A 50 Kg box sits at rest on a 30 degree ramp where the coef of static friction is 0.5773. How hard would you have to push horizontally to get the box to start to move up the ramp?

Given data

m = 50 Kg

Weight (W) = 50*9.81 = 490.5 N

Coefficient of friction (μs) = 0.5773

Angle of ramp = 30 degrees

Determine the horizontal push (P) = ?

P cos Θ = W sin Θ + μs P sin Θ + μs W cos Θ

P (cos Θ - μs sin Θ) = W (sin Θ + μs cos Θ)

P = W (sin Θ + μs cos Θ) / (cos Θ - μs sin Θ)

P = 841.58 N

Harizontal push is required = 841.58