Physics complex reasoning question.?

Question

A block on a loop-the-loop slides without friction. The radius (R) of the loop is 2.5m and the point (B) is the highest position of the loop. If the block starts from a sufficent height (h), it will exert a force (F) to the track when it comes to (B). Find the height (h) when the force (F) is equal to the block's weight.

Answer 1

The centripetal force is m*v^2/r
this must oppose the force of gravity
m*g
so v^2=r*g

using conservation of energy, the difference in the potential energy from the starting height, h,
and the top of the loop is
h-2*r

and
m*g*(h-2*r)=.5*m*v^2
or v^2=g*2*(h-2*r)

from above
r*g=g*2*(h-2*r)
r=2*h-4*r
5*r/2=h

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