Teacher Notes – Activity 15: Impulse and Change in Momentum

Objectives

• 
  use a Motion Sensor to measure the motion of a cart before and after a collision.
  
• 
  use a Force Sensor to measure the force on the cart during a collision.
  
• 
  use the Xplorer GLX to record and display the velocity for the cart and the force for the collision.
  
• 
  use the graphs of velocity versus time and the built-in analysis tools of the Xplorer GLX to determine the velocity before and after for the cart in each collision.
  
• 
  use the graphs of force versus time and the built-in analysis tools of the Xplorer GLX to determine the impulse (area under force versus time curve) in each collision.
  
• 
  calculate the total momentum before and the total momentum after each collision.
  
• 
  compare the change in momentum to the impulse for each collision.
  

Notes

Don’t raise the Motion Sensor end of the track too high. The faster the cart moves, the more likely that it may move to one side or the other during the collision. A smooth but slow collision is better than a fast, jerky one.

If you do not have the Accessory Bracket with Bumpers, the experiment can still be performed. Leave the hook on the Force Sensor. Cut a small slit in a rubber stopper, and place the rubber stopper over the hook. Mount the Force Sensor to the cart and create a barrier at the end of the track for the stopper to hit. Make sure that only the stopper comes into contact with the barrier.

If velocity data does not correspond well to the Force Sensor data, try increasing the sample rate of the Motion Sensor. In the Home Screen, press F4 to open the ‘Sensors’ screen. Select the Motion Sensor icon and select the ‘Sample Rate’ menu.

Sample Data

The screenshot shows the Graph screen for one collision before the ‘Scale/Move’ tool is used to expand the horizontal axis.

Other screenshots show and example of velocity before and after a collision and the area under the curve of force versus time.

Fig. 2: Velocity before	Fig. 3: Velocity after
Fig. 4: Start of collision	Fig. 5: Area under curve

Lab Report – Activity 15: Impulse and Change in Momentum

Answers and Sample Data

Prediction

How does the change in momentum of a cart during a collision compare to the impulse during the collision?

The change in momentum of the cart will equal the impulse.

Data

Sketch a graph for one run of velocity versus time and force versus time. Include units and labels for your axes. (See Sample Data.)

Data Table

Item	Mass (kg)	Velocity, before (m/s)	Velocity, after (m/s)	Momentum, before (kg•m/s)	Momentum, after (kg•m/s)
1	0.221	0.66	-0.59	0.146	-0.130
2
3
4
5

Calculations

C
alculate the momentum before and the momentum after and find the change in momentum.

Compare the change in momentum (∆ momentum) to the impulse (area under the curve).

Calculate the percent difference of the change in momentum (∆mv) and the impulse.

Item	∆ Momentum (kg•m/s)	Impulse (N•s)	Percent Difference
1	0.276	0.287	0.3%
2
3
4
5

Questions

1. 
   Why does the velocity of the cart change from a positive value before the collision to a negative value after the collision?
   
   The positive value of velocity means that the cart is moving away from the Motion Sensor and the negative value means it is moving back toward the sensor after the collision.
   
   
   
2. 
   Why can you use the area under the curve of force versus time to get the value of the impulse?
   
   The area under the curve of force versus time is the product of the force and time; the definition of impulse.
   
   
   
3. 
   What are possible reasons why the change in momentum is different from the measured impulse?
   

There is a component of gravity that accelerates the cart when it is moving down the track and decelerates the cart when it is moving back up the track. In one direction, friction is against the component of gravity but in the other, friction is with the component of gravity. Therefore, there is a small external force that changes momentum but is not measured by the sensor.

4. 
   In general, how does the change in momentum compare to the impulse?
   
   In general, the change in momentum is very close to the impulse.
   
   
   
5. 
   Do your results support your prediction?
   
   Answers will vary.
   
   
   
6. 
   The units of momentum are kg•m/s and the units of impulse are N•s. Show how these two units are equivalent. (Hint: What is the definition of the newton, N?)
   

A newton is a kg•m/s². When this is multiplied by time measured in seconds, the product is kg•m/s. The unit of momentum is equivalent to the unit of impulse.

Introductory Physics with the Xplorer GLX © 2006 PASCO p.

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IntroPhys%20Teacher -> Teacher Notes – Activity 14: Momentum in Collisions

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