19
The impulse-momentum theorem relates impulse, the average force applied to an object times the length of time the force is applied, and the change in momentum of the object:
F
 t
 mv f
 mv i
Here, we will only consider motion and forces along a single line. The average force, F , is the net force on the object, but in the case where one force dominates all others, it is sufficient to use only the large force in calculations and analysis.
For this experiment, a Dynamics Cart will roll along a level track (the table). Its momentum will change as it collides with a hoop spring. The hoop will compress and apply an increasing force until the cart stops. The cart then changes direction and the hoop expands back to its original shape. The force applied by the spring is measured by a Dual-Range Force Sensor. The cart velocity throughout the motion is measured with a Motion Detector. You will then use data-collection software to find the impulse to test the impulse-momentum theorem.
Figure 1
1. In a car collision, the driver’s body must change speed from a high value to zero. This is true whether or not an airbag is used, so why use an airbag? How does it reduce injuries?
2. Two playground balls, the type used in the game of dodgeball, are inflated to different levels. One is fully inflated and the other is flat. Which one would you rather be hit with? Why?
19 - 1 Physics with Vernier © Vernier Software & Technology

Impulse and Momentum
3. Observe the diagram at the right. Use this to write a definition for an Elastic Collision and an Inelastic Collision.
4. Write the equation for Momentum:
Calculate the momentum of a 4.0 kg object traveling at a velocity of 12.0 m/s east.
A 5.00 kg object accelerates uniformly from 5 m/s east to a velocity of 15.0 m/s in the same direction.
What is the change in momentum of the object?
4. Write the equation for Impulse:
A hockey player makes a slap shot, exerting a constant force of 30.0 N on the hockey puck for 0.16 s.
What is the magnitude of the impulse given to the puck?
5. Write the Impulse-Momentum Theorem:
A 26.3 kg object is traveling at 21.0 m/s north. What average net force is required to bring this object to stop in 2.60 s?
A rocket at rest with a mass of 9.5 x 103 kg is acted on by an average net force of 1.5 x 105 N upwards for 15 s. What is the final velocity of the rocket?
Physics with Vernier 19 - 2

1. Measure the mass of the cart and record the value in the data table.
Impulse and Momentum
2. Set up the Motion Detector and bracket to one end of the Dynamics “Track” (see Figure 1).
3. Set up a textbook at the other end of the “Track”.
4. Set the Motion Detector sensitivity switch to Track. Connect the Motion Detector to a digital (DIG) port of LabQuest. Choose File ► New.
5. On the Meter screen, tap Rate. Change the data-collection rate to 250 samples/second and the data-collection duration to 5 seconds. Select OK.
Part I Elastic collisions
6. Practice releasing the cart so it rolls toward the book with the bumper facing forward, bounces gently, and returns to your hand. The book must not shift, and the cart must stay on the “track”. Keep your hands away from the space between the cart and the Motion Detector.
7. Position the cart so that the front of the cart is approximately 50 cm from the book. Start data collection, then roll the cart as you practiced in the previous step.
8. Once you have made a run with good position and velocity graphs, analyze your data. To test the impulsemomentum theorem, you need the velocity before and after the impulse. To find these values, work with the graph of velocity vs . time. a.
Change the y-axis of the position graph to Velocity. b.
Tap and drag to select an interval corresponding to a time before the impulse, when the cart was moving at approximately constant speed toward the book. c.
Choose Statistics ► Velocity from the Analyze menu. Read the average velocity before the collision ( v i
) and record the value in the data table. d.
Choose Statistics ► Velocity from the Analyze menu to turn off statistics. e.
Repeat parts a–c of this step to determine the average velocity just after the impulse, when the cart was moving at approximately constant speed away from the Dual-Range Force Sensor. Record this value in the data table.
9. Repeat Steps 7–8 two more times to collect a total of three trials; record the information in your data table.
Part II Inelastic collisions
10. Replace the book with another cart with the two Velcro pieces facing each other.
11. Practice launching the cart with your finger so that when the Velcro on the front of the cart collides with the
Velcro on the other cart, the cart comes to a stop without bouncing.
12. Position the cart so that the front of the cart is approximately 50 cm from the other cart. Start data collection, then roll the cart so that the Velcro pieces impact one another.
13. Study your graphs to determine if the run was useful. a.
Confirm that the Motion Detector detects the cart throughout its travel and that you can see a region of constant velocity before and after the impact.
Physics with Vernier 19 - 3

