A block moves on a 45° rough inclined plane. The force required to just push it up the plane is 3 times the force required to just prevent it from sliding down. If N = 10μ, find N.
Physics · Newtons law of motion and Friction · friction and single block problem
JEE Mains

Question

A block moves on a 45° rough inclined plane. The force required to just push it up the plane is 3 times the force required to just prevent it from sliding down. If N = 10μ, find N.

G1 Physics · Accepted Answer

For θ = 45°, the force required to just push upward is Pᵤₚ = mg(sinθ + μcosθ), while the force required to just prevent downward slipping is Pₕ = mg(sinθ - μcosθ). Given Pᵤₚ = 3Pₕ, we get 1 + μ = 3(1 - μ), hence μ = 1/2 and N = 10μ = 5.