INVESTIGATION
Collaborative Learning
B3
This investigation is Exploros-enabled for tablets. See page xiii for details.
B3 Momentum
Key Question: How well is momentum conserved in collisions?
The law of conservation of momentum is the second of
the great conservation laws in physics, after the law of
conservation of energy. In this investigation, students
observe elastic collisions between balls of the same and
differing masses. The speed of each ball before and after
each collision is determined, and the total momentum
before and after each collision is calculated. Students
compare the total momentum before and after each
collision to determine how well momentum is conserved.
Learning Goals
✔✔Perform elastic collisions between balls of
each collision.
yy Physics stand*
yy Two photogates*
yy DataCollector*
yy Calculator*
yy B
alance or digital scale, accurate to 1 gram
(for the class)*
O
nline Resources
✔✔Calculate the velocity and momentum of the balls
✔✔Determine whether momentum is conserved in
yy Colliding pendulum kit
*provided by the teacher
various masses.
before and after each collision.
Materials for each group
Available at curiosityplace.com
yy Equipment Video: Colliding Pendulum
yy Skill and Practice Sheets
yy Whiteboard Resources
yy Animation: Changes in Momentum
GETTING STARTED
Time 100 minutes
yy Science Content Video: Newton’s Third Law
yy Student Reading: Newton’s Third Law and Momentum
Setup and Materials
1. Make copies of investigation sheets for students.
2.
W
atch the equipment video.
3. Review all safety procedures with students.
NGSS Connection This investigation builds conceptual understanding and skills for the following performance expectation.
HS-PS2-2. Use mathematical representations to support the claim that the total momentum of a system of objects is
conserved when there is no net force on the system.
Science and Engineering Practices
Using Mathematics and Computational Thinking
Disciplinary Core Ideas
PS2.A: Forces and Motion
Crosscutting Concepts
Systems and System Models
Colliding Pendulum
41
Momentum
Vocabulary
collision – occurs when two or more objects hit
each other
elastic collision – a collision in which the total kinetic
energy remains the same before and after the collision
inelastic collision – a collision in which the total kinetic
energy after the collision is less than it was before the
collision, and which usually involves objects sticking
together or changing shape
law of conservation of momentum – states that in the
absence of external forces, the total momentum of a
system remains constant
momentum – the mass of an object multiplied by
its velocity
Newton’s second law – states that acceleration is force
divided by mass
Newton’s third law – states that for every action force,
there is a reaction force equal in strength and opposite
in direction
BACKGROUND
A collision occurs when two or more objects hit each
other, and the objects exert forces on each other.
Newton’s third law tells us that any time two objects hit
each other, the forces exerted by the objects are equal
in magnitude and opposite in direction. However, the
effect of the collision on each object can differ. During
a collision, momentum and energy are transferred from
one object to another.
Newton’s second law explains why colliding objects
react differently. The second law states that an object’s
acceleration is directly
proportional to the
force exerted on the
object and inversely
proportional to the
object’s mass. The force
felt by two colliding
objects is the same, but
the resulting acceleration
and velocity depend
42 on each object’s mass. The higher an object’s mass, the
more force it takes to deflect its motion.
There are two types of collisions: elastic and inelastic.
When an elastic collision occurs, objects bounce off
each other with no loss in the total kinetic energy of the
system. The total kinetic energy before the collision is the
same as the total kinetic energy after the collision. The
collision between billiard balls is very close to a perfectlyelastic collision.
In an inelastic collision, objects change shape or
stick together, and the total kinetic energy of the
system decreases. The energy is not destroyed, but it is
transformed into forms other than kinetic energy, such as
a permanent change in shape, or sound, or heat. An egg
hitting the floor is one example of an inelastic collision;
two vehicles colliding is another. In both cases, some of
the kinetic energy in the system permanently changes an
object’s shape.
Momentum is a property of moving matter that
depends on both mass and velocity. Momentum
describes the tendency of objects to keep going in the
same direction with the same speed. One way to look at
force is that force is the action that changes momentum.
Conversely, any change in momentum must create force.
