A block of mass m moves on a horizontal circle against the wall of a cylindrical room of radius R. The floor of the room on which the block moves is smooth but the friction coefficient between the wall and the block is μ. The block is given an initial speed u 0 . As a function of the speed u write (a) the normal force by the wall on the block, (b) the frictional force by the wall and (c) the tangential acceleration of the block. (d) Integrate the tangential acceleration to obtain the speed of the block after one revolution.

Question

Philoid · Accepted Answer

The normal reaction will be balancing the centrifugal force. Hence,

So, the normal reaction will be,

(b)

Friction force is at maximum as the body is moving,

Putting the value of N we get,

This will be the force of friction.

(c)

The only force changing the velocity will be friction. The friction is,

As the tangential acceleration will actually decrease the speed, so,

(d)

So, we can write,

For one complete revolution, s=2∏R. so,