lenses. Concave lenses (right) cause parallel incident rays to bend away from each other. In fact, they diverge away from each other as if they all began at the same focal
point (rather than converging at the same focal point, as with concave lenses )
● ●
70
Lab 6: Light
Parallel rays incident on a concave mirror all reflect toward the mirror’s focal point, which lies in front of the mirror. For a convex mirror, rays reflect outward in such a way that, if traced backward, they converge at a focal point behind the mirror (Figure 3). In each case, the focal point is halfway between the mirror surface and the center—the center of the imaginary sphere that the mirror surface shares: In the case of lenses, parallel rays refract through the lens material. For converging lenses, the rays converge at a focal point behind the lens. For diverging lenses, rays are refracted outward so that when traced backward they will intersect at a focal point in front of the lens. If the object is very far away from a concave mirror (we can say “at infinity”), rays hi ng the mirror surface will be pre y much parallel, and an image will form at the focal point in front of the mirror. In the case of a converging lens, rays refract through the lens and converge at the focal distance on the other side. A real image occurs when a mirror or lens focuses rays of light from all points on the object at a specific distance. If you know where all the light rays intersect, you could put a screen at that point and view the real image that forms there. The projec on screen at a movie theater, for instance, cre‐ ates a real image at the precise distance of the movie screen. Without a screen, you can view a real image by placing your eyes at just the right distance beyond where the image forms so that your eyes are focused at the image point—and an image will appear in the air in front of you! A virtual image occurs when rays coming off of a mirror or through a lens appear to originate from a specific spot, when really no actual object exists at that point. Virtual images are usually made with convex mirrors and diverging lenses. Your reflec on in a regular plane mirror is a virtual image—there is nothing really behind the mirror giving off light. With a concave mirror, the forma on of a virtual im‐ age depends on how close the object is to the mirror. An object closer than the mirror’s focal point is virtual and magnified, while an object placed outside the focal point creates a real image in front of the mirror that can only be seen clearly at the right distance (usually with a screen). When images form from spherical mirrors and lenses, o en mes the image appears to be larger or smaller than the original object. The magnifica on of a mirror or lens tells us how large or small the image is compared to the object. It turns out that the magnifica on (M) is also directly related to the image and object distances: Here the magnifica on is expressed as ra os of the image and object heights and distances. By conven‐ on, an inverted image has a nega ve image height, while an upright image is given a posi ve height.
Image distances are posi ve or nega ve depending on the conven ons listed in Figure 4. Consider a 3 cm tall object. If a lens forms an upright image that is 6 cm tall, the magnifica on of that lens is 2(or 2x, meaning “two mes”). On the contrary, an upside‐down image that is 1.5 cm tall yields a magnifica on of ‐0.5. As you can see, magnifica ons greater than 1 imply an image that appears larger than the origi‐ nal object, while magnifica ons less than one produce images that appear smaller than the original object.
f = c 2
M = h = ‐ si h0 so
71
Lab 6: Light
Mirrors: concave: convex: All image and object distances are posi ve on the re‐ flec ng side of the mirror (object side) and nega ve if “behind” the surface.
Lenses: convex: f > 0 concave: f < 0 so > 0 if object is on side of mirror that rays enter si > 0 if image is on side opposite where rays enter (real image) si < 0 if image is on same side as where rays enter (virtual image)
Figure 5: The Lens Equa on The most useful equa on when dealing with mirrors and lenses is called the lens equa on. This equa on works well, as long as the mirror you are working with is not too curved (meaning, small in size compared to the radius of its curvature) and if the lens is thin. It relates the focal length f, the object distance, so , and the image distance, si.
The following sign conven ons allow you to use this equa on with both mirrors and lenses. In gen‐ eral, real images are said to have posi ve distances, and virtual images are said to have nega ve dis‐ tances.
Example Lens Equa on Calcula on: What image is produced when placing an object 9 cm. away from a convex lens that is 3 cm. long. Given: f = 3 cm. so = 9 cm. We need to solve for si to determine the image length. To do this, plug in the known variables and iso‐ late si on one side of the equa on. 1. 1 = 1 + 1 3 si 9 2. 3 ‐ 1 = 2 = 1 9 9 9 si 3. 9 = si 2 1 Answer: Si = 4.5 cm
1 = 1 + 1 f si so
f = ‐ C 2
f = C 2
72
Lab 6: Light
A ray diagram is helpful for showing how to find where images will form. Generally, three rays can be used to locate the image formed by a mirror or a lens. The following examples in Figures 6‐8 will give you a be er picture of how mirrors and lenses affect rays of light from objects.
