A Few Problems . . .

1. A box slides down a semi-circular ramp of radius R, coming to rest exactly at the bottom. Determine the coefficient of kinetic friction between the box and the ramp.

2. Two heavy blocks (mass M) are placed on a frictionless table. A small mass (mass m) is then symmetrically placed in the middle and given an initial speed v towards one of the heavy blocks. Assuming all collisions are totally elastic, determine the asymptotic speed of the heavy blocks after an infinite number of collisions.

3. A metallic sphere of radius R is given a charge Q. A second identical, but uncharged sphere is immediately brought up next to the first one a distance 3R away. Find the spatial and temporal-dependence of the charge distribution on the second sphere.