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CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
Chapter 5: Newton’s Laws: Force and Motion
Section 5.1:
The First Law:
Force and
Inertia
Learning Goals
1. Complete Chapter 5 Pretest.
• Describe how the law of inertia
affects the motion of an object.
• Give an example of a system or
an invention designed to
overcome inertia.
INQ01.1
INQ01.2
INQ01.3
INQ01.4
INQ02.5
PS04.1
Investigation 5.1: The First Law: The
Law of Inertia
• Measure and describe force in
newtons (N) and pounds (lbs).
• Calculate the net force for two or
more forces acting along the
same line.
• Calculate the acceleration of an
object from the net force acting
on it.
INQ01.1
INQ01.2
INQ01.3
INQ01.4
INQ02.5
PS04.1
Investigation 5.2: The Second Law:
Force, Mass, and Acceleration
• Determine whether an object is in
equilibrium by analyzing the
forces acting on it.
• Draw a diagram showing an
action-reaction pair of forces.
• Determine the reaction force
when given an action force.
INQ01.1
INQ01.2
INQ01.3
INQ01.4
INQ02.5
PS04.1
Investigation 5.3: Newton’s Third Law:
Action and Reaction
2. Complete Investigation 5.1:
The First Law: The Law
of Inertia.
Two 45-minute
class periods
3. Read Section 5.1, pp. 100
to 102.
Section 5.2:
The Second
Law: Force,
Mass, and
Acceleration
1. Complete Investigation 5.2:
The Second Law: Force,
Mass, and Acceleration.
2. Read Section 5.2, pp. 103
to 108.
Two 45-minute
class periods
Section 5.3:
The Third Law:
Action and
Reaction
Two 45-minute
class periods
70
National
Science
Standards
Instructional Sequence
1. Complete Investigation 5.3:
Newton’s Third Law: Action
and Reaction.
2. Read Section 5.3, pp. 109
to 112.
3. Complete Chapter 5
Assessment, pp. 115 to 116.
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
Investigations and Materials
Materials (per group): SmartTrack,
Energy Car, Steel marbles, Rubber band,
Track feet (2), Bubble level, Velocity
sensor, Data Collector, Electronic scale
Materials (per group): Physics Stand,
Double pulley, Red safety string, Mass
hangers (2), Steel washers, Plastic
washers, Measuring tape, Photogate,
Data Collector, Electronic scale or triple
beam balance
Materials (per group): SmartTrack,
2 Energy Cars (1 blue, 1 orange), Energy
Car link, Steel marbles, Rubber band,
Track feet (2), Bubble level, Velocity
sensor, Data Collector, Safety goggles
CHAPTER 5 RESOURCES
Assessment Tools
Chapter 5 Pretest
Program Resources
Skill and Practice Worksheets
• 5.1 Isaac Newton
Teaching Illustrations
• 5_1 Force
Technology Resources
Lesson Organizer
CPO Web site—www.cposcience.com
• Equipment Setup Videos
• Science Content Videos
• Simulations
• Presentation Slides
Skill and Practice Worksheets
• 5.2 Newton’s Second Law
Teaching Illustrations
• 5_2 newtons second law
Literature Selections
Teaching Illustrations
• 5_3 action reaction forces
Isaac Newton: The Scientist Who Changed Everything
by Phillip Steele
Recommended by NSTA, this book discusses the
challenges Newton faced early in life and continues to
delve into his accomplishments as an adult. Readers will
find that Newton experienced situations such as bullying
and problems at home—just like many students do today.
It is also an excellent resource for teaching about the
process of science.
Section 5.2 Review Questions
Chapter 5 Assessment
ExamView® Test Bank
• Multiple Choice
• Multi-format
Skill and Practice Worksheets
• 5.3 Applications of Newton’s
Laws
Section 5.3 Review Questions
Connection
Biomechanics
Chapter 5 Problems
Objects in Motion: Principles of Classical Mechanics by
Paul Fleisher
This book uses real-life examples to explain the universal
laws of science in a reader-friendly language. Topics
include Newton’s laws of motion, universal gravitation,
and falling objects.
71
CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
Investigation 5.1: The First Law: Force and Inertia
Newton’s first law states that all objects want to keep doing what they are doing. An
object at rest will remain at rest, and an object in motion will stay in motion at a constant
velocity as long as there are no unbalanced forces acting on it. In this investigation
students use Newton’s first law to explain the motion of a car as it rolls along a flat track.
Next, students modify the experiment as they vary the mass of the car and observe the
impact on its motion. From these observations, students are able to infer the relationship
between an object’s mass and its velocity when the force applied is constant.
Newton’s first law - states that an object at rest remains at
rest until acted on by an unbalanced force. An object in
motion continues with constant velocity in a straight line
unless acted on by an unbalanced force.
mass - a measure of an object’s inertia; the amount of
matter an object has.
Key Question
inertia - the resistance of a body to a change in motion.
How does changing an object’s inertia affect its motion?
force - any action on a body that causes it to change
motion. Force is a vector and always has a magnitude and
a direction.
Objectives
Students will:
•
•
Change the Energy Car’s inertia to see what affect it has on the Energy Car’s motion.
Apply Newton’s first law to describe the Energy Car’s motion.
Setup
1.
One class period is needed to complete the investigation.
2.
Students work in small groups of two to three.
constant velocity - maintained velocity that does
not vary.
net force - the amount of force that overcomes an
opposing force to cause motion. The net force can be zero
if the opposing forces are equal.
Materials
Safety
Each group should have the following:
•
•
•
72
SmartTrack
Energy Car
Steel marbles
•
•
•
Rubber band
Track feet (2)
Bubble level
•
•
•
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
Velocity sensor
Data Collector
Electronic scale
Students should observe general laboratory safety
procedures while completing Investigation 5.1.
INVESTIGATION 5.1: THE FIRST LAW: FORCE AND INERTIA
1
Investigation
The First Law: The Law of Inertia
5.1
1
Investigation
5.1
The First Law: The Law of Inertia
5.1 The First Law: The Law of Inertia
a.
Describe what happens to the Energy Car’s velocity as it moves along the track. Explain why this
happens.
How does changing an object’s inertia affect its motion?
b.
An object at rest remains at rest unless acted upon by an outside force. What is the outside force that
acts on the car to disturb its state of rest at the start of the track?
c.
An object in motion remains in motion unless acted upon by an outside force. What outside force acts
on the car to change its motion as it moves along the track?
Newton’s first law states that objects tend to keep doing what they are
doing unless acted on by an unbalanced force. This law applies to both
objects at rest and objects in motion.
In this investigation, you will:
• change the Energy Car’s inertia to see what affect it has on the
Energy Car’s motion.
