A large sphere was built, with a radius of about 5. Imagine that such a sphere has a radius "R" and a frictionless surface. A small block of mass "M" slides starts from rest at the very top of the sphere and slides along the surface of the sphere. The block leaves the surface of the sphere when it reaches a height "H(critical)" above the ground.
Using Newton's 2nd law, find v(critical), the speed of the block at the critical moment when the block leaves the surface of the sphere.
Assume that the height at which the block leaves the surface of the sphere is H(critical).
Express the speed in terms of R, H(critical), and g (the magnitude of the accleration due to gravity). Do not use (theta) in your answer.
The Attempt at a Solution
I know that the moment that the block leaves the surface of the sphere the normal force will equal 0, so when this happens the gravitational force (it's radial component) will be the only force causing centripetal acceleration.
To find the radial component I decomposed the vector and found that the radial component of the gravitational force was "M*g*sin(theta)". Since the centripetal acceleration of the block at a speed v is (v^2)/R, I thought I could simply set them equal to eachother and then solve for v. This gave me an answer of sqrt(M*g*R*sin(theta))=v. But I cannot use theta or M in my answer, I tried to set up a right triangle to relate sin(theta) to R and H(critical), I found that sin(theta) was equal to h(of block)/R however the computer program I use to submit my answers is telling me I'm off by an additive constant. I cannot think of a way to express sin(theta) in only terms of h and R. Also if I did manage to get past that I am unsure of how I would be able to get rid of M (express it in other terms).
I think I might be on the wrong track with this one.