Impulse and Momentum
14. Once you have made a run with good position and velocity graphs, analyze your data. To test the impulsemomentum theorem, you need the velocity before and after the impulse. a.
Change the y-axis of the position graph to Velocity. b.
Select the interval corresponding to the time before the impact, and choose Statistics ► Velocity from the
Analyze menu. Record the average velocity in the data table. c.
Choose Statistics ► Velocity from the Analyze menu to turn off statistics. d.
Select the interval corresponding to the time after the impact, and choose Statistics ► Velocity from the
Analyze menu. Record the average velocity in the data table.
21. Repeat Steps 12-14 two more times to collect a total of three trials; record the information in your data table.
Physics with Vernier 19 - 4

Impulse and Momentum
1.
Tips for obtaining useful data with a Motion Detector
a.
Motion Detectors with a sensitivity switch (shown at right) will detect objects as close as 0.15 m.
Ideally, an experiment is set up so that the target is nearly this close at the point of closest approach, giving the best possible data. b.
Ultrasound is emitted from the Motion Detector in a cone about 15o off the axis (which is 30o wide); this includes downward. Anything within the ultrasound cone can cause a reflection and possibly an accidental measurement. A common problem is getting unintentional reflections from a desk, chair, or computer. Unintended reflections can be minimized by tilting the Motion
Detector slightly. When collecting data on an incline or ramp, it is usually best to point the
Motion Detector slightly upward. c.
If the velocity and acceleration graphs are noisy, try to increase the strength of the ultrasonic reflection from the target by increasing the target’s area and ensuring the target creates a strong reflection of the ultrasound. d.
If you being with a velocity or acceleration graph and obtain a confusing display, switch back to the position graph for troubleshooting.
Physics with Vernier 19 - 5

Impulse and Momentum
Mass of cart kg
Trial
Elastic 1
2
3
Inelastic 1
2
3
Final velocity v f
(m/s)
Initial velocity v i
(m/s)
Change of velocity
 v
(m/s)
Average force
F
(N)
Duration of impulse
 t
(s)
Impulse
F
 t
(N
 s)
Change in momentum
(kg
 m /s)
% difference between
Impulse and
Change in momentum
Physics with Vernier 19 - 6

Impulse and Momentum
Mass of cart 0.513 kg
Trial
Final velocity v f
(m/s)
Initial velocity v i
(m/s)
Change of velocity
 v
(m/s)
Average force
F
(N)
Duration of impulse
 t
(s)
Impulse
F
 t
(N
 s)
Change in momentum
(kg
 m /s)
% difference between
Impulse and
Change in momentum
Elastic 1 –0.376 0.415
2 –0.458 0.500
3 –0.357 0.402
Inelastic 1 0.000 0.406
2 0.000 0.365
3 0.000 0.436
1.462
1.685
1.311
4.62
3.02
4.00
0.26
0.27
0.26
0.05
0.06
0.06
Physics with Vernier 19 - 7

SHOW WORK HERE:
Impulse and Momentum
Physics with Vernier 19 - 8

Impulse and Momentum
1. Calculate the change in velocities and record the result in the data table. From the mass of the cart and the change in velocity, determine the change in momentum that results from the impulse. Make this calculation for each trial and enter the values in the data table.
How do the Impulse and Change in Momentum for the Elastic Collisions compare to the Inelastic Collisions?
Describe and cite data to support your response.
2. If the impulse-momentum theorem is correct, the change in momentum will equal the impulse for each trial.
Experimental measurement errors, along with friction and shifting of the track or Force Sensor, will keep the two from being exactly the same. One way to compare the two is to find their percentage difference. Divide the difference between the two values by the average of the two, then multiply by 100%. How close are your values, percentage-wise? Do your data support the impulse-momentum theorem?
Physics with Vernier 19 - 9

Impulse and Momentum
3. Look at the shape of the last force vs . time graph. Is the peak value of the force significantly different from the average force? Hint; you will have to calculate the average force; cite that data in your response.
Is there a way you could deliver the same impulse with a much smaller force?
4. Say we used a different hoop spring, that is stiffer than the one used in this experiment. Predict how the results will be similar and how they will be different. Be specific with your predictions.
Physics with Vernier 19 - 10