use Motion Sensors to measure the motion of two carts in a variety of collisions.
use the Xplorer GLX to record and display the velocity for each cart.
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 each cart in each collision.
calculate the total momentum before and the total momentum after each collision.
compare the momentum before and the momentum after for each collision.
Notes
For more information about this activity, refer to the following page on the PASCO Web site:
Students may ask how they can measure momentum in ten different types of collisions. Remind them that they can change the mass of each cart, change the speeds, and change whether the carts ‘bounce’ or ‘stick together’.
Sample Data
The screenshots show the Graph displays of velocity versus time for one collision.
How would you calculate the total momentum for two carts that are about to collide?
Answers will vary. To calculate the total momentum for two carts that are about to collide, calculate the momentum for each cart and combine the two. Note that if carts are moving in opposite directions, the velocity of one of the carts is negative.
How will the momentum of two carts after they collide compare to the momentum of the two carts before the collision?
Answers will vary. The total momentum of two carts after a collision will equal the momentum of the two carts before the collision (if the net external force is zero).
Data
Sketch a graph for one run of velocity versus time. Include units and labels for your axes. (See Sample Data.)
Data Table 1
Cart 1
Cart 2
Before
After
Item
Mass (kg)
Mass (kg)
Velocity, cart 1 (m/s)
Velocity, cart 2 (m/s)
Velocity, cart 1 (m/s)
Velocity, cart 2 (m/s)
1
0.239
0.253
0.25
-0.41
-0.42
0.23
2
3
4
5
6
7
8
9
10
Calculations
Calculate the total momentum before and the total momentum after for each collision.
Item
Momentum Before (kg•m/s)
Momentum After (kg•m/s)
1
-0.0439
-0.0422
2
3
4
5
6
7
8
9
10
Questions
In general, how does the momentum after a collision compare to the momentum before the collision?
Answers will vary. In general, the momentum after a collision will be close to–but probably less than–the momentum before the collision.
In which type of collision was the before-and-after difference in momentum the least? In which type of collision was the difference the most?
Answers will vary.
What factors might cause the total momentum after a collision to not equal the total momentum before the collision?
Friction, misalignment of the carts during collision, and uncertainty in the measurement of mass are some examples of factors that might cause the momentum after to not equal the momentum before.
For a theoretical head-on collision between two carts of equal mass and equal speed, what is the total momentum before the collision?
For a head-on collision between two carts of equal mass and equal speed, the total momentum before the collision is zero.
Discuss the momentum of a firecracker at rest compared to the momentum of the firecracker after it explodes.
The momentum of a firecracker at rest is zero. The momentum of all the fragments of the firecracker after it explodes is also zero.
Imagine two carts, one with twice the mass of the other, that are going to have a head-on collision. In order for the two carts to be at rest after the collision, how fast must the less massive cart move compared to the more massive cart?
For two carts to be at rest after collision, their total momentum before collision would be zero. For that to happen when one cart is half as massive as the other, it must have twice the speed of the more massive cart.