Question

A small, 200-g collar D can slide on portion AB of a rod which is bent as shown. Knowing that the rod rotates about the vertical ACat a constant rate and that α = 30° and r = 600 mm, determine the range of values of the speed v for which the collar will not slide on the rod if the coefficient of static friction between the rod and the collar is 0.30.

Fig. P12.56

Answer 1

Given

The mass of the collar D,

The angle,

The static friction between the rod and the collar,

Now assuming that the impending motion is in the downward direction

We know that

Acceleration

By the equilibrium condition

Substituting the known expressions, we get

Now, by the equilibrium condition

Substituting the known expressions

Now, we know that

Substituting the known expressions in the equation (1), we get

By simplifying, we get

Now assuming that the impending motion is in the upward direction

By the equilibrium condition

Substituting the known expressions, we get

By the equilibrium condition

Substituting the known expressions

Now, we know that

Substituting the known expressions in the equation (2)

By simplifying, we get

Therefore, the range of speed is