OpenStax College Physics for AP User Manual

Lab Manual - Student Edition

College Physics for APⓇ Courses
Lab Manual

Student Version

PAPERBACK BOOK ISBN-13 9781711493350
ORIGINAL PUBLICATION YEAR 2020

10 9 8 7 6 5 4 3 2 1

OpenStax

Rice University
6100 Main Street MS-375
Houston, Texas 77005

To learn more about OpenStax, visit https://openstax.org.
Individual print copies and bulk orders can be purchased through our website.

©2020 Rice University. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution

4.0 International License (CC BY 4.0). Under this license, any user of this textbook or the textbook contents herein
must provide proper attribution as follows:

● If you redistribute this textbook in a digital format (including but not limited to PDF and HTML), then you must
retain on every page the following attribution: “Access for free at openstax.org.”

● If you redistribute this textbook in a print format, then you must include on every physical page the following
attribution: “Access for free at openstax.org.”

● If you redistribute part of this textbook, then you must retain in every digital format page view (including but
not limited to PDF and HTML) and on every physical printed page the following attribution: “Access for free at
openstax.org.”

● If you use this textbook as a bibliographic reference, please include
https://openstax.org/details/books/biology-ap-courses in your citation.

For questions regarding this licensing, please contact [e-mail].

Trademarks

The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, OpenStax CNX logo, OpenStax
Tutor name, Openstax Tutor logo, Connexions name, Connexions logo, Rice University name, and Rice University
logo are not subject to the license and may not be reproduced without the prior and express written consent of Rice
University.

2

OPENSTAX

OpenStax provides free, peer-reviewed, openly licensed textbooks for introductory college and Advanced Placement®
courses and low-cost, personalized courseware that helps students learn. A nonprofit ed tech initiative based at Rice
University, we’re committed to helping students access the tools they need to complete their courses and meet their
educational goals.

RICE UNIVERSITY

OpenStax, OpenStax CNX, and OpenStax Tutor are initiatives of Rice University. As a leading research university with a
distinctive commitment to undergraduate education, Rice University aspires to path-breaking research, unsurpassed
teaching, and contributions to the betterment of our world. It seeks to fulfill this mission by cultivating a diverse
community of learning and discovery that produces leaders across the spectrum of human endeavor.

PHILANTHROPIC SUPPORT

OpenStax is grateful for our generous philanthropic partners, who support our vision to improve educational
opportunities for all learners.

Laura and John Arnold Foundation
Arthur and Carlyse Ciocca Charitable Foundation
Ann and John Doerr
Bill & Melinda Gates Foundation
Girard Foundation
Google Inc.
The William and Flora Hewlett Foundation
Rusty and John Jaggers
The Calvin K. Kazanjian Economics Foundation
Charles Koch Foundation
Leon Lowenstein Foundation, Inc.
The Maxfield Foundation
Burt and Deedee McMurtry
Michelson 20MM Foundation
National Science Foundation
The Open Society Foundations
Jumee Yhu and David E. Park III
Brian D. Patterson USA-International Foundation
The Bill and Stephanie Sick Fund
Robin and Sandy Stuart Foundation
The Stuart Family Foundation
Tammy and Guillermo Treviño

3

Table of Contents

Information for the Student 5

Lab 1: Graphing Motion 9

Lab 2: Projectile Motion 18

Lab 3: Newton’s 2nd Law 23

Lab 4: Forces 29

Lab 5: Circular Motion 34

Lab 6: Hooke’s Law and Spring Energy 40

Lab 7: Impulse and Momentum 49

Lab 8: Conservation of Momentum 55

Lab 9: Simple Harmonic Motion 62

Lab 10: Rotational Motion 67

Lab 11: Mechanical Waves 73

Lab 12: Sound Waves 78

Lab 13: Electrostatics 82

Lab 14: Ohm’s Law 90

Lab 15: Resistor Circuits 97

Lab 16: Kinetic Theory of Matter 102

Lab 17: Gases 108

Lab 18: Fluid Dynamics 117

Lab 19: Thermodynamics 125

Lab 20: RC Circuits 131

Lab 21: Observations of Magnetic Fields 137

Lab 22: Quantitative Magnetism 143

Lab 23: Electromagnetic Induction 150

Lab 24: Mirrors 157

Lab 25: Geometric Optics 165

Lab 26: Light as a Particle 171

Lab 27: Double-Slit Interference and Diffraction 177

Lab 28: Atomic Physics 185

Lab 29: Models of the Hydrogen Atom 190

4

This content was originally authored through a collaboration with the Texas Education Agency (TEA). It is presented
here with modifications, including updates to align with the 2019 Course and Exam Description for AP Biology. These
resources are available to all verified instructors free of charge at the following hyperlink:

https://openstax.org/details/books/biology-ap-courses?Instructor%20resources.

To the Student:

Congratulations on being accepted into, and having the courage to take, an Advanced Placement biology
class! You are about to delve deep into some very detailed biology concepts. This lab manual aims to help
you better understand these concepts through hands-on experiences in the laboratory. In addition, it will
challenge you to critically think about biology concepts, scientific methods, and experimental design as
part of its inquiry-based framework.

