Answer to Question #93478 in Mechanics | Relativity for Aya

Question

a small block of mass m slides along a friction less track as shown .calculate the height h at which mass must be released on the track to be able to go round the track or radius R .if h= 5R, what is the reaction exerted by the track on the block when it is at point A ,B and C

Answer 1

If we assume that there is no energy dissipation, according to law of conservation of energy, the block should start sliding from height

$$h>R.$$

Look closer at the situation: at the very beginning the block had potential and no kinetic energy:

$$E_{initial}=mgh+0.$$

That is why to go round that track with height $R$, block's final energy should include the same potential energy plus some kinetic energy to continue motion as it reaches height equal to the initial height:

$$E_{final}=mgR+KE.$$

Equate the energies:

$$mgh=mgR+KE,\\ h=R+KE,$$

or the height should be a little bit higher than the radius.

It is hard to discuss on reactions since there is no figure neither heights of the points A, B, and C. But what we can say is that you should use Newton's second law and since the block goes round a part of a circle, you should consider the centripetal force directed from the center of the circle to the block.