Momentum is the product of an object’s mass and
velocity. The greater an object’s momentum, the harder
it is to stop. A train car moving at even a very slow speed
is difficult to stop because its momentum is large due to
its mass.
The law of conservation of momentum says the total
momentum in a system of interacting objects cannot
change as long as all forces act only between the
objects in the system. If interacting objects in a system
are not acted on by outside forces, the total amount of
momentum in the system cannot change. If one object
gains momentum, the other loses the same amount,
leaving the total unchanged.
Conservation of momentum can be used to determine
an unknown velocity or mass if all of the other masses
and velocities in the collision are known. It is important to
include the direction of the velocity (positive or negative)
because velocity and momentum are vector quantities.
B3
5E LESSON PLAN
Engage
Newton’s third law tells us that when two objects collide,
they exert equal and opposite forces on each other.
However, the effect of the force is not always the same.
Demonstrate by rolling two balls of different mass
toward each other so they collide. Use two balls with a
significant difference in mass, such as a tennis ball and
a baseball, or a ping pong ball and a golf ball. The force
on each during the collision is the same, but they do not
have the same change in motion after the collision.
When studying motion related to collisions, we
can predict how two colliding objects might move
using momentum and Newton’s third law of motion.
Momentum is the mass of an object multiplied by its
velocity. Because of this, you could also call it “mass
in motion.”
Explore
Have students complete Investigation B3, Momentum.
Students observe elastic collisions between balls of the
same and differing masses. The speed of each ball before
and after each collision is determined, and the total
momentum before and after each collision is calculated.
Students compare the total momentum before and
after each collision to determine how well momentum
is conserved.
Explain
Revisit the Key Question to give students an opportunity
to reflect on their learning experience and verbalize
understandings about the science concepts explored in
the investigation. Curiosityplace.com resources, including
student readings, videos, animations, and whiteboard
resources, as well as readings from your current science
textbook, are other tools to facilitate student
communication about new ideas.
Science Content Video
Newton’s Third Law
Animation
Changes in Momentum
Elaborate
Automakers use
crash test dummies
to study the effects
of collisions on
passengers. Crash
test dummies contain
electronic sensors to
measure the forces
and accelerations
exerted at various
places on the body. The dummies are expensive, costing
more than $100,000 each, but they are also sturdy and
last through years of crash testing.
Results of these tests have been used to make changes
in automobile design. The use of seat belts and airbags
reduces the force on passengers by slowing down the
transfer of momentum, making today’s cars much safer
than their predecessors.
Consider having students study the momentum, force,
and energy changes that are inflicted on a crash test
dummy and how those forces can be mitigated with
safety devices in an automobile.
Evaluate
yy D
uring the investigation, use the checkpoint
questions as opportunities for ongoing assessment.
yy A
fter completing the investigation, have students
answer the assessment questions on the Evaluate
student sheet to check understanding of the
concepts presented.
Colliding Pendulum
43
Momentum
Explore
INVESTIGATION
B3
Name ____________________________________________ Date ________________________
B3 Momentum
Materials:
✔ Colliding pendulum kit
How well is momentum conserved in collisions?
✔ Physics stand
This investigation is about momentum, a property of moving matter. An object’s ✔ Two photogates
momentum depends on its velocity and mass. When a collision occurs between
✔ DataCollector
two objects, momentum is transferred from one to the other. If no outside forces
✔ Calculator
(such as friction) are present, the total momentum of the objects before the
collision is the same as the total after the collision.
✔ Balance or digital scale,
In this investigation, you will observe collisions between objects of varying
masses. You will calculate the momentum before and after each collision to
determine how well the collisions follow the law of conservation of momentum.
accurate to 1 gram
The colliding pendulum apparatus allows you to observe collisions
between two balls of the same or different mass. The balls are made
of hardened steel and the collisions are almost perfectly elastic. (In an
inelastic collision, the colliding objects stick together or change shape as a
result of the impact.)
1. Attach the arc at the lowest possible point in the stand. Secure it
with a threaded knob. Attach the pendulum hanger, leaving nine
uncovered holes between the arc and the hanger.