Inquiry-based learning involves challenging yourself to learn through self-discovery. Instead of simply
presenting you with facts to memorize, this manual encourages you to ask questions about the material
that you will then answer through your own exploration. By creating your own hypotheses and then
planning and carrying out your own experiments on a variety of topics in the lab manual, you will
hopefully learn biology by satisfying your own curiosity.

In this AP lab manual, the inquiry-based structure includes the following components:

1. Pre-assessment section. This section contains a list of questions that you should answer before

starting each activity. These are meant to get you thinking about the main concepts of each lab.
The pre-assessment questions are designed to connect the concepts in each lab to your
experiences in daily life. Whether you realize it or not, you observe biology constantly in the world
around you. Therefore, you are likely familiar with more biology topics than you realize! The
pre-assessment questions are meant to tap into the biology knowledge you already have and
apply it to what you will learn in each lab. As a result, your answers to these questions may not be
graded and you will benefit greatly by discussing your answers as a class. This also allows your
teacher to measure how familiar you and your classmates are with the material.

2. Structured Inquiry. In this section, you will be introduced to an experimental system by doing a

well-laid out experiment with detailed steps. This section is meant to guide you in using the
equipment in a “safer” activity before planning and performing an entire experiment. However,
you will still be posing questions, predictions, and hypotheses in the structured inquiry. You will
also critically think about how to achieve the most accurate and reliable results during the
structured inquiry in preparation for creating your own experiments in the guided inquiry.

3. Guided Inquiry. In the guided inquiry, you will use the familiarity you gained during the structured

inquiry to perform your own self-investigation. The experimental setup of the guided inquiries is
often identical to that used in the structured inquiry. Therefore, you will be working with
equipment and methods that you have already tried in the structured inquiry. This time, you will
pick a variable to study, create a hypothesis, and fully design an experiment to test your
hypothesis. You will determine which equipment and methods you should use to collect accurate
and precise data.

5

Once you have planned your experiment, be sure to have your plan approved by your teacher, who
will also ensure that your plan is safe and appropriate for the equipment available. Finally, you will

analyze your own data and make conclusions based on your experimental evidence. If time allows, you
will then refine and re-run your experiments or test additional hypotheses that you find interesting. In
many ways, the guided inquiry step is meant to engage you in the same processes that scientists have
used to discover information about our world and universe!

Components of Structured and Guided Inquiry Sections

To ensure that an inquiry-based approach is implemented in each activity, both the structured and
guided inquiries also contain each of the following steps at least once:

Hypothesize/Predict: This is where you will be creating hypotheses, which are questions or predictions
about what will happen during an experiment. Be sure that your hypotheses are clear, specific, and
testable.

Good hypothesis: The volume of water in a container will be higher when a 2-gram mass is added
compared to when a 1-gram mass is added.

Poor hypothesis: The volume of water in this experiment will increase as larger objects are added.

Good hypothesis: The speed of a vehicle traveling down the 30ᵒ ramp will be lower than the speed of the

vehicle traveling down the 60ᵒ ramp.

Poor hypothesis: The vehicle will travel fast down the ramp with the greater amount of slant.

Student-led Planning: Each inquiry contains at least one step where you and your lab partners will plan
how to properly conduct your experiment. During the Structured Inquiry, you will generally plan proper
techniques for getting the best results possible using the available equipment and described methods.
As with many things in life, two or more heads are often better than one, and you and your group
members should come to a consensus on a plan before proceeding. This will lay the groundwork for the
Guided Inquiry; you and your group will need to plan an entire experiment in this step.

Critical Analysis: This step typically occurs near the end of each inquiry. Here you will critically analyze
your results, judge their validity, and explain why your hypotheses were supported or not supported by
your results. You will also suggest ways that your experimental methods could have been improved to
get more accurate or precise data as well as determine new questions to ask related to your results.

A Note About Your Notebook

As part of the challenge of taking an AP course, this lab manual does not contain data tables where you
record your findings. Therefore, you will be required to design your own tables, answer assessments,
and do any other note-taking in a separate notebook. You should use the same notebook for biology lab
throughout the year. This will allow you to easily refer back to previous labs when you need to reference
earlier content. Do not put non-biology content in your biology notebook, as your teacher may collect
and grade your notebook throughout the year.

6

Components of a Lab

Main introduction:

Each lab contains an introductory section under the title. This introduces the “big picture” concepts of
the lab as well as how they connect to everyday life. They will also introduce the pioneering physicists
and experiments that led to our current knowledge of each lab topic. Relevant equations that you will
use in the labs are also introduced here, including definitions of their variables. Many of the labs involve
measuring the value of these variables so that you can later perform your own calculations. Please read
the lab and activity introductions carefully before your lab period. Then, before the lab starts, ask your
teacher about any concepts of which you are unsure.

In this lab you will learn

This section presents learning objectives for the lab. These are the “take away points” that you should
be able to explain or perform after doing the activities. It is helpful to read these objectives before each
lab to prime yourself for what you will learn. It is then helpful to reread these at the end of each lab to
ensure that you have achieved all of the learning objectives.

Activities:

Each lab is divided into 2-3 activities. Please note that your teacher may or may not have you perform all
activities in a given lab, so pay close attention to your teacher’s instructions throughout the lab.

Safety precautions:

These bullet points list important safety issues that will prevent injury to yourself or your classmates
during the lab activities. Each activity has its own safety precautions section. Please read and

understand all safety precautions before beginning each activity!

