A 5 kg mass slides down a frictionless slope starting from 18 m above the ground

Question

A 5 kg mass slides down a frictionless slope starting from 18 m above the ground. It then slides over a horizontal rough patch 2 m in length with an unknown coefficient of kinetic friction. it then falls another 7 m before sliding into a spring with spring constant 1.65 kN/m. The spring is compressed by 1.2 m before stopping the mass.

What is the coefficient of kinetic friction? ( draw a piucture, a FBD, and break down any off axis vectors into components)

Thanks for the help. It is greatly appreciated.

Explanation / Answer

initial energy = mgh

initial energy = 5 * 9.8 * (18 + 7)

final energy = 0.5 * k * x^2

final energy = 0.5 * 1.65 * 10^3 * 1.2^2

difference in initial and final energies = energy lost in patch due to friction

5 * 9.8 * (18 + 7) - 0.5 * 1.65 * 10^3 * 1.2^2 = k * 5 * 9.8 * 2

coefficient of kinetic friction k = 0.377

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