Question

If a pushing force making an angle with horizontal is applied on a block off mass m placed on horizontal table and angle of friction is beta, then what is the minimum magnitude of force required to move the block ?

Answer 1

Let us first resolve the pushing force F. The vertical component is F sinβ and the horizontal component is F cos β.

The net normal reaction is, N = mg + F sinβ

The firctional force f is, f = µN = µ(mg + F sinβ)

Since, β is the angle of friction, so, µ = tanβ

Therefore, f = (tanβ)( mg + F sinβ)

The applied force will be able to move the block when the minimum force is,

F/ = f

=> F cos β = (tanβ)( mg + F sinβ)

=> F = (tanβ)( mg + F sinβ)/(cos β)