Figure 6: A real image formed by a concave mir‐ ror. Note the inverted
orienta on and the mag‐ nifica on.
Example Ray Diagrams
Figure 7: A virtual image is formed in a
convex mirror.
73
Lab 6: Light
Experiment 1: Ray Diagrams To complete this lab, you will need to draw three, separate ray diagrams. The start of each diagram has been provided for you in the beginning of Procedure 1, Procedure 2, and Procedure 3, respec vely. It is important that you use a ruler when drawing to ensure that each diagram reflects the correct dimensions (listed at the top of every diagram.) When drawing your diagrams, remember that the distances measured along the axis should begin at the center of each lens (convex or concave). For example, a focal point that is marked at 5 cm should be posi‐ oned 5 cm away from the center of the lens. The diagrams indicate if the focal point or object is placed
to the right or le of the lens. Note: The size of your computer screen and the amount of “zoom” perspec ve you have applied to the manual will affect the scales of the diagrams. It is important for you to rely on the numbers provided at the top of each diagram, rather than measuring the dimensions of the images provided in the manual, to create your diagram. When you have completed your diagram, take a picture of it (using camera phone, digital camera, webcam, etc.) or scan the image onto your computer. These diagrams should be included in the final doc‐ ument you submit with your post‐lab ques ons.
Figure 8: A real image formed by a convex lens. Again, note the inverted orienta on and the magnifica on.
Materials Ruler *White or graphing paper *Pencil *You must provide
74
Lab 6: Light
Procedure 1: Concave Mirror Please submit your ray diagrams and answers for this experiment on the Word document provided to you.
1. To begin, Ray 1 should be drawn horizontal from the top of the “object” and reflect through the focal point f. To help you start the diagram, Ray 1 has been drawn in for you.
2. Since rays trace the same path no ma er what direc on they are going, we can draw Ray 2 as the “reverse” of Ray 1: this ray should be drawn through the focal point first, then reflect off the mirror horizontally.*
3. Finally, Ray 3 should be drawn through the center point C of the mirror, and reflect direc on back through its origin. Why can we draw this ray like this (think about the radius of a circle)?
4. If done correctly, these lines should all intersect at one point! Draw your new arrow from the axis to the point of intersec on—what do you no ce about the orienta on of the real image?
5. Measure and record the resul ng image distance and image height from your diagram.
f = ___________ si = ___________ hi = ___________ * As another op on, a ray may be drawn that reflects off the mirror’s center. This ray will reflect at the same angle at which it is incident, as the mirror center is perpendicular to the horizontal.
so= 12.5 cm, C= 6.5 cm, ho= 4 cm
Ray 1
Object f
75
Lab 6: Light
Procedure 2: Convex Lens A Please submit your ray diagrams and answers for this experiment on the Word document provided to you.
1. To begin, Ray 1 should be drawn horizontally from the top of the object, and refract through the focal
point f. 2. Ray 2 goes directly through the center of the lens and does not refract. 3. Ray 3 goes through the focal length on the object side, then refracts horizontally through the lens. 4. Your three rays should intersect very at or very nearly at a single point. Draw in the resul ng image as
another arrow. 5. Measure and record the resul ng image distance and image height from your diagram.
si = ___________ hi = ___________
so= 8.8 cm, f = 3.2 cm, ho= 3.4cm
Object f f
76
Lab 6: Light
Procedure 3: Convex Lens B Please submit your ray diagrams and answers for this experiment on the Word document provided to you.
1. For this diagram, the first part of Ray 1 is drawn for you. Determine what kind of image will form based
on the placement of the object inside the focal length? Finish this ray by bending the it inward and down so that it passes through the right‐most focal point.
2. Ray 2 is a li le more complicated because the object is placed closer to the lens than it is to the focal point. Thus, the ray must be drawn as if it came from the focal point, travel towards the top por on of the lens, and converge slightly once through the lens.
3. Ray 3 begins at the top of the apex, and travels directly through the center of the lens. Is does not expe‐ rience any deflec on.
