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 31^circ above the horizontal. The crate has mass 210 { m kg}. You are sitting inside the crate (with a flashlight); your mass is 57 { m 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 57^circ with the top of the crate.

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

Explanation / Answer

Mass of the crate is M = 210 kg Mass of the person is m = 57kg Mg cos31 - N = 0 -------1 Mg sin 31 - fK = 0 ----2 and f K = K N From eq 1, N = Mg cos 31 = (210 + 57) cos31 =228.8 From eq 2, fK = Mg sin 31 K N = Mg sin37 K (228.8) = 137.5 K = 137.5/228.8 K = 0.60

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