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.

1 Answer
Mar 29, 2018

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)