4. So far, these rays do not intersect. Therefore, to determine where the image is formed you must ex‐ trapolate the rays backwards un l they create an intersec on point.
5. Indicate where the new image will form on your ray diagram. What do you no ce about the size/ loca on of the image? Is this image real or virtual, and how do you know?
Object f
Ray 1
so= 3.7 cm, f = 6.0 cm, ho= 1.7cm
f
77
Lab 6: Light
Ques ons 1. Is the resul ng image for the concave mirror real or virtual, and how do you know? Use your meas‐
urements to calculate the magnifica on. M=__________________
2. For the concave mirror, use the lens equa on, magnifica on equa on, and the provided distances (not any measured image distances) to calculate si and hi. How do your measured values compare?
3. Is your image for Convex Lens A real or virtual, and how do you know? Use your measurements to
calculate the magnifica on. M=__________________
4. For Convex Lens A, use the lens equa on, magnifica on equa on, and the provided distances to calculate si and hi. How do your measured values compare?
5. Measure and record the image height and image distances for Convex Lens B.
Si =__________ hi =______________ 6. Is the image formed through Convex Lens B real or virtual, and how do you know? Use the lens
equa on to find si and hi , and compare this to the actual measurements.
78
Lab 6: Light
Experiment 2: Exploring Mirrors Concave and convex mirrors can create a variety of different images. A convex mirror reflects incoming rays outward from its center—these rays are perceived by your eye as origina ng behind the mirror as a virtual image. For a concave mirror, the forma on of either a virtual image or a real image depends on how close the object is to its focal point. In this lab you will examine how both types of mirror create real and virtual images.
Procedure / Observa ons 1. Look into the side of the mirror that bulges out toward you. Write down how the image appears
(orienta on and magnifica on) and how many objects you can see in the background. 2. Hold the mirror close to your face, and then gradually move it away. Note what happens to your image
as you get farther from the mirror. 3. Now turn the mirror over and look into the side that bends inward. Note down how the image appears
(orienta on and magnifica on) and how many objects you can see in the background. 4. Place this mirror as close as you can to your eyes and note what you see differently. Write down how
the orienta on and magnifica on change as you move the mirror farther away. Ques ons Please submit your answers for this experiment on the Word document provided to you. 1. What kind of mirror did you use in Procedure/Observa ons 1—is it convex or concave?
2. Is your image in this type of mirror a virtual image or a real image? How do you know?
3. Did the convex mirror give you a good view of a lot of objects to either side of you? Where have you
seen mirrors like this used, and what do you think makes them useful?
Materials Concave/convex plas c mirror
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Lab 6: Light
4. Is the other side of the mirror convex or concave? Comment on the magnifica on of this side of the mirror when it is held very close to your eyes. How does the magnifica on change as you move it away from your eyes?
5. Is this a virtual image or a real image? Draw a ray diagram for a concave mirror with the object placed inside the focal length (so < f ) to verify your answer.
Experiment 3: Exploring Lenses
Procedure 1 1. Hold the convex lens at about 30 cm in front of your eyes, and hold it up to different objects (such as
a ruler or your lab manual page). 2. Gradually move the lens farther from the object, and note what happens to your view of the object
through the lens. Record how the image appears and changes in the space below. 3. Repeat the above steps with the concave lens, and record your observa ons. 4. Use your observa ons to answer Ques ons 1‐2. Observa ons Please submit your observa ons and answers for this experiment on the Word document provided to you. Convex Lens: Concave Lens:
Materials 1 Convex lens 1 Concave lens Plain white paper* Wax paper Ruler * You must provide
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Lab 6: Light
Procedure 2 1. Find an area in your room or home with a bright window. Try to dim the inside lights in the area so
that the window provides most of the light—it helps if you can use a curtain to limit the amount of light coming in.
2. View the window through the lens while holding it at arm’s length. Move the lens back and forth slowly un l you can see a clear image (if you can’t create an image easily, move yourself farther from the window). Once you can see a clear image answer Ques on 3.
3. Try to form an image of the window on your “screen” by changing the distance between the lens and the paper—this should occur when the lens is between 10 cm and 20 cm from the paper. Once you can make a sharp image, move on to Ques ons 4 and 5.
Ques ons 1. Describe the general orienta on and magnifica on of the images formed through the convex lens
before the image became blurry (this occurs when the image distance is larger than the distance from the lens to your eye).
