Circular Motion and block track

[interxavier]

Homework Statement

A frictionless track contains a circular section of radius R as shown. What is the minimum height at which a block must be started in order for it to go around the loop without falling off the track?

Homework Equations

V = r*w
Fr = m*v^2/r = m*r*ω^2

The Attempt at a Solution

I'm sorry I don't have the diagram but you can draw the equation yourselves. I'm considering using the conservation of energy in this problem, but I don't know if it's proper way.

So initially we have:
Ei = 1/2*m*v^2 + m*g*h = 0 + mgH
Ef = 1/2*m*v^2 + m*g*h = 0 + 2mgR

 

[clamtrox]

In particular, you know that the block falls off the track if its speed drops to zero (I'd imagine), and that the speed of the block is the same whenever it's on a given height H.

 

[Doc Al]

I'm considering using the conservation of energy in this problem, but I don't know if it's proper way.

You'll need conservation of energy, but that's not all.

The key to this problem is that there is a minimum speed at the top of the track below which the block will lose contact. (That speed is not zero.) To find that speed, analyze the forces acting and apply Newton's 2nd law.