Question

The density of the sphere as a function of distance r from its center is given by The sphere has radius R = 1.00 × 10-2 m and mass m = 1.50 x 10-4 kg is given an initial impulse that results in an initial velocity of vo. Initially the ball is sliding without rolling on a horizontal surface that extends a distance L, but the surface has a friction coefficient of uk - 0.0600. After the distance L the horizontal surface transforms into a loop-the-loop with radius R 3.00 m. (a) What is the minimum initial velocity of the ball such that it begins to roll without slipping just before entering the loop-the-loop, and rolls all the way through the loop-the- loop without falling? Assume that the static friction coefficient in the loop-the-loop is sufficient for the sphere to roll through without starting to slip again. (b) What is the distance L that the sphere travels before entering the loop-the-loop? (c) If the value found for L above was doubled how much faster would the initial velocity of the ball need to be so that the normal force acting on the ball at the top of the loop-the-loop is 7.35 x 10-3 N

Answer 1