2. What kind of image forms through the convex lens in the above situa on, and how do you know?
3. How does the image of the window appear through the lens at this distance? What kind of image is this, and how do you know?
4. At what distance must you posi on the screen in order to view a clear image on the paper?
5. Explain why the screen allows you to view this kind of image, but would not work in viewing the images from Procedure 1.
Lab 7: Radioac vity
83
Lab 7: Radioac vity
Concepts to explore: Strong force Radioac vity Isotopes Nuclear decay Half‐life
All ma er consists of atoms. Most of ma er is actually empty space defined by electrons spinning around a small nucleus of protons and neutrons. Therefore, there is abundant space within an atom.
Protons and neutrons are a racted to each other by strong and weak forces. The strong force is one of the four basic forces in nature, and measures more than 100 mes stronger than the electric force. However, it is only ac ve in short‐ranges such as in the nucleus of an atom. The larger the nucleus of an atom the less affect the strong force has on the nucleus, as the electric force causes the protons and neutrons to repel each other. For this reason, the resul ng net force decreases as the size of the nucle‐ us increases.
The nucleus can decay and give off ma er and energy when the strong force is not large enough to hold the nucleus together. This process is called radioac vity. Nuclear decay occurs in all nuclei with more than 83 protons; these atoms are both unstable and radioac ve.
The number of protons in an atom is constant and represented by the atomic number (See Figure 2). In contrast, the number of neutrons present can vary. Atoms with the same number of protons and elec‐ trons, but different numbers of neutrons are called isotopes. Isotopes have the same chemical proper‐
Figure 1: If a nucleus was the size of a grain of sugar, the electron cloud would span 10m from the grain in
all direc ons!
84
Lab 7: Radioac vity
es, but the stability of the nuclei may differ. Nuclei that have too many or too few neutrons rela ve to the number of protons are considered unstable. The mass of an electron can be considered negligible com‐ pared with the mass of protons and neutrons; therefore, the mass of an atom can be considered equivalent to the combined mass of protons and neutrons in the atom. The combined mass gives rise to the mass num‐ ber.
Unstable nuclei are constantly changing as a result of the energy imbal‐ ance within the nucleus. As unstable nuclei decay, they emit par cles and electromagne c energy called radia on. Radia on is energy trans‐ mi ed through space in the form of electromagne c waves or energe c par cles. As radioac ve isotopes decay, they emit radia on only once. However, it may take several steps for an unstable atom to become sta‐ ble, and radia on will be given off at each step. For this reason, radioac‐ ve sources become weaker with me. As more and more unstable at‐
oms of a material become stable through successive radioac ve decay, less radia on is produced by the material and eventually the material will cease being radioac ve and unstable.
Radia on is a natural process and is categorized into three types, based on the decay product that is released: alpha, beta, and gamma. When alpha radia on occurs, an alpha par cle made of two protons and two neutrons is emi ed from the decaying nucleus. The alpha par cle has the charge of +2 and an atomic mass of 4. Therefore, when an atom loses an alpha par cle it undergoes a transmuta on, and becomes another element. They are the largest radia on par cle and also have the biggest electric charge, which makes them lose energy quickly when they collide with other ma er. As a result, the alpha par cles are the lowest penetra ng form of radia on, stoppable by a single sheet of paper. A second type of radia on is caused when an unstable nucleus loses an electron from the neutron. This is called beta radia on, and the electron that is lost is referred to as the beta par cle. This par cle is fast‐ er and more penetra ng than an alpha par cle, but can be stopped by a piece of aluminum foil. As with alpha radia on, the atom undergoes a transmuta on when beta decay occurs, becoming an ele‐ ment with one more proton and an atomic number one greater than before. The most penetra ng form of radia on is gamma radia on. Gamma rays have no mass or charge and travel at the speed of light, and require thick, dense materials (such as lead or concrete) to stop their penetra on. Gamma
rays are emi ed from the nucleus when alpha or beta decay occurs.
The behavior and effects of the radioac ve iso‐ tope (radioisotope) are influenced by the half‐ life of that isotope. The half‐life of a radioac ve isotope is the amount of me required for half the nuclei in the sample to decay into something else. It also provides informa on about the fre‐ quency of radioac ve emissions. Note that it does not represent a fixed number of atoms that disintegrate, but a frac on. A radioisotope with a long half‐life will only infrequently emit radia‐ on, while a short‐lived radioac ve isotope will
6C Figure 2: The nucleus symbol includes the mass number (above the C) as well as the
atomic number (below the C). How many neutrons does car‐
bon‐14 have?
