In the figure, a block of mass M slides without friction around the curved track

Question

In the figure, a block of mass M slides without friction around the curved track. (a) If the block starts from rest at A, what is its speed at B? (b) What is the force of the track (the normal force) on the block at B?

I'm stuck on question B? Do I have to go in the direction of taking the derivative of Work?

In the figure, a block of mass M slides without friction around the curved track. (a) If the block starts from rest at A, what is its speed at B? (b) What is the force of the track (the normal force) on the block at B? I'm stuck on question B? Do I have to go in the direction of taking the derivative of Work?

Explanation / Answer

Use mechanical energy of block is conserved :

a) KA + UA = KB + UB

0.5mvA2 + mghA = 0.5mvB2 + mghB         with vA = 0

g(4R) = 0.5.vB2 + g(R)

vB = (6gR)

b) Normal force on B act as a centripetal force so :

NB = m.vB2/R = m.(6gR)/R = 6mg

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