Question

A bead of mass `m` can slide on a thin vertical rod,with sliding coefficient `mu =0.4`.The rod is translated horizontally with a constant acceleration of `a`. QUESTION below.?

For what value of `a` will an observer on earth see equal horizontal and vertical components of acceleration of the bead.

Answer 1

`a = g/(1+mu) = g/1.4 = 7" ms"^-2`

Explanation:

The forces acting on the bead are

• the normal force `N` exerted on it by the rod in the horizontal direction.
• its weight `mg` in the vertically downward direction
• the force of sliding friction `mu N` vertically upward.

The bead has acceleration components of `a` in both the horizontal and vertical direction.

Thus, Newton's second law takes the form

`N = ma`
`mg-mu N = ma`

This implies that

`mg - mu ma = ma implies (1+mu) ma = mg`

Hence `a = g/(1+mu)`