For this activity you will need section:

This section lists all of the materials needed for each activity. Before you start the lab, make sure that
you can identify all items on this list. Also, pay close attention to your teacher’s instructions, as you may
be using different equipment for these labs than those on this list.

Activity introduction:

These are short introductions relevant to specific activities. As with the main introduction, the activity
introductions may contain formulas, equations, or other background information needed to successfully
carry out and understand the activities. As with the main introduction, please read these introductions
carefully before your lab period. Then, before the lab starts, ask your teacher about any concepts of
which you are unsure.

Process steps:

These are the steps you will perform to carry out the activities. Please read through all of the process
steps and setup diagrams before starting Step 1. Ask your teacher if there are any steps you don’t
understand prior to starting. This will help you perform the activities correctly the first time, preventing
the need to redo activities or having to leave your laboratory period with unusable data.

7

Assessments:

The assessment sections provide questions that test your knowledge of the lab material. Your teacher
will instruct you on how to submit answers to the assessments for grading.

College Board® (CB) Standard Alignment:

College Board® standards are summarized in a table format at the beginning of each lab. The College
Board’s® AP Biology Course and Exam Description was used to provide this information.
In addition, standards tags are found on the assessments, allowing you to quickly identify which
standard is addressed by each question.

8

Lab 1:

Graphing Motion

9

In this lab you will learn

● how to measure the speed of an object traveling at a constant velocity

● how to differentiate between motion at a constant velocity and motion with acceleration

● how to use a position or velocity versus time plot to understand motion

Activity 1: Pre-Assessment

1. Would you expect an object that you set in motion to continue moving at a constant speed? Why or why not?

2. Discuss the answers to question 1 with the class.

Activity 1: Constant Velocity

Suppose you graphed the motion of an object using the horizontal axis for the time elapsed, in seconds, and the
vertical axis for the distance traveled. For an object traveling at constant speed, the change in distance would be
proportional to the change in time. Therefore, when you plot your data on a distance-versus-time graph, the points should
fall along a straight line. However, every measurement has some error, so the data points would not be likely to exactly
fall on a straight line. Using a line of best fit helps to average these errors and give a more accurate approximation. To
draw a line of best fit, you would use a ruler to draw a straight line that follows the trend of the data and comes as close
to all of the data points as possible. The slope of that line is given by

The slope equals the speed of the object. Because of measurement errors, some points will lie above the best-fit line and
some will lie below it. This is because the best-fit line passes through the middle of the data and averages the values. As a
result, the slope of the line of best fit provides a more accurate value of the speed than a single pair of data points would.

Safety Precautions

● Keep the cart on the track to avoid damage or injury.

For this activity, you will need the following:

● Straight track*

● Cart with spring

● Stopwatch*

● Masking tape*

● Meter stick

For this activity, you will work in pairs.

*Note—If you have access to air tracks, using them will improve your approximation of a frictionless system that can move
at a constant speed.
**Note—For increased accuracy, photogate timers or other technology can be used in place of the stopwatch and
masking tape. The distance between the photogate timers would replace the distance between pieces of masking tape,
and the timers instead of a stopwatch would record the time.

10

Structured Inquiry

Step 1: Place your track with one end against a wall. Rest the cart against the wall, as shown in Figure 1.1, so that releasing

its spring can launch the cart. Place one piece of masking tape on the track ahead of the starting position of the cart and
another piece of tape further down the track. Measure the distance between the two pieces of tape. Create a data table in
your notebook for recording the distance and travel time for the cart’s motion. You will be moving the second piece of
tape at least three times, so you will need space in the table to record at least four separate times and distances.

Figure 1.1: The speed of the cart can be measured by using the spring to launch the cart from the wall and then measuring how long the cart takes

to travel a fixed distance. This can be done either by having it pass through two photogate timers or by using a stopwatch to measure the time of

travel between two pieces of masking tape.

Step 2: Hypothesize/Predict: Knowing that, ideally, the cart should move at a constant speed, predict how your
measurements would change as you vary the location of your second tape marker. How would this prediction differ if the
cart did not move at a constant speed? Realistically, do you expect your data to resemble the ideal situation?

Step 3: Student-Led Planning: You will now use your photogates, or a stopwatch and meter stick, to measure the speed of
your cart. You should vary the position of your second piece of tape or photogate timer to measure the speed for at least
four distances. If your class uses photogates, listen closely to your teacher’s instructions on how to use them. Discuss with
your partner what data you need to collect and how to use the data to determine the speed of the cart.

Step 4: Critical Analysis: Record the time it takes for the cart to travel each distance in the data table in your notebook.
Then calculate the speed of the cart for each trial, as well as the average speed across all trials. Were the predictions you
made in Step 2 supported by your data? Why or why not? How could you improve your results? Discuss your answers with
your partner and then write them in your notebook.

Guided Inquiry

Step 1: Hypothesize/Predict: Is this experimental setup a good choice for observing motion at a constant speed? What

potential issues does it have, and what improvements could you make?

Step 2: Student-Led Planning: Discuss with your partner how to use the data in your table to plot a graph from which you
can determine the speed of the cart. Now plot your data and use the graph to find the speed of the cart in your
experiment.

