Procedure Momentum, Energy, Collisions

Momentum, Energy, and Collisions (Motion Detector)

Momentum, Energy, and Collisions (Motion Detector)

Graphical Analysis 18

Momentum, Energy, and Collisions

(Sensor Cart)

The collision of two carts on a track can be described in terms of momentum conservation and, in some cases, energy conservation. If there is no net external force experienced by the system of two carts, then we expect the total momentum of the system to be conserved. This is true regardless of the force acting between the carts. In contrast, energy is only conserved when certain types of forces are exerted between the carts.

Collisions are classified as elastic (kinetic energy is conserved), inelastic (kinetic energy is lost) or completely inelastic (the objects stick together after collision). Sometimes collisions are described as super-elastic, if kinetic energy is gained. In this experiment, you can observe elastic and inelastic collisions and test for the conservation of momentum and energy.

Figure 1

objectives

· Observe collisions between two carts, testing for the conservation of momentum.

· Measure energy changes during different types of collisions.

· Classify collisions as elastic, inelastic, or completely inelastic.

Materials

Chromebook, computer, or mobile device

Graphical Analysis 4 app

two Go Direct Sensor Carts with magnetic and hook-and-pile bumpers

Vernier Dynamics Track

Preliminary questions

1. Consider a head-on collision between two identical billiard balls. Ball 1 is initially in motion toward ball 2, which is initially at rest. After the collision, ball 2 departs with the same velocity that ball 1 originally had. Disregard any friction between the balls and the surface. What happens to ball 1? What happens to ball 2?

2. Sketch a position vs. time graph for each ball in Preliminary Question 1, starting with the time before the collision starts and ending a short time after the collision.

3. Based on your graph from Preliminary Question 2, is momentum conserved in this collision? Is kinetic energy conserved?

Procedure

1. Set up the Sensor Carts.

a. Insert the hook-and-pile pads so they will be facing each other when both +x arrows are pointing to the right.

b. Measure the masses of the carts and record the values in Table 1.

c. Label the carts as cart 1 (cart 1 = G) and cart 2 (cart 2 = Y).

2. Set up the Dynamics Track so that it is horizontal. Test this by releasing a cart on the track from rest. The cart should not move.

3. Connect to the data-collection software and reverse the coordinate system for one cart.

a. Launch Graphical Analysis.

b. Connect the Sensor Carts to your Chromebook, computer, or mobile device.

c. To reverse the coordinate system for one cart, click or tap the Position meter for the second cart and select Reverse.

4. Practice creating a gentle collision: Position cart 2 at rest in the middle of the track. Release cart 1 so it rolls toward cart 2 with the . The carts should collide, stick together, and roll together.

5. Click or tap Collect to start data collection. Repeat the collision you practiced and use the position graphs to verify that the carts are recording throughout the entire range of motion.

6. Place the two carts at rest in the middle of the track, with their hook-and-pile bumpers toward one another and in contact. Zero both sensors by clicking or tapping each Position meter and choosing zero. This procedure will establish the same coordinate system for both sensorsVerify that the zeroing was successful by starting data collection and allowing the still-linked carts to roll slowly along the track. The graphs for each cart should be nearly the same. If not, repeat the zeroing process.

Part I  Hook-and-pile bumpers

7. Reposition the carts as in Step 4. Click or tap Collect to begin taking data and repeat the collision.

(both with Velcro and cart 2 at rest)

8. From the velocity graphs, you can determine a mean velocity before and after the collision for each cart. To measure the mean velocity during a time interval, select the data in the interval. Click or tap Graph Tools, , and choose View StatisticsRecord the mean value, and then dismiss the Statistics box. Measure the mean velocity for each cartbefore and after collision, and enter the four values in Table 2.

9. Repeat Steps 7–8 to collect a second run with the hook-and-pile bumpers. Note: The previous data set is automatically stored (See video)

Part II  Hook-and-pile to empty bumpers

10. Remove the hook-and-pile inserts from one cartMeasure the mass of this cart and record it in Table 1. The other cart’s mass should stay the same.

