For this problem, cart A is given an initial velocity towards a stationary cart B. Velcro at the end of each cart allow the carts to stick together after the collision.
1. Draw two pictures, one showing the situation before the collision and the other one after the collision. Is it reasonable to neglect friction? Draw velocity vectors on your sketch. Define your system. If the carts stick together, what must be true about their final velocities?
2. Write down the momentum of the system before and after the collision
3. Write down the energy of the system before and after the collision
4. Which conservation principle (energy or momentum) should you use to predict the final velocity of the stuck-together carts? Do you need both? Why? Write your equation for final velocity in terms of the cart masses and initial velocity of cart A
5. Write an equation for the efficiency of the collision in terms of the final and initial kinetic energy of the carts, and then in terms of the cart masses and their initial and final velocities. Combining this efficiency equation with the final velocity found in question 4, what does variables does your efficiency depend on?
Prediction
Consider the three cases described in the problem, with the same total mass of the carts for each case (ma + mB=constant).
Calculate the final velocity of the combined carts for each case.
Rank the collisions from most efficient to least efficient. Use your calculations to determine which collision will cause the most damage.