• apply Newton’s first law to describe the Energy Car’s motion.
A
1
Materials List
•
•
•
•
•
•
•
•
SmartTrack
Energy Car
Steel marbles
Rubber band
Track feet (2)
Bubble level
Velocity sensor
DataCollector
C
Making a prediction
Newton’s first law of motion applies to objects at rest and objects in motion. The first law can also be called
the law of inertia. To understand why, consider what inertia is. Inertia is a property of matter that resists a
change in motion. Inertia comes from an object’s mass. Because of inertia, objects at rest remain at rest, and
objects in motion remain in motion, unless acted upon by a net force. You will investigate the first law by
launching the Energy Car on a flat track, and seeing what happens when you change the car’s inertia (by
changing its mass).
a.
B
You will launch an Energy Car several times on the flat track, and you will change the number of
marbles in the car each time. Write a hypothesis to address the question “How will changing the inertia
of the car affect the car’s motion on the flat track?” Your hypothesis should follow this format: “If
inertia affects the car’s motion on the flat track, then when I add more marbles to the car, the car____ .
Setting up the experiment
1.
2.
3.
4.
5.
6.
7.
8.
9.
Conducting the experiment and reporting back
a.
Design an experiment to test the hypothesis you stated in 1a. What is your procedure?
b.
Create a data table and a graph to communicate your results.
c.
Summarize your findings. Be sure to refer back to your hypothesis.
D
Reflecting on Newton’s first law
a.
State Newton’s first law in your own words.
b.
Place the energy in the center of the track so it stays at rest. What do you know about the forces on the
Energy Car? Identify the forces acting on it.
c.
If the Energy Car is moving and there are no unbalanced forces acting on it, does its speed increase,
decrease, or remain the same? Explain.
d. Were any forces acting on the Energy Car as it rolled along the level track? Identify the forces. Explain
how Newton’s first law is applied to describe the motion you observed.
e.
What changes occur in the forces acting on the Energy Car when the track is tilted slightly up or down?
Explain how the first law is applied to describe the observed motion in the case of uphill or downhill
slope.
Attach a foot to each end of the SmartTrack so it sits level on the table. Check it with the bubble
level and adjust the feet as necessary to make the track level.
Attach the velocity sensor to the end of the SmartTrack.
Fasten a rubber band on the launcher.
Plug the velocity sensor into the DataCollector.
Turn the DataCollector on. At the home window, select data collection mode.
At the Go window, choose setup at the bottom of the screen.
At the setup window, choose standard mode, 200 samples, and 0.02 Hz. This will allow the
DataCollector to collect 50 samples of data from the velocity sensor each second.
Practice launching the Energy Car with no marbles. Once you have a consistent launch technique,
get the car ready to launch, press the Go button on the DataCollector, and launch the car.
Switch from meter to table and graph view to study your data.
27
28
73
CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
Teaching Investigation 5.1
A
Sample answer:
Making a prediction
In this investigation we will be studying Newton’s first law. What does the first law say?
Prompt a discussion on the different ways the first law can be stated. Some possibilities are an
object at rest will tend to remain at rest, and an object in motion will tend to remain in motion;
objects tend to keep doing what they are already doing; objects have inertia and resist changes
in their motion.
What is required for an object to change its state of motion or its state of having no motion?
An unbalanced force is needed. If students simply answer “force” then discuss the difference
between a force and an unbalanced force.
Do all objects have the same ability to remain in their state of motion?
No. This ability depends on an object’s inertia. An object with more inertia has a greater
tendency to remain in its state of motion. Mass is a measure of an object’s inertia.
Newton’s first law is also known as the law of inertia, which refers to the fact that inertia is a
property of matter that resists a change in motion. By resisting, we mean that if an object is at rest,
it would resist changing its current state of rest unless something caused it to do so. Likewise, a
moving object would continue to move unless something stopped it from moving. The
“something” that causes a change in the object’s motion is a net force. What do you think I mean
when I say net force?
Net force is the sum of all forces acting on a body.
The concept of net force means that many different forces may be acting on an object. Consider
what happens when you play tug of war with your friends. One group of friends is pulling the rope
in one direction while the others are pulling in the opposite direction. If the net force is zero, does
anyone win the competition?
No one wins.
That is correct. The force exerted by one team must be enough to overcome the effects of the
other team’s efforts in order for someone to win. You know this by observing the losing team
being pulled across the neutral zone. In other words, the net force is no longer zero.
Today you will investigate Newton’s first law by launching the Energy Car on a flat track, and
then observing what happens when you change the car’s inertia. You will change the car’s inertia
by altering its mass. How do you think altering the mass of the car will influence its motion?
Don’t tell me what you think just yet. Instead, write your answer in the form of a hypothesis that
will complete the statement in Part 1.
Students complete question 1a.
74
A Making a prediction
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
a.
If inertia affects the car’s motion on a flat track, then
when I add more marbles to the car (thus increasing the
car’s mass and inertia), the car’s initial velocity after
launch will decrease.
INVESTIGATION 5.1: THE FIRST LAW: FORCE AND INERTIA
B Setting up the experiment
Set up the experiment exactly as directed in Part 1. It is important to have a level track, so use the
level and adjust the feet as needed to get the track level.
Students set up the experiment. Instruct students to stretch the rubber band a few times and
show them how to position the rubber band to get good launches.
B Setting up the experiment
Sample answers:
a.
As the Energy Car moves along the track, the velocity is
greatest right at the launch and then decreases over time.
The car decelerates because the force of friction opposes
its motion. The car would move at a constant velocity
forever if all forces acting on it remained balanced, with
no net force causing any changes in motion.
b.
At the start of the track, the rubber band supplies a net
force to get the car moving.
c.
Friction is the outside force that changes the motion of
the car after it is launched.
Before you actually collect data, you will need to work on developing a consistent launch
technique. Watch as I demonstrate.
Do a few launches with emphasis on maintaining consistency in the deflection in the rubber
band and the actual launch technique.
Practice a few times until you feel confident about your method. The Energy Car should contain
no marbles during your practice launches. Once you have a consistent technique then you should
go forward with the experiment. Press the Go button and then launch the Energy Car.
Students do the experiment.
Let’s talk about what the graph of your data suggests. What happened to the car’s velocity as it
moved along the track?
It decreased.
When we started this investigation, we established that a moving object continues to move unless
some net force acts upon it. Did the car maintain its velocity all along the track or did it
gradually decrease?
The velocity should have decreased gradually.
Why do you think the car’s velocity decreased with time?