Step 3: Critical Analysis: How did the speed you calculated using your graph compare with the speeds you calculated for
each trial, and the average speed across all the trials, in your table? Which is a better method for measuring the speed of
the cart, and why? Did your graph look as you expected for an object moving at a constant speed? Discuss your answers
with your partner and record them in your notebook.

11

Assessments

1. Consider a baseball player who hits a home run and runs around all of the bases on the field.
a. Considering that he started and ended at home plate, is the distance he traveled equal to zero? What about

the displacement? Explain.

b. Is the player’s average speed over his entire base run equal to zero

c. Based on this, is it important to know the path an object followed to calculate its speed, or do you only

need to know where and when it started and ended? Explain.

2. In a particular city, each block is 50 m long. A runner goes two blocks north in 10 seconds, then five blocks south in

20 seconds, then eight blocks north in 50 seconds.

a. Plot the runner’s distance traveled as a function of time.
b. Calculate the runner’s speed for each interval.

c. Calculate the runner’s average speed for the entire run.

12

Activity 2: Pre-Assessment

1. What does it mean for an object to travel at constant acceleration? How could you set an object in motion at

constant acceleration?

2. Describe at least two different types of accelerated motion.

3. Discuss the answers to questions 1 and 2 with the class.

Activity 2: Constant Acceleration

An object is accelerating if its velocity is changing. The acceleration a of an object is calculated by dividing Δv, the

change in the object’s velocity, by Δt, the time over which the velocity changed

The SI unit for acceleration is m/s2, or meter per second per second. The slope of a position versus time graph for an
accelerating object is still the object’s velocity, but, by definition, the velocity of an accelerating object is changing.
However, for an object with constant acceleration, the slope of the velocity versus time graph is

and the graph should be a straight line whose slope is the acceleration.

Safety Precautions

● Keep the cart on the track to avoid damage or injury.

● Limit the angle of incline of the track to less than 10°, so that the cart reaches the end of the track at a reasonable

speed, avoiding damage or injury.

For this activity, you will need the following:

● Straight track

● Cart

● Stopwatch*

● Masking tape*

● Meter stick

● Ring stand or blocks

For this activity, you will work in pairs.

*Note —For increased accuracy, photogate timers or other technology can be used in place of the stopwatch and masking
tape. The distance between the photogate timers would replace the distance between pieces of masking tape, and the
timers instead of with the stopwatch would record the time.

13

Structured Inquiry

Step 1: Position the track so that one end is slightly lifted above the ground, using either the ring stand mounts or blocks.

Using your meter stick, place pieces of masking tape along the track to divide the track into five even intervals, as shown in
Figure 1.2 Create a data table in your notebook to record the distance and time for the cart’s motion.

Figure 1.2: A cart that is free to move on an incline will accelerate and will have different velocities at different locations.

Step 2: Hypothesize/Predict: Now that the track is no longer horizontal, predict what should happen to the speed of the

cart as it travels down the track. How will this differ from the motion of the cart at constant speed?

Step 3: Student-Led Planning: You will now use your stopwatch to measure the speed of the cart as it travels different
distances down the ramp, starting from rest. Discuss with your partner what data you will need to collect in each trial to
measure the average speed for the given distance. Explain in your notebook why the final speed at the end of this distance
is twice the average speed if the cart starts from rest. Be sure to think carefully about the start and end points you choose
for each measurement of the cart’s speed. Your procedure may be different if you are using photogates to time the arrival
times at several different locations in each trial.

Step 4: Record the time it took for the cart to travel between each marker in the data table in your notebook. Calculate
the final speed of the cart at the end of each interval. Given that the cart started at rest, calculate the acceleration of the
cart for each interval, and calculate an average value for the acceleration across the trials.

Step 5: Critical Analysis: Were the predictions you made in Step 2 supported by your data? Why or why not? What
methods could you have used to improve your results? Discuss with your partner and then write your answers in your
notebook.

Guided Inquiry

Step 1: Hypothesize/Predict: What makes the experimental setup here different from that in Activity 1? How will that

make your graphs different from those in Activity 1? What do you expect the position and velocity versus time graphs to
look like for your data?

Step 2: Student-Led Planning: Discuss with your partner how the data in the table you created can be used to create
position and velocity versus time graphs and how you can use these graphs to determine the acceleration of the cart. Now
plot your data and use the graph to find a value for the acceleration of the cart in your experiments.

14

Step 3: Critical Analysis: Given that gravity accelerated the cart down the ramp, does the value you measured for the
acceleration of the cart make sense? Why or why not? Did your graphs look like you expected for an object moving with
constant acceleration? Did the value you calculated using your line of best fit agree with the average value from your trials
for the acceleration? Discuss your answers with your partner and record them in your notebook.

Assessments

1. How does the acceleration of a cart on an incline relate to the angle of the incline? Give an expression that relates

the acceleration of the cart, acceleration due to gravity, and the ramp angle. Assume that friction can be ignored.

2. If a car speeds up from rest to 30 m/s in 6.0 seconds and then returns to rest in 12.0 seconds, what is its

acceleration?

a. While speeding up?
b. While slowing down?

3. In the first activity, you observed the motion of a cart moving at constant speed. However, the cart started at rest

and then began moving. Therefore, the cart did accelerate in Activity 1 because the velocity changed. How did one
experimental procedure produce motion at constant speed whereas the other produced accelerated motion?

