1. A train, of massm, comes into a station travelling slightly too fast to stop in time before it hits the buffers at the end of the track. The buffers are effectively metal plates attached to a spring which obeys Hooke's law with a spring constantk. The trains wheels lock and it skids along the horizontal rails with sparks flying so that at the point that the train first touchs the buffers it has a speedv. If the maximum compression of the spring in the buffers is 1m what is the minimum coefficient of kinetic friction between the locked wheels of the train and the rails for the buffers to be able to stop it given that the gravitational field isg?

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2. [Difficult] Quarks are the particles that make up the proton and neutron inside an atomic nucleus. For a particular choice of units (not SI) the attractive force between two quarks is given by the equation:

where is a constant and is the separation between the quarks. If the potential energy, U, of the quarks is zero at equilibrium what is their potential energy as a function of ?

For this particular question, I indefinitely integrated to find:

This is partially correct, but for some reason I cannot solve for the constant of integration. Even when I set U=0, it doesn't make sense.Any help is greatly appreciated.