^Oblique pull

^Oblique pull

Suppose a block of mass ‘m’ placed on a rough horizontal plane is pulled by a constant force F acting at an angle θ to horizontal,

let Fsinθ < mg, then,  N = mg – Fsinθ

Force needed to start the block moving is,

Fcosθ = f_L

Using law of friction the limiting friction is,

f_L = μ_S N

Combining above equations, we get,

Using tanα = μ_S, we get,

At θ = α, the force required to pull becomes minimum & given by