15

Activity 3: Graph Matching

A position or velocity versus time graph can tell you about the motion of an object. Figure 1.3 is an example of a
graph with a straight line. The slope, which is the object’s acceleration, is therefore constant. The slope is positive, so the
object keeps moving faster over time.

Figure 1.3: An object speeding up with constant acceleration has a straight-line velocity versus time graph.

Safety Precautions

● Keep the cart on the track to avoid damage or injury.

● Limit the angle of incline of the track to less than 10° so that the cart reaches the end of the track at a reasonable

speed, avoiding damage or injury.

For this activity, you will need the following:

● Straight track

● Cart with spring

● Stopwatch*

● Masking tape*

● Meter stick

● Ring stand or blocks

For this activity, you will work in pairs.

*Note—For increased accuracy, photogate timers or other technology can be used in place of the stopwatch and masking
tape. The distance between pieces of masking tape would be replaced by the distance between the photogate timers, and
the time would be recorded by the timers instead of with the stopwatch.

Structured Inquiry

Step 1: Hypothesize/Predict: Look at the graphs in Figure 1.4. For each graph, describe the motion shown. Does it

describe an object accelerating or one moving at a constant velocity? In what direction is the object moving? If the object
is accelerating, is it speeding up or slowing down?

Figure 1.4: Position and velocity versus time graphs describe an object’s motion.

16

Step 2: Student-Led Planning: You will now use the equipment from Activities 1 and 2 to get the cart to move in a way
that would produce each of the graphs in Figure 1.5. Discuss with your partner how to do this, and what measurements
you will make to recreate the motion described by the graphs.

Step 3: Critical Analysis: Record the appropriate time and distance measurements for the three graphs in data tables in
your notebook. Were the predictions you made in Step 1 supported by your data? Why or why not? How could you have
improved your results? Discuss your answers with your partner and then write them in your notebook.

Guided Inquiry

Step 1: Hypothesize/Predict: Did you choose the correct motions for the cart to recreate the motions described in the

graphs in Figure 1.5? If not, what could you change to make them better agree?

Step 2: Student-Led Planning: Discuss with your partner how the data in the tables you created can be used to recreate
the graphs in Figure 1.5. Now plot your data and compare the graphs with the expected graphs.

Step 3: Critical Analysis: Did your graphs agree with the graphs you were trying to recreate? If they differ, in what ways do
they differ? How can you change your experimental procedure to produce better agreement? Discuss your answers with
your partner and record them in your notebook.

Assessments

1. An object slows down at a constant acceleration, and then speeds up with the same constant acceleration.
a. Sketch a velocity versus time plot for this motion.
b. What experimental procedure could you use to recreate this motion with a cart and tracks?

2. Using dimensional analysis, what quantity would you find by calculating the area under a velocity-versus-time

graph?

3. Two velocity versus time graphs have the same shape, but their y-intercepts are different.
a. What must be the same about the motion of the two objects?
b. What must be different about the motion of the two objects?

17

Lab 2:

Projectile Motion

18

In this lab you will learn

● how to describe the trajectory of a projectile mathematically and graphically

● how to design an experimental investigation of the trajectory of a projectile

● how to analyze experimental data describing the trajectory of a projectile mathematically and graphically

Activity 1: Pre-Assessment

1. How could you calculate the velocity of an object that is travelling horizontally? What lab equipment would you use
and what data would you collect?

2. Qualitatively describe the vertical acceleration of a falling object. In which direction does a free-falling object
accelerate? How does this acceleration affect the velocity of an object initially moving upward? How does this
acceleration affect the velocity of an object initially moving downward?

3. Discuss your answers to questions 1 and 2 with the class.

Activity 1: Dart Gun Speed

The introduction pointed out that motions along perpendicular axes are independent; because of this, you need to

analyze horizontal and vertical components separately from each other. These components are the horizontal and vertical
parts of a vector. It is important to remember that the downward component of velocity changes during the dart’s motion
because of the acceleration due to gravity. In this activity, we fire a dart gun horizontally to determine the velocity at the
point at which the dart exits the gun.

Safety Precautions

● Be aware of what is in front of the dart gun. Do not shoot the dart gun if someone could get hit.

● Wear safety goggles at all times while dart guns are being fired.

For this activity you will need the following:

● Dart gun with one dart

● Tape measure or meter stick

For this activity, you will work in pairs.

Structured Inquiry

Step 1: Pick a location where you will fire your dart gun horizontally. The location should be at least 3 meters away from a

wall on which the dart will stick. Measure the height of this location from the ground in centimeters and measure how far
away from the wall the position you are firing from is in centimeters. Create a data table for your measurements and show
your calculations in your notebook.

Step 2: Hypothesize/Predict: Predict where the dart will strike the wall. Why did you make this prediction? What
knowledge have you used about motion in the vertical direction to make your prediction? Add your predictions to the
data table you created in Step 1.

