Question

A body of mass 2kg slides down with acceleration of 3m/s2 on a rough inclined plane having a slope of 30°. The external force required to take the same body up the the plane with same acceleration will be?

Answer 1

mass of the body , m = 2kg
acceleration of body in downward direction, a = 3m/s²
inclined angle , $\theta=30$
Let coefficient of friction is u .

if body moves downward , friction force acts upwards direction.
so, net force = $mgsin\theta-umgcos\theta$
a = gsin30° - ugcos30°
3 = 10 × 1/2 - u × 10 √3/2
-2 = u × 5√3
u = 2/5√3

now, if body moves upward with acceleration 3m/s² , frictional force acts downward direction. Let required external force is F.

so, F - mgsin30° - umgcos30° = ma

or, F = ma + mgsin30° + umgcos30°

or, F = 2 × 3 + 2 × 10 × 1/2 + 2/5√3 × 2 × 10 × √3/2

or, F = 6 + 10 + 4 = 20N

hence, required force is 20N