 

 (Only one cart with Velcro and cart 2 at rest)

11. Face the hook-and-pile bumper on one cart to the empty bumper on the other. Practice this collision, again starting with cart 2 at restThe carts will not stickbut they will not smoothly bounce apart either.

12. Click or tap Collect to start data collection and repeat the new collision. Use the procedure in Step 8 to measure and record the cart velocities in Table 2.

13. Repeat the previous step to collect a second run with the hook-and-pile to empty bumpers.

Part III  Magnetic bumpers

14. Insert magnets into both carts, set so the carts will repelMeasure the masses of the carts and record in Table 1.

15. Place the carts on the track with the magnetic bumpers facing each other. Practice making this new gentle collision, again starting with cart 2 at rest. The carts should smoothly repel each other without physically touching.

16. Click or tap Collect to start data collection and repeat the collision you practiced in Step 15. Use the procedure in Step 8 to measure and record the cart velocities in Table 2.

17. Repeat the previous step as a second run with the magnetic bumpers.

Data Table

Table 1 2 (cart 1 = G , cart 2 = Y)
Part Mass of cart 1 (kg) Mass of cart 2 (kg)
I 0.2925 0.2925
II 0.2925 0.2925
III 0.2925 0.2925

 

Table 2 (cart 1 = G , cart 2 = Y)
Bumper type Run number Velocity of cart 1 before collision (m/s) Velocity of cart 2 before collision (m/s) Velocity of cart 1 after collision (m/s) Velocity of cart 2 after collision (m/s)
Part I: Hook-and-pile 1 0.169 0  0.070  0.070
  Hook-and-pile 2        
Part II: Mixed 3        
  Mixed 4        
Part III: Magnetic 5        
  Magnetic 6      

 

Table 3 2 (cart 1 = G , cart 2 = Y)
Run number Momentum of cart 1 before collision (kg•m/s) Momentum of cart 2 before collision (kg•m/s) Momentum of cart 1 after collision (kg•m/s) Momentum of cart 2 after collision (kg•m/s) Total momentum before collision (kg•m/s) Total momentum after collision (kg•m/s) Ratio of total momentum after/before
1   0          
2   0          
3   0          
4   0          
5   0          
6   0          

 

Table 4 2 (cart 1 = G , cart 2 = Y)
Run number KE of cart 1 before collision (J) KE of cart 2 before collision (J) KE of cart 1 after collision (J) KE of cart 2 after collision (J) Total KE before collision (J) Total KE after collision (J) Ratio of total KE after/before
1   0          
2   0          
3   0          
4   0          
5   0          
6   0          

Analysis

1. For each run, determine the momentum (mv) of each cart before the collision, after the collision, and the total momentum before and after the collision. Calculate the ratio of the total momentum after the collision to the total momentum before the collision. Enter the values in Table 3.

2. For each run, determine the kinetic energy (KE = ½mv2) for each cart before and after the collision. Calculate the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision. Enter the values in Table 4.

3. If the total momentum for a system is the same before and after the collision, we say that momentum is conserved. If momentum were conservedwhat would be the ratio of the total momentum after the collision to the total momentum before the collision?

4. If the total kinetic energy for a system is the same before and after the collision, we say that kinetic energy is conserved. If kinetic energy were conserved, what would be the ratio of the total kinetic energy after the collision to the total kinetic energy before the collision?

5. Inspect the momentum ratios in Table 3. Even if momentum is conserved for a given collision, the measured values may not be exactly the same before and after due to measurement uncertainty. The ratio should be close to one, however. Is momentum conserved in your collisions?

6. Repeat the preceding question for the case of kinetic energy, using the kinetic energy ratios in Table 4. Is kinetic energy conserved in the magnetic bumper collisions? How about the hook-and-pile collisions? Is kinetic energy conserved in the third type of collision? Classify the three collision types as elastic, inelastic, or completely inelastic.

Extensions (VOID)

1. Using the magnetic bumpers, consider other combinations of cart mass by adding weight to one cart. Is momentum or energy conserved in these collisions?

2. Using the magnetic bumpers, consider other combinations of initial velocities. Begin with having both carts moving toward one another initially. Are momentum and energy conserved in these collisions?

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