Question

a block slides down a frictionless ramp. at the bottom of the ramp is a vertical circular loop with a radius of 75 cm. from what minimum height does the block need to be released in order to make it around the loop?

Answer 1

let h be the height of the release.
Then h-2r is the altitude of the top of the loop.
Initial PE=finalPE+final KE
mgh=mg( 2r)+1/2 m v^2

but v^2/r= g to keep it at the top of the loop.

mgh= 2mgr+1/2 mg*r

h= 2r+1/2 r=2.5 r

check my math.