Momentum Conservation and Collisions Lab Report #3

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Apr 30, 2024

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Momentum Conservation and Collisions Lab Sophia Tran November 17th, 2023 Physics 1301W, Professor: Dr. Dan Cronin-Henessey, TA: Evan Skinner Abstract In this experiment, the purpose was to explore the conservation of energy within inelastic collisions. The scientists tested this by using a moving cart that collides with a mass and then collecting data on the velocities of the carts after the collisions. The result for the velocity ratio vs mass was 0.588x 土 2.188. The result for the kinetic energy vs mass was 0.518x 土 4.518. The conclusion is that momentum is conserved in inelastic collisions. Introduction Hypothetically, scientists want to analyze an inelastic car accident. They want to know the initial velocity of the incoming car and how the collision accident affected it. Scientists model this by using two carts with masses and colliding them. The carts have velcro that keeps the collision inelastic. Prediction These scientists used conservation of momentum to derive the initial equation/expected trend for the velocity ratio vs mass. They predicted the slope of this trend to be 1 divided by the total mass of the two carts. Our prediction was 0.663. This predicted value represents the amount of momentum that was conserved when the two carts collided. This value is the same value that they would get for the kinetic energy vs mass.

Procedure Push a cart with a mass so that it collides with a stationary cart with a prerecorded mass. Record it and analyze the motion using Vernier Video Analysis. Repeat with different masses, although keeping the total mass identical throughout every trial. Position uncertainty will be the smallest increment on the meter stick. The velocity uncertainty will be position uncertainty divided by Δt. The velocity ratio uncertainty will be the maximum of: The kinetic energy ratio uncertainty will be: Errors during data collection, negligence of friction, and unaccounted-for air resistance can affect the accuracy of the results.

Analysis (Figure 1) Velocity Ratio vs Cart 1 Mass graph. The slope is 0.588 土 2.188. (Figure 2) Kinetic Energy vs Cart 1 Mass graph. The slope is 0.518x 土 4.518.

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In Figure 1, we can see that the result is 0.588 土 2.188. Our prediction of 0.663 is correct because it fits within the uncertainty. Figure 2 gives us the result of 0.518x 土 4.518. Our prediction of 0.663 is correct because it fits within the uncertainty. A big factor that could have skewed the results is the scientists not accounting for friction, as friction increases it causes momentum to decrease. Another couple of error factors could be inaccurate point analysis from Vernier and negligence of air resistance. Hypothetically, if the scientists wanted to know the velocity of the incoming car, they could use the conservation of momentum to figure out the velocity, but they would have to include friction in their calculations. Conclusion Scientists tried to find if momentum is conserved in inelastic collisions. They tested this by having two carts collide with different masses and tracking their velocities. The result for the velocity ratio vs mass was 0.588x 土 2.188. The result for the kinetic energy vs mass was 0.518x 土 4.518. The conclusion is that momentum is conserved in inelastic collisions. Both values were within the uncertainty of the prediction. Scientists can use the conservation of momentum to figure out the velocity of an incoming vehicle in the aftermath of a collision.

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