2. Loosen the hanger’s left post and insert the string from one of the
medium-sized balls. Gently tighten the post to secure the string so
the ball hangs a little below the bottom of the arc.
3. Stand back and look at the string relative to the alignment mark
on the arc. The string should be in line with the mark. Adjust the
leveling feet on the base of the stand if necessary.
4. Loosen the post and readjust the length of the string until the bottom
of the ball is 2 millimeters above the arc. Attach the other medium-sized ball to the right-hand post the
same way. The two balls should be at the same level relative to the arc.
5. Place two photogates in the notches at the bottom of the arc. Set the Data Collector to CPO timer mode,
and select the interval function by tapping the “I” icon. Attach the right photogate to input A and the left
photogate to input B.
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B3 Momentum
Colliding Pendulum
If you wish to complete the investigation in a
shorter period of time, you can partially set up the
equipment by attaching a hanger and arc to each
physics stand ahead of time. Then, during class,
students will only have to attach and align the
projectile and target balls to the correct height.
Accident reconstruction Police forensics
specialists use conservation of momentum
and other physics knowledge to analyze traffic
accidents. Skid marks, debris such as broken
glass, and other clues allow investigators to
reconstruct the events of an accident scene
with surprising accuracy.
Skid marks are used to
determine the directions of
m1
the vehicles before and after
v1
the crash. Skid marks can
also be used to estimate velocities. With
information on friction, skid distances, and
directions, forensic specialists use momentum
conservation to determine the vehicles’
velocities before and after the crash.
To correctly align the lengths of the pendulum
strings, first align the projectile ball by putting the
starting block in the 30-degree notch of the arc. Fit
the projectile ball against the hole on the front of the
starting block. Adjust the pendulum string so the ball
fits exactly against the hole. Next, let the projectile
ball hang at its lowest point. Adjust the length of the
target ball string so its center aligns with the center of
the projectile ball.
If necessary, adjust the leveling feet of the physics
stand to align the balls in the center of the
photogates. It is important that the balls pass directly
through the center of the photogates to ensure
accurate velocity readings. The physics stand pole
does not need to be completely vertical. It may lean
forward, but shouldn’t lean to the side.
STEM CONNECTION
44  Setting up the experiment
The steel balls connect to the hanger by threading
the strings through the holes in the two posts. You
can see the holes if you unscrew the post a few
millimeters. The posts do not unscrew completely,
so do not try to remove them. The posts that hold
the string in place only need gentle tightening;
over‑tightening may damage the strings.
Setting up the experiment

Copyright © CPO Science
Can be duplicated for classroom use
Guiding the INVESTIGATION
m2
v2
B3
Explore
INVESTIGATION
B3
6. Slide the starting block into the 30-degree notch on the arc. To release the ball, grip it between two
fingers and hold it against the hole in the front side of the starting block. The hole positions the projectile
ball so it will hit the center of the target ball. Release the ball by opening your fingers evenly, allowing
the ball to drop straight out of the hole.
7. It can be tricky to get the balls to collide head-on. You can tell when this has occurred because the target
ball moves straight along the same line that the projectile ball followed. Practice dropping the projectile
ball until you can get a head-on collision most of the time.
B3
INVESTIGATION
5. How does the momentum of the target ball after the collision compare to the momentum of the projectile
ball before the collision? Calculate the percent difference between the two momentums.
The momentum of the target ball after the collision is very close to
the momentum of the projectile ball before the collision. It is only
very slightly less, with a difference of 3.6%.
Larger projectile colliding with smaller target

Collisions with equal masses

When recording data during this experiment, only include measurements for head-on collisions. Repeat the
trial and do not record the data if one or both of the balls moves to the side after the collision.
1. With the target ball at rest, drop the projectile ball. Catch the target ball when it flies up. Record the times
for trial 1 in Table 1. Repeat for a total of 3 trials and find the averages.
