Impulse and Momentum
Introduction
Newton’s Second Law of Motion was originally written in terms of the “quantity of motion,” today called
momentum. It can be rewritten to state that the change of momentum of a system is equal to the sum
of the impulses applied to the system by forces external to it: . P =  J
What does that sentence mean in practice? How does impulse change the momentum of an object?
What happens to the momentum of a system when no external forces act on it? In this laboratory
you’ll investigate these questions using both probes of force and motion and digitized videos.
Textbook Reading
Halliday, Resnick, and Walker: Chapter 10, Sections 10-2, 10-5 (pages 216, 225, 226)
Overview
This laboratory includes two investigations. The first uses the air track, glider, motion and force probes
that were used in the Energy laboratory. The momentum of the glider before and after its collision with
the bumper is calculated. The force the bumper exerts on the glider is measured and the impulse the
bumper delivers to the glider is also calculated. These calculations will allow you to compare the
momentum change of the glider with the impulse the bumper gives it.
The second part uses the World in Motion software you first used to analyze the motion of the toy
airplane. This time you will analyze video clips of collisions. You’ll analyze the collisions of billiard
balls and hockey pucks and determine whether or not momentum and kinetic energy are conserved.
Objectives
·
To explore the relationship between impulse and momentum change in one dimension.
·
To develop an understanding of impulse as the integral of force over the time interval of the interaction.
·
To use measurements of the position of an object in two dimensions to calculate its momentum.
·
To examine the momentum of a system moving in two dimensions to see if momentum is conserved.
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 1 of 8
Pre-lab Questions
1.
A 300-g glider was moving at –0.57 m/s toward the left (negative direction). After colliding with the
end of the air track its speed was 0.46 m/s toward the right. What is the magnitude and sign of the
change in its momentum?
2.
The graph shows the variation of the force exerted on the glider as a
function of time. Find the impulse delivered to the glider by the
bumper by finding the area under the curve. How closely does the
impulse match the change in momentum?
3.
A 0.150 kg ball was moving with a velocity of vx = –0.75 m/s,
vy = –1.50 m/s before being hit. After being struck its velocity was vx
= +1.75 m/s, vy = –0.50 m/s. On the graph below draw arrows that
represent the ball’s momentum before and after the collision. Draw an
arrow representing the change in momentum of the ball.
Calculate the change in momentum by subtracting the components of
the initial and final momentum, then find the magnitude and direction
of the momentum change.
x-component
y-component
p (before)
p (after)
Δp = p – p
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 2 of 8
Magnitude of p = | p |= (  p x ) + (  p y )
2
2
|Δp| = ___________ kg m/s
Angle θ given by tan θ = Δpy /Δpx
θ = _________ 
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 3 of 8
Glider Collisions
Name______________________________
Equipment
· Air track with glider, extra masses, flag
· ULI with motion detector and force probe
· File Impulse
Partner _____________________________
Predictions
1. In the space to the right draw motion
diagrams for a glider that moves at
constant speed to the left, the collides
with a bumper and moves to the right
at a slightly slower speed.
2. Draw vectors representing the
momentum of the glider just before
and just after the collision. Subtract
these two vectors graphically to obtain
a vector that represents the change in
momentum, Δp.
3. According to the impulse-momentum
theorem, J = Δp. Draw a vector
representing J.
4. Repeat these three steps for a glider that moves with the same velocity, hits the same bumper, but,
rather than rebounding, stops at the bumper. If Δp and J have different magnitudes in this case,
be sure that your arrows are of different length.
Equipment
The air track, probes, and glider
should be set up as shown at the
right. The force probe should be
adjusted so that the knife edge on the
glider strikes the center of the elastic
cord bumper. When viewed from above the motion detector and force probe should point along the
center of the track and the flag on the glider should be perpendicular to the motion detector. When the
glider is resting against the elastic cord the flag should be about 45 cm from the motion detector.
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 4 of 8
Push the glider gently and observe its motion. Make sure that the track is level and that the glider
moves without sticking and bounces smoothly off the bumper. Start LoggerPro and open the file Impulse.
Gently push the glider and click on Collect to take data. Make sure that the motion detector “sees” the glider
from its collision with the bumper until it is at least 1.0 m from the detector. If the graphs are noisy carefully
adjust the location of the motion detector (or ask your instructor for help).
Checking the force probe
Check that the switch on the top of the force probe is on 10 N. Zero the probe.
Impulse and Momentum: Quantitative
In this section you will investigate the relationship between momentum change and impulse for three
trials.
1.
2.
3.
The “bare” glider colliding with the elastic band bumper.
The glider moving with the same speed, but having two 50-g masses attached.
The glider with added masses colliding with a soft clay bumper.
Gently push the unweighted glider from the far end of the track at about 0.5 m/s and record a single
collision with the bumper.
Displaying glider momentum
To find the change in momentum you need to know the glider’s momentum before and after the
collision. As you did in the energy lab, modify the Momentum column by changing the mass of the
glider from the preset value (0.500) to the measured mass of your glider. When you change the
mass of the glider in later parts of the experiment, be sure to change the definition of momentum in
LoggerPro.
Finding the impulse
The impulse, J, is defined as the integral of the external force on the system over the collision

time J = F dt
t
You can let the .program do this integral, the area under the force-time curve. First select the region
of the
forcetime
graph
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 5 of 8
that you
want to
analyze.
To make
the
selection,
position
the
mouse at
the lefthand end
of the
region.
Press
and hold
the left
mouse
button as
you slide
the
mouse to
the righthand end
of the
region.
