A mass M slides downward along a rough plane surface inclined at angle \\Theta\\

Question

A mass M slides downward along a rough plane surface inclined at angle Theta:= 27.21 in radians to the horizontal. Initially the mass has a speed V_0: = 4.43 m/s, before it slides a distance L = 1.0 m down the incline. During this sliding, the magnitude of the power associated with the work done by friction is equal to the magnitude of the power associated with the work done by the gravitational force. What is the coefficient of kinetic friction between the mass and the incline?

uk A mass M slides downward along a rough plane surface inclined at angle e 27.21 in radians to the horizontal. Initially the mass has a speed Vo 4.43 m/s, before it slides a distance L 1.0 m down the incline. During this sliding, the magnitude of the power associated with the work done by friction is equal to the magnitude of the power associated with the work done by the gravitational force. What is the coefficient of kinetic friction between the mass and the incline?

Explanation / Answer

wg = fg*l = mgsintheta*l

wf = fs*l = mue*n*l = mue*mgcostheta*l

if wg = wf

mgsintheta*l = mue*mgcostheta*l

mue = tantheta = tan27.21 = 0.514

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