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 34 above the horizontal. The crate has mass 212 kg . You are sitting inside the crate (with a flashlight); your mass is 50 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 74 with the top of the crate.

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

Explanation / Answer

The string is inclined at angle 69-39 =30 to the vertical .
hence tan30 = a/g where a is the acceleration of the washer .
a = g*tan30

The acceleration of the crate down the plane is therefore A= a/cos 30 = g*tan 30 /cos30
= 6.21m/s^2

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