There is a crate with a mass of 200 kg on a ramp going down to the ground. The angle the ramp makes with the ground is 30 degrees. The crate does not slide down the ramp but is held in place by the force of static friction. Calculate the coefficient of static friction between the ramp and the crate by assuming that the coefficient is the minimum coefficient needed to keep the crate from sliding.

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## Answers (1)

so in this case, we state that the friction force equals the gravitational force.

Ff - Fg = 0

Ff = Cf * Fn (since the crate is on a slope Fn = mg*cos 30)

Fg = mg sin 30

solve for Cf

Cf = mg sin 30 / mg cos 30 = tan 30 = 1/3^0.5 -> 0.58