Question

Find the force required to move a load of 300 N up a rough plane, the force being applied
parallel to the plane. The inclination of the plane is such that when the same load is kept
on a perfectly smooth plane inclined at the same angle, a force of 60 N applied at an
inclination of 30° to the plane, keeps the same load in equilibrium. Assume coefficient of
friction between the rough plane and the load to be equal to 0.3

Answer 1

Explanation:

Let the max friction be f

Case 1: body is just about to move up

friction and gravitational force will act in downward direction so

2F=mgsinθ+f                  ...1

Case 2; body is just prevented to slip

Friction will act upwards and gravitation will act downwards

F=mgsinθ−f                    ..2 

Using equation 1 and 2

mgsinθ−3f=0

max friction=μmgcosθ

∴mgsinθ=3μmgcosθ

∴tanθ=3μ

θ=tan−13μ