Students may not readily identify the role of friction in slowing the car. Guide students in the
discussion until they are able to see how the force of friction acts against the motion of the car
along the track and causes it to slow down.
Now think about the car before you started the experiment. Was it moving or at rest?
The car was at rest.
What net force initiated the car’s change in motion from a position of rest?
The rubber band initiates the motion.
Imagine the car at rest once more, but this time when it is set into motion by the force of the
rubber band, it moves along a frictionless track. How would the car’s velocity be different from
what you observed in the experiment?
Without the force of friction acting to slow the car down as it moved along the track, the
Energy Car would move at constant velocity indefinitely. Friction is discussed in greater detail
in Lesson 6.2; but, this is a good opportunity to get students thinking about the different
applications of the force of friction to humans’ daily lives. If time permits, have students
generate a list of examples.
75
CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
C Conducting the experiment and reporting back
In the initial experiment, you observed how the velocity of the car changed once it was set in
motion by the rubber band and rolled along the track. Let’s go back to the hypothesis you stated in
Part 1.
Students review their hypotheses.
In this part of the investigation, your goal is to design an experiment to test your hypothesis. One
key word in your hypothesis is inertia. When thinking about inertia, it is important to recall that
inertia comes from an object’s mass. Therefore, a change in inertia is accompanied by a change in
mass. Do you have any materials that will allow you to change the mass of the car?
Students should identify the presence of the steel marbles.
Take a few moments to brainstorm with your group members and then devise your plan of action.
Students develop a plan and share their experimental procedure. Allow students to execute
their own plan, collect and analyze data, and summarize their findings before sharing
your ideas.
C Conducting the experiment and reporting back
a.
Sample procedure: First, I set everything up just like I
did in Part 2 of the investigation. Then, making sure I
used the same launch force each time, I launched a car
with no marbles, a car with 1 marble, then 2 marbles,
and finally, 3 marbles. I recorded all data in the
table below.
b.
Sample data table and graph:
Table 1: Changing mass with constant force
Number of marbles Mass of car Velocity of car at
added to car
launch
(kg)
(cm/s)
Here is a the dialogue to accompany the sample procedure mentioned in 3a (at right). You may
do this as a demonstration if time or supplies are limited.
Let’s examine how motion is affected by changing mass. The force applied will remain constant.
In my experiment, I will launch cars with four different masses. The first car will have no added
mass. I will add one marble to the second car, two marbles to the third car, and then three marbles
to the fourth car. Because mass is a factor in this experiment, I will record the mass of each car
with or without marbles. This is where the data table comes in handy.
Mass each car and say the measurement aloud as you record the data in the table.
0
0.0568
99.0
1
0.0851
81.3
2
0.1133
70.4
3
0.1415
64.1
The graph shows an inverse relationship. The greater the
mass of the car, the lower the velocity.
Speed of the Car vs. Mass
I have a consistent launch technique and I am using the same amount of force with each launch.
Let’s observe what happens to the velocity with each launch.
Do the experiment with each car and have a student volunteer verify the data you collect and
record in the table.
120
Speed (cm/s)
100
Now we can analyze the graph of our data to better understand the results. How accurate were
your hypotheses? Did your results confirm or refute your expectations?
Students share findings.
As the mass of the car increased, its velocity increased. In other words, the relationship between
velocity and mass is inverse because as one variable increased the other decreased.
80
60
40
20
0
0
0.05
0.1
0.15
Mass of car (kg)
c.
76
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
My hypothesis was confirmed. Cars with greater inertia
had less velocity at launch. Inertia resists changes in
motion, and my results verify this first law of motion.
INVESTIGATION 5.1: THE FIRST LAW: FORCE AND INERTIA
D Reflecting on Newton’s first law
D Reflecting on Newton’s first law
Newton’s first law of motion is often called the “law of inertia.” Recall when you changed the
mass of the car but kept the force constant. How can you explain your observations in terms of
Newton’s first law?
Inertia comes from mass, and it is an object’s resistance to a change in motion. The more
massive the car, the more resistant it is to changing its motion. In the same manner, the least
massive car would be the least resistant to changing its motion. Students can sometimes grasp
this concept a little better when they are asked, “Which is easier (or harder) to get moving: a
very massive object or an object with a small mass?” For example, is it easier to move a
pebble or a boulder? The pebble, with its small mass does not offer much resistance to motion
when a force is applied to it. However, if a person tried to move a boulder with the same
amount of force applied to the pebble, the boulder would be much more resistant to motion.
Consequently, the greater mass will experience slower speed because of this resistance,
whereas the less massive object will experience faster speed.
a.
An object at rest remains at rest, and an object in motion
remains in motion, unless acted upon by an unbalanced
(net) force.
b.
The forces acting on the Energy Car when it is at rest are
balanced. The weight of the car acts downward, and the
normal force of the track acts upward. The forces are
equal and opposite.
c.
If there are no unbalanced forces acting on the moving
car, its velocity remains constant. I noticed that the car
moved at a pretty constant speed for awhile on the track,
but friction did slow it down a little.
Place the Energy Car in the center of the track. The car should be at rest. Are any forces acting on
the car? If so, identify the forces acting on the car.
Since the car is at rest it is affected by the normal force and the force of the car’s weight.
Remind students that the if the car is at rest then the forces acting on it must be balanced.
Otherwise, the car’s motion would be changed in some way.
d.
As the Energy Car rolled along the level track, friction
provided a net force that opposed the forward motion of
the car. Newton’s first law applied, because an object in
motion, like the moving car, would remain in motion, at
a constant velocity, if it weren’t for the outsides force of
friction, and the end of the track.
e.
If the track is tilted slightly up, gravity and friction will
oppose the motion of the car, and the car will decelerate
more than when the track is flat. If the track is tilted
slightly downward, gravity works with the car, and
friction opposes the car. If you tilt the track downward
just enough so that the help from gravity offsets the
opposition from friction, you can create a balanced force
that would allow the car to move at a very constant
speed the whole way down the track.
What forces acted on the car as it moved along the track?
Once the car was set in motion along the track, it encounter the force of friction. This explains
why the car’s velocity decreased over time. The car stopped when it reached the end of the
track because it encountered a barrier. When considering Newton’s first law, the car in motion
remained in motion until it was acted upon by net forces of friction and the track’s end.
Suppose you altered the setup of the investigation so the track inclined upward or had a
lightly downward tilt. How would the forces acting on the car and its motion be affected by
these changes?
Have students lead the discussion here. Students should consider the impact of friction and
gravity here. If time permits, allow students to design an experiment to test their predictions.
Direct students to use relevant vocabulary and to apply what they know about Newton’s first
law to explain their observations.