Step 3: Student-Led Planning: You will now solve for the velocity at which the projectile exits the dart gun in terms of
distances you can measure. Start by looking at the kinematic equations listed in Table 2. Discuss with your partner how
you can obtain the time of flight of the dart from the distance downward it moves on its way to the wall. Write an
equation in your notebook that expresses the time of flight in terms of how far downward the dart strikes the wall if it had
traveled horizontally. Next, discuss with your partner how you will use the time of flight and other data you can measure
to find how fast the projectile left the dart gun. Write the expression for the speed in terms of the variables you can
measure and the time of flight in your notebook. Remember to separate the horizontal and vertical components of motion
in obtaining these equations.

19

Step 4: Critical Analysis: After obtaining the necessary equations, aim the dart gun as close to horizontal as possible, fire
the dart, and collect your data. Record your data and use the data to determine the velocity of the projectile. List your
results in your data table. Were your predictions in Step 2 supported by your data? Why or why not? How could you have
improved your results? Discuss your answers with your partner and then write them in your notebook.

Guided Inquiry

Step 1: Hypothesize/Predict: How will the time of flight, and the displacement downward of the dart during flight, change

if you fire the dart horizontally from a distance closer to the wall? Will it strike higher or lower than before? How will it
change if the dart gun is farther from the wall? Why? Write your predictions and your reasoning in your notebook.

Step 2: Student-Led Planning: Assume the dart leaves the gun at the same velocity you determined in the first part of this
lab. Work with your partner to use the kinematic equations to obtain an expression for the time of flight of the dart in
terms of the distance of the gun from the wall. Write the expression in your notebook. Discuss with your partner how to
calculate, in terms of the time of flight, the distance downward that the dart should fall before reaching the wall. Then
choose two distances from the wall, one closer and one farther than you used in the first part of the lab. Calculate the
expected displacement downward from where the dart strikes the wall. Then carry out the actual measurement of this
displacement by firing the dart horizontally from the measured distances. Write your results in your notebook at each
step.

Step 3: Critical Analysis: How did the displacement downward of the dart compare with your prediction of whether it
would be higher or lower than in the first part of the lab? How well did its precise measured value compare with the value
predicted from your calculations? Discuss with your partner the possible sources of any disagreement and write your ideas
in your notebook.

Assessments

1. In your notebook, draw a position in the x-direction versus time graph, a velocity in the x-direction versus time
graph, and acceleration in the x-direction versus time graph for the dart launch experiment. Repeat this for the
y-direction for a total of six graphs. You can omit numbers on your x- and y-axes and just show the shape of each
graph line. After each graph, write a brief explanation of why the graph has the shape that it does.

2. A baseball outfielder throws a baseball horizontally with an initial velocity of 38 m/s. If the player releases the
baseball from a height of 2.25 m, how far does the baseball travel horizontally before it strikes the ground? Be sure
to include a table of horizontal and vertical variables and show all of your work.

20

Activity 2: Marble Launch Landing Spot

In the first activity of this lab, you determined the velocity of a projectile as it left a dart gun. Each time you

performed this activity, the projectile was launched horizontally, so the vertical component of its initial velocity was
always zero. In this activity, you will launch your projectile at an angle above the horizontal direction so that its initial
velocity has a non-zero vertical component. You will predict where this angled shot strikes the floor.

Safety Precautions

● Be aware of what is in front of the marble launcher. Do not shoot the marble if someone could get hit.

● Do not fire the marble into the ceiling or windows of the classroom.

● Wear safety goggles at all times while marble guns are being fired.

● Be sure all breakable objects, including cell phones, are out of range of the marbles.

For this activity you will need the following:

● Marble launcher with one marble

● Tape measure or meter stick

● Protractor or any other tool to determine the angle of launch

● Stopwatch

For this activity, you will work in pairs.

Structured Inquiry

Step 1: First you will measure the speed of the projectile as it leaves the launcher. Pick a location where you will fire your

marble launcher vertically. Remember all of the safety precautions and only fire the marble when it is safe. Launch your
marble straight up. Use the stopwatch to time how long the marble is in the air. From the measured time of flight and the
known value of the acceleration due to gravity (g = 9.80 m/s2), calculate the speed of the projectile as it left the launcher.
(Remember that the vertical component of velocity of the marble is zero at the top of its flight.) Create a data table in your
notebook to show your measurements and calculations.

Step 2: Hypothesize/Predict: Assuming the marble exits the launcher at the same speed as in Step 1, predict how far you
think the marble will travel before hitting the floor if it is launched horizontally from a table. Mark your prediction with a
piece of tape or a similar object. Also predict where the marble would land if fired at an angle of 30o. Add your predictions
to the data table you created in Step 1.

Step 3: Student-Led Planning: You will now use the kinematic equations to solve for how far the marble will travel when
fired horizontally, given the initial speed you determined in Step 1 and the height of the launcher. Discuss with your
partner how you will use your collected and previously known data to solve for the horizontal displacement using the
kinematic equations.

Step 4: After you have solved for a displacement, mark that position with a piece of tape or a similar object. Once it is safe,
fire the marble launcher and see if your calculated value and observed value are in reasonable agreement. If they aren’t,
return to your equations to see if you can explain why before moving on to Step 5.

Step 5: Student-Led Planning: You will now solve for the horizontal displacement the marble will travel when fired at an
angle of 30o using the height of the launcher, the initial speed you determined in Step 1, and the kinematic equations.
Discuss with your partner how you will use your collected and previously known data to solve for the horizontal
displacement using the kinematic equations.

