For Problem 10.43

1. Conserve mechanical energy before the collision (explain why mechanical energy is conserved before the collision). Conserve momentum during the collision (explain why momentum is conserved during the collision). Extension: show that for this inelastic (sticking) collision, the kinetic energy after the collision is less than before, even though the momentum just before and just after the collision is conserved.
2. Conserve mechanical energy before the collision. In the very special case of an elastic collision, both momentum and mechanical energy are conserved for the collision.

For Problem 10.74: Transform your reference frame to be in the frame where the carts aren’t moving (imagine you are moving with the carts initially, like you are in a car moving at 1.0 m/s to the right, next to the carts). When the string burns through, both mechanical energy is conserved (explain why) and momentum is conserved (explain why). Use this to figure out the speed and direction of the two now separated carts. Then, transform back to the reference frame where the carts were moving initially to the right at 1.0 m/s.