Based on what you have observed in today’s investigation, would you say that force causes
velocity, or that force causes a change in velocity?
Force causes a change in velocity, or acceleration. Remind students that acceleration is the
change in velocity that occurs over a period of time and that acceleration may be positive or
negative. This is a great lead in to discussion about Newton’s second law, which is the topic of
Lesson 5.2.
77
CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
Investigation 5.2: The Second Law: Force, Mass,
and Acceleration
It takes force to get an object moving and more force to make it stop. If you think about
the words “get moving” or “stop,” you realize that force is linked to acceleration because
both phrases imply changes in motion. Students will construct an Atwood’s machine and
use it to explore the relationship between force, mass, and acceleration.
Key Question
What is the relationship between force, mass, and acceleration?
newton (N) - the SI, or metric unit of force.
net force - the amount of force that overcomes an
opposing force to cause motion. The net force can be zero
if the opposing forces are equal.
line of best fit - a line drawn to show how two variables
are related. A line of best fit comes closest to most points
on a x-y scatterplot.
Objectives
Students will:
•
•
•
Newton’s second law - states that the acceleration of an
object is directly proportional to the force acting on it and
inversely proportional to its mass.
Measure the acceleration for an Atwood’s machine of fixed total mass.
Create a graph of force versus acceleration for the Atwood’s machine.
Determine the slope and y-intercept of the graph and then relate them to Newton’s second law.
mass - a measure of an object’s inertia; the amount of
matter an object has.
Setup
1.
One class period is needed to complete the investigation.
2.
Students work in small groups of two to three.
3.
Students should be familiar with the concept of acceleration as discussed in previous
investigations.
4.
Secure sponges or some other small cushions that can be used to protect the Physics Stand
base from the impact of falling masses (Part 2). Each group will need one sponge or cushion.
Materials
Each group should have the following:
•
•
•
•
•
78
Physics Stand
Double pulley
Red safety string
Mass hangers (2)
Electronic scale or triple beam balance
•
•
•
•
•
Data Collector
Steel washers (18)
Plastic washers (6)
Measuring tape
Photogate
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
Safety
Students should observe general laboratory safety
procedures while completing Investigation 5.2.
INVESTIGATION 5.2: THE SECOND LAW: FORCE, MASS, AND ACCELERATION
5.2
1
Investigation
The Second Law: Force, Mass, and Acceleration
5.2 The Second Law: Force, Mass, and Acceleration
What is the relationship between force, mass, and acceleration?
British scientist George Atwood (1746-1807) used two masses on a light
string running over a pulley to investigate the effect of gravity. You will
build a similar device, aptly called an Atwood’s machine, to explore the
relationship between force, mass, and acceleration.
In this investigation, you will:
• measure the acceleration for an Atwood’s machine of fixed total
mass.
• create a graph of force vs. acceleration for the Atwood’s machine.
• determine the slope and y-intercept of your graph, and relate them to
Newton’s second law.
A
1
1
Investigation
Materials List
•
•
•
•
•
•
•
•
•
Physics stand
Double pulley
Red safety string
2 mass hangers
Steel washers
Plastic washers
Measuring tape
Photogate
DataCollector
B
To accelerate a mass, you need a net force. Newton’s second law shows the
relationship between force, mass, and acceleration:
NEWTON’S SECOND LAW
Force (N)
Mass (kg)
F = ma
Acceleration (m/s )
Set up the Atwood’s machine as shown in the photo at right. Attach the
double pulley to the top of the physics stand. You will only use the
striped pulley.
2.
Attach the mass hangers to the red safety string. Place 8 steel washers and
6 plastic washers on one mass hanger. This will be m2. Place 10 steel
washers on the other mass hanger. This will be m1. Place the string over
the dynamic pulley.
Pull m2 down to the stand base. Place a sponge or some other small
cushion on the base to protect it from the falling m1. Let go of m2 and
observe the motion of the Atwood’s machine.
a.
Which mass moves downward, and why?
b.
What would happen if m1 and m2 were equal masses? Why?
c.
Do the masses accelerate when they move? Explain.
e.
The Atwood’s machine is driven by an external force equal in magnitude to the
weight difference between the two mass hangers. You will vary the two masses, m1
and m2, but you will keep the total mass constant. As you move plastic washers
from m2 to m1, you will use a photogate to measure the acceleration of the system. If you know the
acceleration and the total mass of the system, you will be able to calculate the force that is responsible for
accelerating the system. The equation for the system’s motion is a variation of the basic second law formula:
(m1 + m 2 )a
An ideal pulley would be frictionless and massless, and would just redirect the one-dimensional motion of
the string and attached masses, without interfering with the motion. However, the pulley you will use has
mass and there will be some friction involved. For the purpose of this investigation, we will neglect the mass
of the pulley, but we will be able to analyze the friction involved with our Atwood’s machine. To represent
the friction present in the system, you must subtract it from the external force, since the friction opposes the
external force.
Fext friction
(m1 + m 2 )a
It is easiest to move the friction force (f) to the other side of the equation, so you get:
Fext
1.
5.2
1
The Second Law: Force, Mass, and Acceleration
Investigation
Table 1: Acceleration and force data
Acceleration
(m/s2)
Calculated net force
(N)
d. How does the acceleration of m1 compare to the acceleration of m2?
2
Fext
The Second Law: Force, Mass, and Acceleration
Setting up the Atwood’s machine
3.
Analyzing the Atwood’s machine
5.2
(m1 + m 2 )a + f
29
The machine’s external force equals the weight difference of the mass hangers. Write a simple formula
that will allow you to use the mass difference and g, the acceleration due to gravity, to calculate the
weight difference of the mass hangers (the external force).
D
a.
C
Collecting data
1.
2.
Find the total mass of m1 and m2 and record in Table 1.
Attach a photogate to the double pulley as shown at right. Plug the
photogate into the DataCollector (input A). The striped pattern on the
pulley will break the light beam of the photogate as the pulley rotates.
3. Turn on the DataCollector. At the home window, select data
collection mode.
4. At the Go window, tap on the setup option at the bottom of the screen.
5. In the setup window, choose standard mode.
6. For photogate A (PGA), select acceleration in m/s2. Set the PGB
option to none.
7. Pull m2 to the base. Tap Go at the bottom of the setup window.
8. When the experiment has started, release m2. When the hanger falls
onto the cushion, press the button on the DataCollector enclosure to
stop the experiment.
9. Select the table and/or graph option at the bottom of the screen, and
study the acceleration data. The acceleration should be constant. Record the acceleration in Table
1. Calculate the net force (see your answer to 2e) and record it in Table 1.
10. Transfer one of the plastic washers from m2 to m1.
11. Press the button on the DataCollector enclosure to resume data collection. Repeat steps 7 - 10 until
you have transferred all of the plastic washers to m1.
