A 280 kg piano slides 4.4 m down a 30° incline (with respect to the horizontal d

Question

A 280 kg piano slides 4.4 m down a 30° incline (with respect to the horizontal direction) and is kept from accelerating by a man who is pushing back on it parallel to the incline. The effective coefficient of kinetic friction is 0.40.

(a) Calculate the force exerted by the man.

______ N

(b) Calculate the work done by the man on the piano.

_______ J

(c) Calculate the work done by the friction force.

_______ J

(d) What is the work done by the force of gravity?

_______ J

(e) What is the work done by the normal force on the piano?

_______ J

(f) What is the net work done on the piano?

________ J

Explanation / Answer

a) F = mgsin(30)-umgcos(30) = 280*9.8*0.5-0.40*280*9.8*0.866 = (1372-950.52) = 421.48 N towards upwards slope

b) W = F*X = -421.48*4.4 = - 1854.51 J (-tive as force is opposite to displacement)

c) Wf = umgcos(30)*X = -0.40*280*9.8*0.866*4.4 = -4182.29 J ( -tive as ( as force is opposite to displacement)

d) Wg = mgsin(30)*X = 280*9.8*0.5 = 6036.8 J

e) Wnormal = 0

f) Wnet = 0

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