Question

A small block slides down a frictionless track whose shape is described by y = x2/d for x<0 and y=-x2/d for x>0. The value of d is .600 meters, and x and y are measured in meters as usual.

(a) Suppose the block starts from rest on the track, at x = -200 meters. What will the block’s speed be when it reaches x = 0?

(b) Suppose the block starts on the track at x = 0 and is given an initial velocity of .640 m/s to the left. The block then begins to slide up the track to the left. At what value of x will the block turn around and begin to slide down again?

(c) Now suppose the blocks starts on the track at x = 2.200 m. The block is given a push to the left and begins to slide up the track, eventually reaching its maximum height at x = 0, at which point it turns around and begins sliding down. What was its initial velocity in this case?

(d) Suppose the block starts on the track at x = 0. What minimum initial velocity (moving to the right) must the block have such that it will leave the track at x = 0 and go into freefall?

e)You start the block on the track at rest, somewhere to the left of x = 0. You then release the block from rest and let it slide down. What is the maximum value of x from which you can release the block from rest and have it leave the track at x = 0 and go into freefall?

Answer 1