Problem

A small block of mass m is in contact with the inner wall of a large hollow cylinder. As...

A small block of mass m is in contact with the inner wall of a large hollow cylinder. Assume the coefficient of static friction between the object and the wall of the cylinder is μ. Initially,the cylinder is at rest, and the block is held in place by a peg supporting its weight. The cylinder starts rotating about its center axis, as shown in the figure, with an angular acceleration of α. Determine the minimum time interval after the cylinder begins to rotate before the peg can be removed without the block sliding against the wall.

Step-by-Step Solution

Solution 1

Step #1 of 6

THINK:

By determining the values of the angular speed of the cylinder, we calculate the minimum time interval after the cylinder begins to rotate before the peg can be removed. Here, the frictional force will be compensated by the gravitational force.

Step #2 of 6

SKETCH:

The situation of the problem is shown in the below figure.

Step #3 of 6

RESEARCH:

The frictional force acting on the block is given by the equation

Here is the coefficient of static friction between the object and the wall of the cylinder and the normal force () will be equal to the centripetal force (). Hence