5.4 Cons of Linear Momentum

Impulse:

1. From the data in the data table, 

   1. Determine the change in velocity (Δv) for each cart during the collision. 

   2. Given the mass of each, calculate the impulse experienced by each cart. 

   3. How do the impulses compare?

2. To the right is a graph of the force acting on Cart A during the collision. Sketch the force acting on Cart B.

3. The area under the force vs. time curve represents the impulse. How does the impulse on Cart A compare to the impulse on Cart B? Why?

4. Using the force vs. time graph, calculate the impulse (J=F⋅Δt) for Cart A. How does this relate to the change in momentum for Cart A? What can you infer about Cart B's change in momentum based on your sketched graph?

Conservation of Momentum:

5. Given the masses of the two carts (m_1​ and m_2​), calculate the momentum of each cart before and after the collision. Verify that the total momentum is conserved.

Conservation of Energy

6. Using the velocities before and after the collision, calculate the total kinetic energy of the system. How does it compare before and after the collision? If kinetic energy is not conserved, how might the "lost" energy be accounted for?

7. Based on the final velocities of the carts after the collision, is this collision elastic, inelastic, or perfectly inelastic? Justify your answer.

8. Identify the time interval during which the collision occurs. What does the steepness of the velocity changes tell you about the magnitude of the forces involved?

9. Without knowing the mass of each cart, propose a method to determine if the total momentum is conserved using only the velocity vs. time graph.