14
Radioisotope Half‐life
Polonium‐215 0.0018 seconds
Bismuth‐212 60.5 seconds
Sodium‐24 15 hours
Iodine‐131 8.07 days
Cobalt‐60 5.26 years
Radium‐226 1,600 years
Carbon‐14 5,730 years
Uranium‐238 4.5 billion years
Table 1: Half lives of Some Radioisotopes
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Lab 7: Radioac vity
emit radia on repeatedly over a short period of me. Half‐life varies widely among the radioisotopes, from a frac on of a second to billions of years, as shown in Table 1.
Since the number of atoms present decreases by one half with the passing of each half‐life, the frac on of atoms remaining can be calculated as:
½n = undecayed atoms
where n is the number of half‐lives that have passed. A er one half‐life, 1/2 of the atoms remain un‐ stable (and undecayed), and the other half became something else to achieve stability. A er two half‐ lives, 1/4 ((½)2) of the atoms in the sample are undecayed. A er three half‐lives, 1/8 ((½)3) atoms re‐ main undecayed, and so on. This expression demonstrates how sequen al decay events result in a re‐ duc on in the amount of unstable radioisotopes present. The decay pa ern follows the characteris c curve demonstrated in Figure 3 showing the decay rate of Carbon‐14.
Figure 3: Carbon‐14 has a half life of 5,730 years. A er 11,460 years (5,730 x 2) pass by, you might think that there are zero elements remaining. However, there are half as many as were present a er 5,730 years passed. The concept of half‐life is depicted in the graph above, showing how much of the element is present a er se‐
quen al half‐lives pass.
86
Lab 7: Radioac vity
Materials Ski les bag (approximately 60 candies) 5x8in. Resealable bag
Experiment 1: Es ma ng Half‐Life While it would be nice to do an actual decay experiment, the me, money, and equipment required is unrealis c. Instead, you will use Ski les™ candies to demonstrate the concept of half‐life. The Ski les™ represent atoms.
Procedure 1. Count the number of candies in the Ski les bag. Record this number in Table 2.
2. Place all of the candies into the resealable bag.
3. Seal and shake the bag gently.
4. Pour out the candy onto a flat surface, and count the number of candies with the print‐side up (with the S on it). This represents the decayed atoms. Record this number in Table 2 next to the Trial number.
5. Return ONLY the pieces with the print side down into the resealable bag. Remove the print‐side up candies and set them aside (Note: You will repeat this experiment two more mes, so do not dis‐ card the Ski les™ you set aside!).
6. Repeat steps 3‐5 un l all of the atoms have decayed (Note: you may not need all rows in the table or you might need more rows).
7. Repeat the above procedure two mes, recording the results in Table 2. Average the number of decayed atoms for each trial, repor ng the calcula on in Table 2.
8. Calculate the percentage of decayed atoms based on the average number of decayed atoms for each trial. Put a check next to the trial with the calculated percentage of decayed atoms that most closely matches 1/2 (50%), 1/4 (25%), 1/8 (12.5%), and 1/16 (6.25%). You will use this data to plot a graph similar to Figure 3 showing the half‐life of Carbon‐14 for Ques on 3.
87
Lab 7: Radioac vity
Please submit your table data and answers for this experiment on the Word document provided to you.
Table 2: Half‐life experimental results
Ques ons 1. What is meant by the term half‐life?
2. At the end of two half‐lives, what percentage of atoms (Ski les™) have not decayed? Show your calcula on.
Total number of atoms
Trial Number of decayed atoms
Average
1st Round 2nd Round 3rd Round
1
2
3
4
5
6
7
8
9
10
Percentage of decayed atoms
(from original number)
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Lab 7: Radioac vity
3. Using your data, graph the number of undecayed atoms vs. trials below to show when 1/2, 1/4, 1/8, and 1/16 of your Ski les remain (use the values next to the boxes you put checks next to in Step 8 of the procedure).
4. How would the graph change if 20 Ski les were used in this experiment?
5. If 1/8 of a radioac ve element remains a er 600 years, what is that element’s half‐life?
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