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 36 above the horizontal. The crate has mass 169 kg . You are sitting inside the crate (with a flashlight); your mass is 70 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 70 with the top of the crate. What is the coefficient of kinetic friction between the ramp and the crate?

Explanation / Answer

Newton's II law:

Fsultant = ma

if the crate were at rest on the incline the string would make an angle of 54° with the crate top surface.

therefore for equilibrium of the washer normal to the incline surface:

=> Tsin70° = mgcos36°

or T = 0.861m(9.81) = 8.446m N

also the common acceleration 'a' of the crate and washer along the incline = gsin36° - gcos36°

also along the incline surface for a neutral ground observer:

Tcos70° = mg[sin36° - cos36°]

8.446cos70° = g[sin36° - cos36°]

2.8886 = 5.766 - 7.936

=> 7.936 = 2.8777

=> = 0.363 = coefficient of kinetic friction between the ramp and the crate

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