Analyzing the data
Make a graph of net force vs. acceleration (force on the y-axis and acceleration on the x-axis). Draw a
best-fit line through the data points.
b. What kind of relationship does the graph show? Is this consistent with Newton’s second law? Explain.
c.
Determine the slope of your line. What is the significance of the slope in your experiment?
d. Compare your slope and the known total mass of the system. What is the percent difference? What
could account for any difference?
e. Determine the y-intercept of your line. The equation for a line is y = mx + b (m is the slope and b is the
y-intercept). Substitute your variables in for y, m, and x. Compare this equation to the one presented in
part 1:
Fext
f.
(m1 + m 2 )a + f
Based on your answer to the previous question (4f), what does the y-intercept represent? Does this
value make sense? Explain.
30
31
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CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
Teaching Investigation 5.2
A
There are no questions to answer in Part 1.
Analyzing the Atwood’s machine
Newton’s second law is one of the most useful relationships in all of physics. The second law tells
you how an object’s motion will change if you know its mass and the forces acting on it. The
second law also tells you how much force you need to apply to an object to create a specific
change in its motion. Today’s investigation will use a clever device called an Atwood’s machine
to explore an application of the second law.
An Atwood’s machine is a pulley with a string over it. Each end of the string has a different mass
attached. When you let the string go, one mass rises and the other mass falls.
Set up an Atwood’s machine with the pulley in front of the class and demonstrate.
Why does one mass rise while the other mass falls?
Start a discussion. The system is not in equilibrium because one mass is larger than the other
and therefore there is a net force acting.
Recall from Investigation 5.1 that we talked about how force causes a change in velocity over
time. This change is acceleration. In order to accelerate a mass, there must be a net force. So when
you look at the form of Newton’ second law shown in Part 1, the F in the equation is really the
net force.
Use the Newton’s second law teaching illustration to reinforce this point.
The Atwood’s machine is driven by an external force, Fext that is equal in magnitude to the weight
different between the two mass hangers. Although you will vary the two masses, which we will
call m1 and m2, the total mass will remain constant. As you move the plastic washers from m2 to
m1, you will use a photogate to measure the acceleration. You can use the acceleration and the
known mass to calculate the force that caused the system to accelerate.
Prepare a model setup that you can use as a visual aid to the discussion. It will also come in
handy in Part 2 as students setup their own Atwood’s machine. Write the equation on the
board (as shown in Part 1). Point to each variable as you describe its relationship to what
students will do in the investigation.
A perfect pulley would be massless, have no friction, and it would simply redirect the onedimensional motion of the string and the attached masses without affecting the motion. However,
the effects of mass and friction will be a factor in the pulley you will use. You will neglect the
mass of the pulley, but you will be able to analyze the effects of friction. Let’s look at how you
will do this.
Reproduce the equations shown in Part 1 on the board. Show students how the equation can be
manipulated to include the effects of friction.
80
A Analyzing the Atwood’s machine
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
A challenge
Many devices use acceleration to
measure the mass of an object. Often the
technique used is to cause something to
vibrate. A vibration is a rapid back-andforth motion that results in similarly rapid acceleration.
If the mass of an object changes, its acceleration
changes and the frequency of vibration changes.
Electronic devices can easily be made that are very
responsive to small changes in frequency. As a result,
this technique is used to measure very small amounts of
mass quickly, such as the mass of a single drop of water.
Challenge students to measure the mass of a single steel
washer by making acceleration measurements. To do
this they will first have to calibrate the apparatus for the
effects of friction. This means measuring the
acceleration for a known mass of washers on both sides
of the pulley. Once the system is calibrated, a single
washer added to one of the hangers will result in a
measurable change in acceleration. The change in
acceleration can be used to determine the mass.
The sensitivity of the technique depends on the
accuracy with which acceleration can be measured. Two
factors are important: the repeatability of triggering the
stopwatch with a finger, and the resolution of the
stopwatch (0.01 s). Have the students measure the
repeatability of their timing measurements. If the timing
is repeatable to within 5 percent, then the acceleration
may also be accurate to 5 percent if there are no other
significant sources of error. To determine the effect of
limited time resolution, have the students estimate the
difference in acceleration that would result from a
time measurement being +/- 0.1 second from its
nominal value.
INVESTIGATION 5.2: THE SECOND LAW: FORCE, MASS, AND ACCELERATION
B Setting up the Atwood’s machine
Follow steps 1 and 2 exactly as stated in Part 2 to set up the Atwood’s machine.
Place the model setup you prepared earlier in a very visible location. Modify it to the
specifications discussed in Part 2 as students prepare their own version. Be prepared to assist
students with the setup.
Pull the m2 mass down to the base of the Physics Stand. Place your sponge on the base to protect
it from the impact of the falling m1. Let go of m2. What happens?
Students share observations.
Suppose the masses m1 and m2 were equal. How might this change what you observed?
The difference in masses caused an unbalanced force and was responsible for the motion
students observed. If the masses are equal, then the forces are balanced. Balanced forces mean
there is a net force of zero and the objects remain in place.
In previous discussions about acceleration, we established that a net force causes a change in
motion. Consider the motion of the masses. Do the masses accelerate when they move?
The masses do accelerate. Remind students that acceleration is defined as the change in
velocity over time. This change in motion is caused by the net force.
Acceleration is caused by unbalanced force. According to Newton’s second law, the acceleration
of an object is equal to the net force acting on the object divided by the mass of the object. In fact,
the metric definition of force is based on mass and acceleration. A force of 1 newton is exactly the
force required to create an acceleration of 1 meter per second squared for a 1 kilogram object.
Write the definition of force on the board: 1 N = 1 kg-m/s2, or F = ma. Point out that this is a
different, but equivalent arrangement of the same relationship, a = F ÷ m.
Acceleration may be positive or negative. This is because acceleration is a vector quantity that
considers both the magnitude and direction of motion. Did both masses accelerate in the
same way?
The masses had equal magnitude but accelerated in opposite directions.
The external force of the Atwood’s machine is equal to the weight difference of the mass hangers.
Newton’s second law is represented as Fnet = ma. How do you think you can use Newton’s second
law to calculate the weight difference of the mass hangers?
Walk students through the explanation if needed. The weight difference of the mass hangers
implies subtraction, so students should substitute (m1-m2) for m. The acceleration due to
gravity is defined as g and should replace the variable a in the equation. Therefore, the
external force should be expressed as Fnet = (m1-m2)g.
B Setting up the Atwood’s machine
a.
