Slide physics need help Please

Question

1. A block of mass m slides down a frictionless ramp that becomes a circular loop of radius R. What must be the initial height h of the block above the ground for the centripetal force on the block at the top of the loop to be twice the weight of the block? (Notice that this is the centripetal force, not the net force.) Hint: The centripetal force on the block is given by Fc = mv2/R.

2. A block of mass M, initially at rest, falls from a height y onto the end of a uniform thin rod of length L and also of mass M that is pivoted through its center of mass, perpendicular to its length; the pivot is frictionless. If the block comes to a (momentary) stop after hitting the rod, find the resulting angular velocity of the rod.

Answer 1

1.

Let the blocks initial height is h:

At the top of the loop height is 2*R

Conservation of energy:

m*g*h=m*g*(2*R)+.5*m*V^2

solve for V^2  (1)

At the top of the loop:

Fc=2*m*g=m*V^2/R (2)

substitute V^2 to eq. (2) from eq. (1)

and solve for h