Table 1: Time data for equal mass balls
Trial 1
Trial 2
Trial 3
0.0218
0.0217
0.0217
0.0217
Target time (s) after collision
0.0225
0.0225
0.0226
0.0225
2. Measure the mass of each ball and record it in Table 2.
Table 2: Velocity and momentum for equal mass balls
Mass (g)
Diameter (cm)
Velocity (cm/s)
Projectile before collision
66.6
2.54
116.9
7,784
Target after collision
66.6
2.54
112.7
7,507
Momentum (g∙cm/s)
3. Calculate the velocity of each ball. The distance each ball moves while it blocks the photogate
beam is equal to the ball’s diameter. For the time, use the “average” values in Table 1. Velocity is
direction-dependent. Decide in your group which direction is positive and which is negative. The
projectile’s initial direction of travel is usually considered positive.
Answers are shown in Table 2.
4. Calculate the momentum of each ball by multiplying its mass by its velocity.
Answers are shown in Table 2.
2 of 6
Remove the projectile ball and replace it with the largest ball. Align
the two balls so their centers are at the same height.
1. Make a hypothesis to predict what you think will happen when
the two balls collide.
The projectile will slow down but keep
moving, and the target will move quickly.
The centers
of the balls
should be on
the same line
Target
Projectile
Average
Projectile time (s) before collision
Copyright © CPO Science
Can be duplicated for classroom use
Explore
B3 Momentum
Colliding Pendulum
2. Drop the projectile ball and observe the collision. Describe what
happens to each ball. Was your hypothesis correct?
The projectile ball slows down but keeps moving after the collision.
The target ball moves away from the target ball quickly.
3. Perform another collision and catch the balls right after the collision, before they fall back through the
photogates. In this collision, both balls pass through photogate B. To get the time for the target ball after
the collision, you must select memory by clicking the “m” at the bottom of the DataCollector screen
when the B light is on. Record the times for trial 1 in Table 3. Repeat for a total of 3 trials and find the
average times.
Table 3: Time data for larger projectile/smaller target collision
Trial 1
Trial 2
Trial 3
Average
Projectile time (s) before collision
(photogate A)
0.0282
0.0282
0.0282
0.0282
Projectile time (s) after collision
(photogate B)
0.1096
0.1095
0.01125
0.1105
Target time (s) after collision
(photogate B - memory)
0.0173
0.0172
0.0170
0.0172
Copyright © CPO Science
Can be duplicated for classroom use
3 of 6
B3 Momentum
Colliding Pendulum
Guiding the INVESTIGATION
 Collisions with equal masses
To make a collision, pull the target ball up the arc
and hold it against the starting block between your
thumb and first finger, with your hand over the top of
the ball and starting block. Release the ball carefully
by opening your fingers. You want the ball to swing
straight down the arc with no sideways motion. A
sideways motion will cause the target ball to move
off at an angle during the collision. You want to make
head-on collisions where the target ball moves in the
same direction as the projectile ball was originally
traveling. It takes some practice to get the balls to
collide perfectly head on.
Encourage students to be patient and give each group
member a chance to try creating collisions. They may
have to perform each collision several times to get valid
velocity data. They should only record data for perfect
head-on collisions.
Colliding Pendulum
45
Momentum
Explore
INVESTIGATION
B3
4. Record the masses, velocities, and momentums in Table 4.
Mass (g)
Diameter (cm)
Velocity (cm/s)
Momentum (g∙cm/s)
Projectile before collision
129.4
3.18
112.8
14,592
Projectile after collision
129.4
3.18
28.8
3,723
Target after collision
66.6
2.54
148.0
9,854
13,577
5. Add the momentums of the projectile and target balls to find the total momentum after the collision.
How does it compare to the projectile’s momentum before the collision? Calculate the percent difference
between the momentum before and after the collision.
Total before collision = 14,592 (projectile momentum)
+ 0 (target momentum) = 14,592
Percent difference = (14,592 – 13,577)/14,592 = 0.07 x 100 = 7%
The total momentum after the collision is slightly less than the
momentum of the projectile ball before the collision. The
difference is 7%.
Smaller projectile colliding with larger target

Switch the locations of the target and projectile balls. The projectile
is now the medium ball. Align the two balls so their centers are at the
same height.