The m1 mass hanger has more mass than m2, resulting in
an unbalanced force. The external force is in the
downward direction on the more massive side of the
machine, which is the m1 side.
b.
If m1 and m2 were equal masses, the Atwood’s machine
would be in equilibrium, and there would be no motion.
c.
Yes, the masses accelerate, because there is a net force
created by the difference between the two masses.
d.
The accelerations are equal in magnitude and opposite
in direction.
e.
Formula:
Forcenet = ma
Forcenet = (m1 -m 2 )g
C Collecting data
Sample data:
Table 1: Acceleration and force data
Acceleration (m/s2)
Calculated force (N)
0.175
0.098
0.269
0.127
0.376
0.157
0.438
0.186
0.536
0.216
0.594
0.245
0.695
0.274
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CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
C Collecting data
In Part 3, you will use a photogate attached to the double pulley to collect force and acceleration
data. Keep everything else from the setup you used in Part 2 the same. First you need to determine
the total of masses 1 and 2. Write this measurement down on your handout or in your notebook.
Then attach the photogate to the double pulley and use a knob to secure everything in place.
Students set up the equipment.
D Analyzing the data
a.
Sample graph:
Review the acceleration data you collected. What do you observe? Write the value from the Data
Collector in your notebook.
Students should observe constant acceleration data.
b.
The graph shows a direct relationship between force and
acceleration, just as Newton’s law states.
In Part 2e, you figured out a way to determine the force if mass and acceleration data is known.
Use the formula and the mass and acceleration data you recorded to calculate the net force.
c.
The slope of the line is 0.345.
d.
Force divided by acceleration equals the mass of the
system. In my experiment, the total mass was 0.288 kg.
Rise over run is force over acceleration. According to
Newton’s second law, force divided by acceleration
equals mass. The slope of the line equals the mass of the
system. The percent difference is 20%. I was not careful
with acceleration measurements!
e.
The y-intercept of the line is 0.03. The equation is:
Plug the photogate into Input A on the backside of the Data Collector. With the Data Collector in
Data Collection mode, select the setup option and choose standard mode. You are only using one
photogate A which is denoted as PGA. Set the PGB option to none. You want to measure
acceleration in meters per second squared.
Students should still have the sponge in place to cushion the falling mass.
One person in your group should pull the mass, m2 to the base of the stand. Lightly tap the Go
button and then release m2. When the hanger falls onto the sponge, stop the experiment.
Demonstrate the process if needed.
Now you will consider how changes in mass, caused by moving the plastic washers from m2 to
m1 one at a time changes your observations of force and acceleration. Start by transferring the
first plastic washer from m2 to m1. Resume data collection and then repeat the steps you took
(steps 7–10) until the six plastic washers have been transferred over.
D Analyzing the data
Use the data you recorded in Table 1 to make a force versus acceleration graph. Does your graph
coincide with Newton’s second law?
Student graphs should show that force and acceleration are directly proportional. This is in
line with Newton’s second law. Draw students’ attention to Table 5.1 on page 105 of the text
which shows three forms of Newton’s second law. Focus on the third row to emphasize how to
find the mass of an object if acceleration and force are known. The graphs generated from the
experiment should reflect that the slope of the line is equal to the mass of the system.
y = mx + b
force = mass( acceleration) + friction force
f = ma + f
f.
82
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
The y-intercept represents the force of friction. I know
there is some friction in the system, but it is so small that
it doesn’t show up in the data we collected. Friction is
truly negligible in this Atwood’s machine.
INVESTIGATION 5.3: NEWTON’S THIRD LAW: ACTION AND REACTION
Investigation 5.3: Newton’s Third Law: Action and
Reaction
Newton’s third law deals with action-reaction pairs. We rely on this law when we walk,
place an item on a table, push a shopping cart, or travel in a car. Examples and
demonstrations of Newton’s third law are everywhere in our lives yet the subtle way it
affects us can often be overlooked without careful analysis of what is actually taking
place. For example, when you apply a force to throw a ball, you also feel the force of the
ball against your hand. This is because all forces exist in pairs called action and reaction.
There can never be a single force (action) without its opposite (reaction) partner. Action
and reaction forces always act in opposite directions on two different objects. In this
investigation students use the Energy Cars to study Newton’s third law.
force - any action on a body that causes it to change
motion. Force is a vector and always has a magnitude and
a direction.
Newton’s third law - states that whenever one object
exerts a force on another, the second object exerts an
equal and opposite force on the first.
action, reaction - the equal and opposite forces which
comprise the action-reaction pair according to Newton’s
third law.
Key Question
What happens when equal and opposite forces act on a pair of Energy Cars?
Objectives
•
•
•
Link two Energy Cars to create an action/reaction force pair.
Use different numbers of marbles in each car to see how motion is affected.
Relate the cars’ motion to Newton’s third law.
Setup
1.
One class period is needed to complete the investigation.
2.
Students work in small groups of two to three.
3.
It is important that the track remains level throughout the experiment. Prepare a setup in
advance so you will be able to demonstrate proper procedure in Part 1.
Materials
Each group should have the following:
•
•
•
•
•
SmartTrack
2 Energy Cars (one blue, one orange)
Energy Car link
Steel marbles
Rubber band
Safety
•
•
•
•
•
Track feet (2)
Bubble level
Velocity sensor
Data Collector
Safety goggles
Students should wear safety goggles for the duration of
the investigation. This is necessary to protect eyes from
the car-connector accessory, as it may fly off.
83
CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
1
Investigation
5.3
Newton’s Third Law: Action and Reaction
5.3 Newton’s Third Law: Action and Reaction
What happens when equal and opposite forces act on a pair of Energy Cars?
When you apply a force to throw a ball you also feel the force of the ball
against your hand. That is because all forces come in pairs called action
and reaction. Newton’s third law of motion states that there can never be
a single force (action) without its opposite (reaction) partner. Action and
reaction forces always act in opposite directions on two different objects.
You can set up two Energy Cars to study Newton’s third law.
In this investigation, you will:
• link two Energy Cars to create an action/reaction force pair.
• use different numbers of marbles in each car to see how motion is
affected.
• relate the cars’ motion to Newton’s third law.
A
1
Materials List
• SmartTrack
• 2 Energy Cars (blue
and orange)
• Energy Car link
• Steel marbles
• Rubber band
• Track feet (2)
• Bubble level
• Velocity sensor
• DataCollector
Newton’s Third Law: Action and Reaction
B
1.
Place one steel marble in each car, and wrap one car with a rubber band.
2.
3.
Place the 2 cars, “nose to notch” in the middle of the track.
Squeeze the cars together and attach them with the Energy Car link.
4.
5.
