2-5. A block of kg rests on a horizontal platform at a distance of m from the center of the platform. The angular motion of the platform is slowly increased so that the block’s tangential acceleration of the block is negligible. The coefficient of static friction between the block and the platform follows a normal distribution . Determine the probability that the block will slip off the platform when its speed is .

Solution

Referring to the free-body diagram of the block, we have

When the block is on the verge of slipping,

The block will slip off the platform when

Let

Therefore,

Ans.