21

Step 6: Use your protractor or a similar tool to make sure your marble launcher is positioned at the correct angle. Mark
that position with a piece of tape or a similar object. When it is safe, fire the marble launcher and see if your calculated
value and observed value are in reasonable agreement. If they aren’t, return to your equations to see if you can explain
why before moving on to Step 7. Repeat this step for two other angles that you choose and create a data table for the
angle of launch and horizontal components of initial velocity.

Step 7: Critical Analysis: After completing your calculations, record your collected data in your data table. Also include the
initial velocity of the projectile from Step 1 and the displacements solved in Steps 4 and 6. Did your data support your
predictions in Step 2? Why or why not? How could you have improved your results? Discuss your answers with your
partner and then write them in your notebook.

Guided Inquiry

Step 1: Hypothesize/Predict: The range of the projectile is how far it lands from the launcher. How does the launch angle

affect the range? Discuss with your lab partner what the range of the projectile should be if the projectile is fired straight
up and if it is fired horizontally starting just barely above the tabletop. What angle would you predict gives the maximum
range? Should the range get smaller or larger if the angle is increased from this maximum-range launch angle? What if the
launch angle is decreased? Discuss your answers and your reasoning with your partner and write them in your notebook.

Step 2: Student-Led Planning: Discuss with your partner how you will test the range produced by launch angles of 10°,
30°, 45°, 60°, and 80°. Collect your projectile range data, measured from the exit point of the launcher, for each of the five
launch angles. Write the data for each one in your data table.

Step 3: Critical Analysis: Did your data support your prediction of which angle would give the maximum range for the
projectile? What does your data show is the effect on the range if the launch angle is made larger than the angle that gave
the largest range? How about if the launch angle was made smaller? If you were to choose a distance smaller than the
maximum range, how many different launch angles would there be that make the projectile land at this distance? Discuss
your answers with your partner and write them in your notebook.

Assessments

1. If you were to know the initial velocity and the angle of launch, could you accurately predict whether or not a
basketball player could make a free throw? Explain how you would design an experiment that could determine if a
player will make or miss a free throw before the ball reaches the rim.

2. Whether a projectile is launched at 20o or 70o, it will land in the same spot as long as the projectile’s initial speed
leaving the launcher is the same. How can you explain this phenomenon?

3. Your friend is leaving your house when you discover your friend’s wallet in your room. You quickly run to your
second-story window. You call out and throw the wallet horizontally from the window, and your friend catches
it, 13.0 m away from the house. If your window is 3.5 m above the ground, how fast did you throw the wallet? Be
sure to include a table of horizontal and vertical variables and show all of your work.

22

Lab 3:

Newton’s 2nd Law

23

In this lab you will learn

● how to use free-body diagrams to determine and visualize experimental variables for force and motion

● how to graph velocity versus time

● how to measure and calculate velocity

● how to calculate acceleration

Activity 1: Pre-Assessment

Figure 3.1: The cart of mass m1 accelerates along the table. Rate of acceleration is directly proportional to mass m2.

1. Using Figure 3.1, draw a free-body diagram, indicating all the forces acting on the cart and its cargo.

2. Answer the following questions based on Figure 3.1:

a. What is the strength of the force accelerating the system, in terms of the masses involved?
b. What is the relationship between the acceleration of mass m1 and the acceleration of mass m2?

c. Does the force accelerating the system change or remain constant until mass m2 reaches the floor? Does

the acceleration itself change?

d. What total mass does the gravitational force acting on mass m2 accelerate?

3. Imagine that you placed all the masses you intend to test as cargo in the cart, except the one that is hanging
(Figure 3.1). You then exchange the hanging mass with one from the cargo section that is heavier. How will that
affect

a. the mass that is being accelerated, and
b. the net force causing the acceleration?

4. Discuss the answers to questions 1–3 with the class.

Activity 1: Applying Constant Force

When a constant force is applied to an object or system, the object or system will accelerate at a constant rate. If

the applied force and mass of the system are known, the acceleration predicted by Newton’s Second Law can be
calculated.

In this lab, you will measure acceleration of various masses by various forces using the setup shown in Figure 3.1.

The lab cart starts at rest and accelerates at a constant rate. According to the kinematic equations, the distance Δx that
the cart travels in time Δt is then

for acceleration a. This can provide a useful method for determining the acceleration by timing the motion.

24

Safety Precautions

● Heavy weights that fall can cause injury. It is safest to use a cart and hanging weight of modest mass whenever

possible.

● Make sure your experimental setup includes a means of stopping the cart to prevent it from rolling off the table.

For this activity you will need the following:

● Cart, weights, and pulley and string setup; note—If no pulleys are available, then dental floss over the edge of the

table will work

● Scale capable of weighing the cart and weights used

● Meter stick

● Visible tape or chalk for marking positions

● Stopwatch or video capture device

For this activity, you will work in pairs or small groups.

Structured Inquiry

Step 1: Hypothesize/Predict: Using the notation from your free-body diagram, apply Newton’s Second Law to derive an

equation predicting the acceleration of the cart for given masses m1 and m2. Ignore friction and air resistance as well as
the mass of the pulley and string.

