Measurements of velocity and mass of two objects colliding, support the conservation of linear momentum. The dynamics of different masses distinguish velocity values experimentally. Video recordings of two colliding masses can be manipulated to extract frames displaying distance verses time. Computer software enables us to derive the velocity. Different masses were tested to determine an increase, decrease, or equal
effect. From this data, we ultimately derive the momentum of each cart and test the Law of Linear momentum. The following trials were measured:
1. An elastic collision with a cart moving at constant speed with a cart of
equal mass originally at rest;
2. An elastic collision with a car moving at constant speed and a cart of
one-third the mass originally at rest.
3. An elastic collision with a cart of three times the mass originally at
4. An inelastic collision with a cart moving at constant speed and a cart
of two times the mass originally at rest.
*two carts of equal mass
*two 500g weight blocks
1. Set-up camera according to the correct settings noted in 3.4 (pp. 19)
2. Establish four points of reference visible in the camera frame. Place
the initial motionless cart at the second reference point from the end
opposite of the oncoming cart. Record an elastic collision with a
cart moving at constant speed with a cart of equal mass originally at rest.
3. Save the video (refer to 3.4 pp.19 for instructions).
4. Open video point to begin analysis of the motion (3.4.1 pp. 19-20).
5. Construct a distance vs. time graph, and a velocity vs. time graph for
(A) the cart in motion before the collision (B) the cart(s) in motion after
the collision. Three sets of the distance and velocity graphs may
6. On the velocity vs. time graph, find the average velocity; click the F
button on the top right-hand side of the graph and select average. Print
both graphs – distance, velocity.
7. Repeat this procedure from the step number two for the entire four scenarios.
8. The mass of each cart is 500 grams. The mass of each block is 500 grams.
In the first scenario, with both masses equal, momentum is virtually conserved with a P of 0.0035kgm/s. The second scenario contains a cart three times the mass as the other. Our information concludes that P equals 0.0735 as the initial cart continues in the same direction after collision. So far our measurement supports the law of momentum conservation. The third scenario involves the opposite mass components of the second scenario; the initial mass in motion is one-third the mass of the motionless cart. The P is -0.1655kgm/s as the original moving mass changes direction after collision. The collision in the fourth scenario is inelastic. The components stick together and have the same ending velocity although starting masses were different; the cart at rest is one-half the mass of the cart moving towards it. The resulting P equals -.3013kgm/s. This indicates a large difference in the initial momentum verses the final momentum. In the video, the two carts came to rest 20cm from collision.
The experimental results vary in accuracy according to the theoretical results. In an elastic collision, one expects the momentum to be conserved. However, we found our P off by a range of 0.0035kgm/s to -0.1655kgm/s. We found this error partially due to the points that were graphed. Some exceeded the range of motion that was needed to calculate. The other margin of error may be due to the small distance between the reference points. In the inelastic collision, energy is lost, perhaps to thermal energy. This might explain the large P.