1. Make a hypothesis to predict what you think will happen when the
two balls collide.
The projectile ball bounced back, and the target ball moved slowly
away from the projectile ball.
3. To measure the times, catch the balls right after a collision, before they fall back through the photogates.
Allow the projectile ball to pass through photogate A twice. To get the time before the collision, you must
select memory by clicking the “m” icon at the bottom of the DataCollector screen. Record data for three
trials in Table 5.
Table 5: Time data for smaller projectile/larger target collision
Trial 1
Trial 2
Trial 3
Average
Projectile time (s) before collision
(photogate A - memory)
0.0223
0.0222
0.0224
0.0223
Projectile time (s) after collision
(photogate A)
0.0910
0.0883
0.0898
0.0897
Target time (s) after collision
(photogate B)
0.0429
0.0432
0.0424
0.0428
a. Record the masses, velocities, and momentums in Table 6. The projectile ball reverses direction during
the collision, so it has a negative velocity and momentum after the collision.
Table 6: Velocity and momentum for smaller projectile/larger target collision
The centers
of the balls
should be on
the same line
Target
Projectile
Mass (g)
Diameter (cm)
Projectile before collision
66.6
2.54
113.9
7,586
Projectile after collision
66.6
2.54
–28.3
–1,886
Target after collision
129.4
3.18
74.2
9,607
Total after collision
7,721
The projectile will bounce back, and the target will move slowly away
from the projectile ball.
Copyright © CPO Science
Can be duplicated for classroom use
4 of 6
B3
INVESTIGATION
2. Drop the projectile ball and observe the collision. Describe what happens to each ball. Was your
hypothesis correct?
Table 4: Velocity and momentum for larger projectile/small target collision
Total after collision
Explore
B3 Momentum
Colliding Pendulum
Copyright © CPO Science
Can be duplicated for classroom use
5 of 6
Velocity (cm/s)
Momentum (g∙cm/s)
B3 Momentum
Colliding Pendulum
ADDRESSING MISCONCEPTIONS
Students often have difficulty with the terms elastic
and inelastic. Elastic and inelastic are conventions used
to make it easier to analyze the forces, motion, and
energy of a collision. The collisions seen in everyday
life are a mix of elastic and inelastic. When two billiard
balls collide, it looks like they bounce without a loss
of kinetic energy. But the sound of the collision tells
you a small amount of kinetic
energy is being changed into
sound energy. We approximate
the collision of the balls as
elastic because it is very close
to a perfectly-elastic collision,
even though a small amount
of energy is lost (to sound) in
the collision.
46 Be aware of students classifying all objects that
bounce off each other as elastic collisions. The objects
do not have to stick together in order for the collision
to be classified as inelastic. Consider the situation
where two cars crash and the cars bounce off each
other, but both have damage. This is considered an
inelastic collision because both objects sustained
permanent deformations.
B3
Explore
SCIENCE AND MATH
Using momentum to analyze problems can be
challenging for students. Practice applying
conservation of momentum in a collision with the
following problem.
Two 0.165-kg
billiard balls roll
toward each other
and collide headon. Initially, the 10
ball has a velocity
of 0.5 m/s. The 5
ball has an initial
velocity of –0.7
m/s. The collision
is elastic, and the
5 ball rebounds
with a velocity of
0.4 m/s, reversing
its direction. What
is the velocity of
the 10 ball after
the collision?
Before collision
m1
m2
v1
v2
m1= m2 = 0.165 kg
v1 = 0.5 m/s
v2 = – 0.7 m/s
After collision
v3
v4
INVESTIGATION
B3
b. Add the momentums of the projectile and target balls to find the total momentum after the collision.
How does it compare to the projectile’s momentum before the collision? Calculate the percent difference
between the momentum before and after the collision.
Percent difference = (7,586 – 7,721)/7,586 × 100 = 0.018%
The total momentum after the collision is very close to the
projectile’s momentum before the collision. The difference is 1.8%.
c. According to the law of conservation of momentum, the total momentums before and after a collision
should be the same. Discuss some reasons why the momentums before and after the collisions in this
investigation may have been slightly different.
