Consider a homogeneous billiard ball of mass m and radius R that moves on horizontal table. Gravity acts downward. The coefficient of kinetic friction between the ball and the table is ?, and you are to assume that there is no work done by friction for pure rolling motion. At time ? = 0, the ball is struck with cue, which delivers a force pulse of short duration. Its impulse is ? = ∫-E+E F(t) dt a) The point of contact between the cue and the ball is at the “equator” and the direction of the force is toward the center of the ball. Calculate the time at which pure rolling begins. What is the final speed of the center of mass of the ball? b) At what height ℎ above the center must the cue strike the ball so that rolling motion starts immediately (see Figure)

Consider a homogeneous billiard ball of mass m and radius R that moves on horizontal table. Gravity acts downward. The coefficient of kinetic friction between the ball and the table is ?, and you are to assume that there is no work done by friction for pure rolling motion. At time ? = 0, the ball is struck with cue, which delivers a force pulse of short duration. Its impulse is ? = ∫-E+E F(t) dt a) The point of contact between the cue and the ball is at the “equator” and the direction of the force is toward the center of the ball. Calculate the time at which pure rolling begins. What is the final speed of the center of mass of the ball? b) At what height ℎ above the center must the cue strike the ball so that rolling motion starts immediately (see Figure)