Step 2: Student-Led Planning: You will need to determine the acceleration of the cart for several different applied forces.
The total mass should be kept the same. Discuss with your partner the details of how to accomplish that goal by timing the
travel of the cart between two lines marked by chalk or by visible pieces of tape. What precisely will you measure and how
will you analyze your data? Then, discuss with your partner what masses you will use for m2. Using the values for m2 you
selected, create a data table to structure your data. Include in the table the predicted values for each mass that you can
calculate using the equation you derived in Step 1.

Step 3: Procedure: Execute the planned experiment, repeating the procedure for each of the selected values of m2.
Record the numerical results in the prepared data table(s). Display your experimental data in a graph of acceleration
versus applied force. Plot the theoretically predicted graph line from your equation in Step 1 on the same graph for
comparison.

Step 4: Critical Analysis: Were the results from your experiment in reasonable agreement with your calculated
predictions? Why or why not? If your experimental results did not reasonably agree with your predictions, what factors do
you think affected the results? What, according to your equation in Step 1, is the meaning of the slope of the acceleration
versus force graph? Are your experimental data consistent with this? Discuss your answers with your lab partner and write
them in your notebook.

Guided Inquiry

Step 1: Hypothesize/Predict: What do you predict the acceleration vs. applied force for fixed mass should look like? If

your experimental results weren’t the same as you predicted, what factors do you think affected the results? Consider
some of the assumptions that were made about the setup when you did your initial calculations in Step 1. How much do
you think those factors affected the results? How could you alter the experiment to test this prediction? Write your ideas
in your notebook.

Step 2: Student-Led Planning: Discuss and decide as a team which modifications to the experiment you should make to
test your ideas. Check with your teacher before conducting additional experiments.

25

Step 3: Critical Analysis: Were you able to determine how much impact the setup assumptions have on your experimental
results? Could you use this data to improve your predictions for the acceleration of the cart with different values of m2?
How?

Assessments

1. What is velocity?

2. What is acceleration?

3. What is the source of the force causing the acceleration of the system?

4. How did you change the acceleration of the cart?

5. When you increased the hanging mass, did that increase or decrease the acceleration of the cart? Why? ]

6. What measurements did you make that enabled you to calculate acceleration?

26

Activity 2: Effect of Force on Different Masses

Newton’s Second Law tells us that the acceleration of an object or system is inversely proportional to the mass of

the object or system. The greater the mass of the system for a given force, the smaller the acceleration.

Safety Precautions

● Heavy weights that fall can cause injury. It is safest to use a cart and hanging weight of modest mass whenever

possible.

● Make sure your experimental setup includes a means of stopping the cart to prevent it from rolling off the table.

For this activity, you will need the following:

● Cart, weights, and pulley and string setup; note—If no pulleys are available, then dental floss over the edge of the

table will work

● Meter stick

● Visible tape or chalk for marking positions

● Stopwatch or video capture device

For this activity, you will work in pairs or small groups.

Structured Inquiry

Step 1: Hypothesize/Predict: The experimental setup in Figure 3.1 shows mass m1 resting on the cart and mass m2

hanging from the string. Can you predict what will happen when you change mass m1 while keeping m2 constant? Choose
a value for m2. Then, choose several values for m1 to test. Using the equation you derived in Activity 1, calculate your
prediction for the acceleration of the cart for each value of m2. Record your calculations in your notebook.

Step 2: Student-Led Planning: In Activity 1 of this lab, you established a procedure for finding the acceleration of the cart.
Using the values for m1 you selected in Step 1, create a data table to structure your inquiry.

Step 3: Procedure: Execute the planned experiment, repeating the procedure for each of the selected values of m1.
Record the numerical results in the prepared data table(s) and determine the measured acceleration of the cart for each
value of m1.

Step 4: Critical Analysis: Compare the experimental results from Step 4 to your calculated predictions from Step 2. Were
the results from your experiment in reasonable agreement with your calculated predictions? Why or why not?

Guided Inquiry

Step 1: Hypothesize/Predict: Based on what you know about Newton’s Second Law, what do you expect would happen if

you did the experiment with both masses, m1 and m2, now 1.5 times larger than before? Or, what if m1 and m2 were
multiplied by some other number, such as 0.5? By what factor would that multiply the force that accelerates the cart? By
what factor would it multiply the total mass being accelerated? Considering the effect of increasing the force along with
the effect of increasing the mass, what changes would this cause? Write your prediction and rationale in your notebook.

Step 2: Student-Led Planning: Work with your lab partner to plan an experiment to test your hypothesis on the effect of
changing the masses. Describe your planned experiment in your notebook and get your plan approved by your teacher.
Then, carry out the experiment.

Step 3: Critical Analysis: Did your results match your prediction? What is the effect on acceleration if both mass and
applied force are multiplied by the same factor, per Newton’s Second Law? How does that relate to your data? If your
results differed from your prediction, try to explain why. Discuss your answers with your lab partner and write the analysis
in your notebook.

27

Assessments

1. When you increased the mass on the cart, did that increase or decrease the acceleration of the cart? Why?

2. Apply the same idea as in the Guided Inquiry to an object in free fall by considering replacing the object with one
k times as massive. How will this change in mass (k) affect the force of gravity? By what factor does this change
the acceleration of the object? How does this account for Galileo’s observation that all objects in free fall have
the same acceleration regardless of mass?

28

Lab 4:

Forces

29