Release
the
button.
You
should
see black
vertical
bars at
each
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 6 of 8
end. To
calculate
the
integral,
click on
the
Integrate
icon,
The
value of
the
integral is
displayed
in a
small
box.
Does the size of the integral make sense? Since the force-time curve is almost triangular in shape,
you can estimate its area as ½ (base)(height). If the computer gives an obviously wrong answer you
have probably selected the wrong region. Recheck your work.
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 7 of 8
Experimental results
In trial three you should remove the bumper from the force probe. Replace it with a cone of clay that is about
1.5 cm long and 1 cm in diameter. The knife edge on the cart should hit the center of the cone and stick in the
clay. Be sure to remove the clay and replace the bumper when you have completed the experiment.
Report your results in the table below. Also hand in printed copies of the three graphs you record. Be
sure to label your graphs.
Trial
Glider
Mass
(kg)
Initial
Final
vi
pi
vf
pf
(m/s)
(kg m/s)
(m/s)
(kg m/s)
Δp
J
Fmax
Collision
Percent error
(kg m/s)
(N s)
(N)
time
100%
Δt (s)
|Δp – J|/Δp
1
2
3
Questions
1. When the mass of the glider was increased (assuming that the glider’s speed was the same) was
the change in the glider’s momentum changed? If so, by what percentage amount?
Was the impulse increased? If so, by what amount?
2. Compare trials 1 and 2. Did the bumper exert a greater force, or did the collision occur over a
longer time (or both)?
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 8 of 8
3. Describe the difference in the impulse delivered by the bumper when the glider stopped in the clay
as opposed to when it bounced off the bumper. (How did the impulse change? Did the maximum
force change, the time interval change, or both? In what way did it change? Be specific.)
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 9 of 8
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 10 of 8
Collisions in Two Dimensions
Equipment
·
World in Motion program
·
Video clips
Introduction
Force, velocity, momentum, and impulse are all vectors. In one dimension, of course, this means that
the sign is important. In more than one dimension the vector nature of these quantities means that
they require more careful attention. While the motion and force detectors are fine for one-dimensional
motion, a video clip provides a good record of motion in two dimensions. You will analyze two
collisions, one of a pair of billiard balls, the second a pair of pucks on an air hockey table. Your task
is to find out if the two objects act as a system in which momentum is conserved. You will also find
out if kinetic energy is conserved in these collisions.
Analyzing a collision
After quitting LoggerPro, click on World in Motion. Your instructor will tell you which video files to
open. Open the correct clip. According to the textbook, under what conditions is the momentum of a
system conserved?_______________________________________________________
For the system of the two objects, either billiard balls or hockey pucks, using the textbook criterion,
would you expect the momentum to be conserved? Give reasons for your prediction.
______________________________________________
The balls and pucks are extended objects. You must mark the same point on each object in each
frame. The reflection of the light is a good point to mark on the billiard balls. The center of each puck
is clearly marked. Begin by marking the location of one ball or puck (use the large brown puck) on
each video frame. When you have reached the last frame click on the button Data Set 1 (lower righthand corner). The video clip will return to the first frame and you should mark the location of the
second ball or puck (the small yellow puck) on each frame.
When you have marked all the frames click on the Graphs button. On the Data analysis choices menu
choose Option 3. On Direction of Motion menu choose both objects moving in the X and Y directions,
with Y horizontal. On the Plots menu choose momentum and energy versus time. Click on the Next
button.
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 11 of 8
Click on the Graph>> button to display the first graph, the momentum of object 1. The graphs will be
cluttered. To view only one graph at a time, open the Graph Tools menu and click on Jog. Click on
Jog again to see the second graph; again to see the third. To see the momentum of object 2, click on
the Graph>> button.
Use your judgment to find best values for the momenta of the two objects in both the x- and ydirections before they hit and near the end of the clip. Subtract the components to find the momentum
change Δp of each. In this collision, the system is the two objects. To find out if the momentum of the
system is conserved, find Px = p1x + p2x and Py = p1y + p2y before the collision and at the end of the
clip. If momentum is conserved, then the change in momentum of the system should equal zero (or at
least be much smaller than either the initial or final momentum).
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 12 of 8
Quantity
Ball 1
p1x (kg m/s)
Ball 2
p1y (kg m/s)
System
p2x (kg
p2y (kg
m/s)
m/s)
Px (kg m/s)
Py (kg m/s)
pInitial
pFinal
Δp
Within the percent differences, is the momentum of the system conserved? (Explain your reasoning)
__________________________________.
The program calculates the kinetic energy of each object. Determine the kinetic energies of each ball
before and after the collision. Add them to find the kinetic energy of the system. Report your results
in the table below:
Quantity
Ball 1
Ball 2
System
KInitial
KFinal
ΔK
Is the kinetic energy of the system conserved? Explain your conclusion _______________________.
Repeat the analysis for a video clip of a collision of two pucks.
Quantity
Puck 1
p1x (kg m/s)
p1y (kg m/s)
Puck 2
System
p2x (kg
p2y (kg
m/s)
m/s)
Px (kg m/s)
Py (kg m/s)
pInitial
pFinal
Δp
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 13 of 8
Within the percent differences of your measurements, is the momentum of the system conserved?
(Explain your reasoning) __________________________________.
Quantity
Puck 1
Puck 2
System
KInitial
KFinal
ΔK
Is the kinetic energy of the system conserved? Explain your conclusion _______________________.
Physics Laboratory Manual Jan 1999
Impulse and Momentum - Page 14 of 8