Position the attached car pair in the middle of the track so the blue car is closest to the velocity
sensor. Make sure all 4 wheels of both cars are on the track.
Plug the velocity sensor into input 1 on the DataCollector.
6.
7.
Turn the DataCollector on. At the home window, select data collection mode.
At the Go window, choose setup at the bottom of the screen.
8.
At the setup window, choose standard mode, 200 samples, and 0.02 Hz. This will allow the
DataCollector to collect 50 samples of data from the velocity sensor each second.
How does Newton’s third law of motion explain the motion of the cars when you remove the car link?
c.
You will use different numbers of marbles in each car to see how that affects the cars’ motion. Write a
hypothesis to address the question “What happens when equal and opposite forces act on objects that
have different masses?” Your hypothesis should follow this format: “If equal and opposite forces act on
objects of different masses, then ______”. Finish the statement to create your hypothesis.
1
Investigation
9. Press Go on the DataCollector.
10. With a very quick upward motion, pull the link straight up and out from the cars. CAUTION:
Wear eyeglasses or safety glasses to avoid injury.
11. When the cars stop moving, press the button on the DataCollector enclosure to stop the
experiment.
12. Switch from meter to table and graph view to study your data. Go to setup to note the name of the
experiment in case you want to go back and look at the data later. Record the maximum velocity of
the blue car in Table 1. You can only record the blue car’s data, because it was the car the motion
detector could “see.”
13. Attach the cars with the energy link again, and position them so the orange car is closest to the
velocity sensor. Each car should still have one marble. Set up a new experiment on the
DataCollector and repeat steps 9 - 13.
14. Change the marble configuration as listed in Table 1 and repeat the experiment. Continue until you
have completed Table 1. For each trial, you will have to collect two sets of data—one with the blue
car facing the velocity sensor, and one with the orange car facing the velocity sensor.
Table 1: Action/reaction pair data
Attach a foot to each end of the Smart track so it sits level on the table. Check it with the bubble
level and adjust the feet as necessary to make the track level.
2. Attach the velocity sensor to the end of the Smart track.
3. Place one steel marble in each car, and wrap one car with a rubber band.
4. Place the 2 cars, “nose to notch” in the middle of the track.
5. Squeeze the cars together and attach them with the car link.
6. Position the attached car pair in the middle of the track so the blue car is closest to the velocity
sensor. Make sure all 4 wheels of both cars are on the track.
7. With a very quick upward motion, pull the link straight up and out from the cars. CAUTION:
Wear eyeglasses or safety glasses to avoid injury.
Describe how the cars move when you remove the car link.
b.
Investigation
Collecting data
Setting up and action/reaction force pair
1.
a.
5.3
1
Trial
1
2
3
4
32
C
a.
Marble pairings for
connected cars
Blue
Orange
1 marble
1 marble
0 marbles
2 marbles
2 marbles
2 marbles
0 marbles
3 marbles
Maximum Velocity
(cm/s)
Blue
Orange
Experiment file name
Blue
e.
Which of Newton’s laws of motion best explains the answer to the previous question (3d)?
f.
Compare and contrast the velocity/time graphs for the blue car from trial 1 and trial 3.
g.
Compare and contrast the velocity/time graphs for the orange car from trial 2 and trial 3.
h. What is one common characteristic from all of the velocity/time graphs for each car at every trial?
Explain why this characteristic is true about all of the motion scenarios.
D
Why don’t equal and opposite forces cancel each other out?
It is easy to get confused about action-reaction forces. People often ask, “Why don’t they cancel each other
out?” The reason is that the action and reaction forces act on different objects. Prove that action-reaction
forces never act on the same object by doing the following:
a.
Create a sketch showing your calculator sitting on top of your textbook which is sitting on top of your
desk which is standing on the tile floor.
b.
Identify the forces that serve as the action-reaction forces and draw them in your sketch.
c.
Now draw a free body diagram that shows each object by itself (the calculator, the textbook, the table,
the tile floor, and Earth) and uses arrows to represent the forces acting on each particular object.
d. Look at the forces on any one object. Does that one object have both forces from any single actionreaction pair acting on it? Is this true for all of the objects? (This is the key to Newton’s third law: The
action-reaction forces are equal in size and opposite in direction but since they act on different objects,
they do not cancel each other out.)
Orange
Analyzing the data
How does the velocity of each car compare when masses are equal?
Explain how your velocity data supports the idea that equal and opposite action and reaction forces
acted on the once-linked car pairs.
33
34
84
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
Newton’s Third Law: Action and Reaction
d. If the action/reaction forces are equal in strength when the cars separate, why does one car move at a
different velocity than the other car when the masses are unequal, as in trials 2 and 4?
b. How does the velocity of each car compare when one car has 2 or 3 times the mass of the other car?
c.
5.3
INVESTIGATION 5.3: NEWTON’S THIRD LAW: ACTION AND REACTION
Teaching Investigation 5.3
Newton’s first and second laws of motion deal with single objects and the motion that results from
forces that act on them. Newton’s third law of motion pertains to pairs of objects and the
interactions between them. The important thing to remember about Newton’s third law is that it
always applies to two objects. In fact, an isolated force can never be created without its twin. If I
throw this eraser, I apply a force to it. Call that the action force. I feel the eraser against my hand,
resisting my action force through its inertia. That means the eraser exerts a force back against my
hand, which is what I feel. This is the reaction force. The action is me acting on the eraser. The
reaction is the eraser acting back against my hand. Suppose Joe is pulling a heavy wagon. What is
the action-reaction pair in this scenario?
Joe exerts a force on the wagon, and the wagon exerts an equal and opposite force on Joe. He
feels the handle of the wagon against his hand, that is the reaction force.
It is obvious that Joe exerts a force on the wagon, but why is it true that the wagon exerts an equal
and opposite force on Joe? It is one of the rules of the universe. If object A exerts a force on object
B, object B exerts an equal and opposite force on object A. The pair of forces occur in unison as
part of an interaction. Which one we call the action and which one we define as the reaction
makes no difference. Practically speaking, you know that the wagon must exert a force on Joe,
because imagine how it feels on your arm to pull a heavy wagon. It sometimes feels as though the
wagon is pulling on you, and it is, because it is automatically part of a force pair that is created as
soon as you grab the handle and start pulling.
A Setting up an action/reaction force pair
Sample answers:
a.
When you remove the car link, the cars move apart, in
opposite directions.
b.
The compressed rubber band applies a force to the cars
when they are unlinked; the force exerted on the blue
car is equal and opposite to the force exerted on the
orange car.
c.
