A steel washer is suspended inside an empty shipping crate from a light string a

Question

A steel washer is suspended inside an empty shipping crate from a light string attached to the top of the crate. The crate slides down a long ramp that is inclined at an angle of 33 above the horizontal. The crate has mass 159 kg . You are sitting inside the crate (with a flashlight); your mass is 54 kg . As the crate is sliding down the ramp, you find the washer is at rest with respect to the crate when the string makes an angle of 61 with the top of the crate.

What is the coefficient of kinetic friction between the ramp and the crate?

Explanation / Answer

On steel Washer:

along the incline,

mgsin33 - Tcos61 = ma

perpendicular to the incline,

Tsin61 = mgcos33

T = 0.96mg

putting in previous eqtn

mgsin33 - 0.96mg cos61 = ma

a = 0.783 m/s^2

Now in crate:

perpendicular to the incline,

N = Mgcos33

friction force = u N = u Mg cos33

along the incline,

Mgsin33 - f = Ma

Mgsin33 - u Mgcos33 = 0.783 M

sin33 - ucos33 = 0.783/9.81

u = 0.55

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