The momentums may have been slightly different because it was
hard to create perfect head-on collisions. If the balls did not move
straight through the photogates, the times would not be perfectly
accurate because it takes more time to move diagonally through
a photogate than straight through it. The distance for which a ball
blocked the photogate would also be inaccurate if the ball did not
go straight through or if it was slightly higher or lower than it should
be. The distance measurements assumed that the entire diameter
passed through the beam of the photogate.
d. Newton’s third law states that the forces on two colliding objects are equal in strength and opposite in
direction. Newton’s second law explains the relationship between acceleration, force, and mass. Use
these two laws to explain what happened during the three collisions.
The force felt by two colliding balls has the same strength. If the
balls have equal masses, they accelerate equally. One slows down
and the other speeds up by the same amount. If the masses are
unequal, the lighter ball accelerates more as a result of the force.
The lighter ball’s velocity therefore changes by a greater amount.
v3 = ?
v4 = 0.4 m/s
Copyright © CPO Science
Can be duplicated for classroom use
6 of 6
B3 Momentum
Colliding Pendulum
Looking for: The velocity of the 10 ball after
the collision
Given: The initial mass and velocity of both balls.
You are also given the velocity of the 5 ball after
the collision.
Relationships: Both balls are of equal mass. Using the conservation of momentum, the sum of the momentums
of both balls before the collision (mv1 + mv2) is equal to the sum of the momentums of both balls after the
collision (mv3 + mv4).
Solution:
mv1 + mv2 = mv3 + mv4
(0.165 kg)(0.5 m/s) + (0.165 kg)(−0.7 m/s) = (0.165 kg)(v3 ) + (0.165 kg)(0.4 m/s)
−0.033 kg i m/s = (0.165 kg)(v3 ) + 0.066 kg i m/s
v3 = −0.6 m/s
The 10 ball travels at –0.6 m/s, the negative value indicating its movement in the opposite direction as shown by
the arrow in the diagram.
Colliding Pendulum
47
Momentum
Evaluate
B3
INVESTIGATION
Notes and Reflections
Name ____________________________________________ Date ________________________
1. Which object has the most momentum? Circle the correct answer.
a. A 5-kilogram cat running at 5 m/s
c. A 50-kilogram person walking at 1 m/s
b. A 1,000-kilogram car that is not moving
d. A 1-kilogram bird flying at 15 m/s
2. In which scenario will the projectile ball continue moving in its original direction after the collision?
Circle the correct answer.
a. A large projectile ball hits a small target ball
b. A small projectile ball hits a large target ball
c. A medium projectile ball hits a medium target ball
3. In which scenario will the target ball’s velocity after the collision equal the projectile ball’s velocity
before the collision? Circle the correct answer.
a. A large projectile ball hits a small target ball
b. A small projectile ball hits a large target ball
c. A medium projectile ball hits a medium target ball
Before collision
4. A 50-gram ball moving at 6 m/s hits a 10-gram ball at rest. After the
collision, the 10-gram ball is moving at 10 m/s.
50 grams
After collision
10 grams
50 grams
10 grams
a. Calculate the momentum of the 50-gram ball before the collision.
50 g × 6 m/s = 300 g∙m/s
Before
b. Calculate the momentum of the 10-gram
ballcollision
after the collision.
50 grams
10 g × 10 m/s = 100 g∙m/s
stopped
6 m/s
10 grams
c. How much momentum must the 50-gram ball have after
stopped
the collision?
6 m/s
After collision
50 grams
10 grams
10 m/s
?
The total momentum must add up to 300 g∙m/s, so the 50-gram ball
must have a momentum of 200 g∙m/s.
d. Calculate the velocity of the 50-gram ball after the collision.
200 g∙m/s ÷ 50 g = 4 m/s.
B3 Momentum
Colliding Pendulum
Copyright © CPO Science
Can be duplicated for classroom use
WRAPPING UP
Have your students reflect on what they
learned from the investigation by answering the
following questions:
1. What is momentum?
2. How is momentum calculated?
3. What does it mean to say momentum
is conserved?
48 ?
10 m/s