If equal and opposite forces act on objects of different
mass, then the object with the most mass will experience
less change in motion than the object with the least
mass. In other words, the more massive car will take off
with less velocity than the less massive car.
A Setting up an action/reaction force pair
Set up the SmartTrack with a foot attached to each end. Use the bubble level to set the track level.
A level track is essential to this experiment. Emphasize this fact to students.
Attach the velocity sensor to the end of the SmartTrack. Place one steel marble in each car, and
wrap the blue car with a thick rubber band as shown in Part 1. Place the cars “nose to notch,”
squeeze the cars together, and then attach them with the car-connector. Center the attached car
pair on the track, with the blue car closer to the velocity sensor. Make sure all four wheels of both
cars are on the track.
Ensure that students are wearing their safety glasses before proceeding.
With a very quick upward motion, pull the connector straight up and out from the cars.
Use the prepared setup to demonstrate the procedure. Students should wear safety glasses to
avoid injury from the flying connector. Students who wear prescription eyeglasses do not need
to wear goggles over them.
What happened when you removed the car connector?
Students should observe that the cars moved away from the each other, in opposite directions.
85
CHAPTER 5: NEWTON’S LAWS: FORCE AND MOTION
Newton’s third law states that whenever one object exerts a force on another, the second object
exerts an equal and opposite force on the first. How can you use this statement to explain what
you observed when the car connector was removed?
Lead a brief discussion to describe what happened when the connector was removed. Use your
students’ existing understanding of potential energy and what it means if something is elastic
to describe the transfer of energy from the rubber band to the cars.
B Collecting data
Sample data:
Table 1: Action/reaction pair data
Trial
In the next part of the investigation you will use different numbers of marbles in each car to test
the effect on the motion of the cars. What do you think will happen when equal and opposite
forces act on objects with different masses? Write a hypothesis to express your answer. Your
hypothesis should be in the form of an if-then statement, as shown in Part 1c.
Students make predictions.
1
2
3
4
B Collecting data
Let’s move on from the prediction stage to actually testing your hypothesis. Repeat the setup from
Part 1, but this time you will place one steel marble in each Energy Car.
Have students verify that the track is still level. The cars should be connected “nose to notch”
in the center of the track. The rubber band should be wrapped around the blue car, which is
positioned closer to the velocity sensor.
Plug the velocity sensor into Input 1 on the Data Collector and turn the Data Collector on. Place it
in Data Collection mode. Setup the Data Collector as described in Part 2, steps 7–9.
Ensure that students are wearing their safety glasses before proceeding.
With a very quick upward motion, pull the connector straight up and out from the cars. When the
cars are no longer moving, press the button on the Data Collector to stop the experiment.
Go to the table and graph view to see the data you collected. You can obtain the name of the
experiment if you go to the setup. Write it in Table 1 or in your notebook in case you need to go
back to it later. Record only the blue car data because it was this car’s motion that was detected by
the velocity sensor.
Students record data.
You now need to collect data for the orange car with only one marble. Use the Energy Car
connector to reattach the cars. This time place the orange car closer to the velocity sensor. Set up a
new experiment on the Data Collector and repeat steps 9–13.
Students repeat this procedure for each of the marble pairings described in Table 1.
C Analyzing the data
Look at the data you recorded in Table 1. When the masses are equal how do the velocities of the
cars compare?
The velocities are nearly the same when the masses are equal.
86
UNIT 2: MOTION AND FORCE IN ONE DIMENSION
Marble pairings for
connected cars
Maximum velocity
(cm/s)
Blue
Orange
Blue
Orange
0 marbles
0 marbles
2 marbles
2 marbles
2 marbles
0 marbles
0 marbles
2 marbles
29.9
24.3
13.7
15.0
12.7
26.1
28.3
16.3
C Analyzing the data
Sample answers:
a.
When the masses are equal the velocities are very close.
b.
The car that has twice the mass has half the velocity.
c.
The forces were equal and opposite in all cases. The
only case when the velocities were also equal was in the
case of equal mass.
d.
With the same force on both objects, the object with
more mass will have less of a change in motion.
e.
Newton’s second law of motion.
f.
Both graphs show a very gradually decreasing velocity;
the blue car velocity in trial 1 starts higher than the blue
car velocity in trial 3.
g.
The graphs for the orange car in trial 2 and 3 are nearly
identical, as would be expected.
h.
For each car at every trial, the velocity/time graph
shows a gradually decreasing velocity. In all cases,
friction opposes the motion of the car and it gradually
slows down.
INVESTIGATION 5.3: NEWTON’S THIRD LAW: ACTION AND REACTION
What happens to the velocity of each car when the mass of one car is doubled?
The velocity is reduced by about half when the mass is doubled.
don’t equal and opposite forces cancel
D Why
each other out?
Considering what you have already learned about the first and second laws, is this what you
would have expected to happen?
Students should recall that the mass of an object is inversely proportional to its velocity.
a.
Sample sketch:
b.
See 4a.
c.
Free body diagram:
d.
None of the objects have both forces from actionreaction pairs acting on it.
You observed that the velocities of the car were the same or almost the same when the masses
were equal. How does this observation explain the idea that the forces acting on the cars were
equal and opposite?
At equal masses, the cars experience similar motion (closely related velocities), but travel in
opposite directions. This is an indication that the forces must be action-reaction (equal and
opposite) forces.
Action-reaction forces are equal in strength, but when the cars separate one car moves at a
different velocity than the other when their masses are unequal. Why does this happen?
When one car is twice as massive as another, its resistance to motion will be greater than the
less massive car. Consequently, there will be differences in acceleration. Even though the
forces are equal and opposite, the resulting motion (net force) will be different. Review the
concept of net force and Newton’s second law with students.
How do the velocity versus time graphs compare in the different trials. Generate the graphs and
then we can talk about what they tell us.
Have different groups lead the discussions to compare and contrast the graphs. Direct them to
tell whether their observations support what the graphs indicate about the motion of the cars.
D Why don’t equal and opposite forces cancel each other out?
We have consistently stated that action/reaction pairs do not cancel each other out. Do you agree
with this statement?
Students share opinions.
In this part of the investigation, we will draw a series of free body diagrams to prove this fact. A
free body diagram is a sketch showing all the forces acting on an object. Let’s begin with 4a.
At this point in the study of Newton’s third law, students may or may not be very comfortable
with drawing action-reaction force pair diagrams. However, the visuals may enhance their
understanding of what is meant by action/reaction. This activity will further drive home the
key to Newton’s third law: action-reaction forces are equal in size and opposite in direction,
but since they act on different objects, they do not cancel each other out. Students will see this
clearly when they study each object in their diagram. None of the objects have both members
of any force pair acting on it.
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