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)#