A loaded penguin sled with weight W rests on a plane inclined at angle ? to the

Question

A loaded penguin sled with weight W rests on a plane inclined at angle ? to the horizontal (see figure). Between the sled and the plane, the coefficient of static friction is µs, and the coefficient of kinetic friction is µk. (Use any variable or symbol stated above as necessary.)

(a) What is the minimum magnitude of the force , parallel to the plane, that will prevent the sled from slipping down the plane?

(b) What is the minimum magnitude F that will start the sled moving up the plane?

(c) What value of F is required to move the sled up the plane at constant velocity?

Explanation / Answer

a)
in this case friction acts upwards

friciton force f = s*Wcos()
minimum magnitude of the force , parallel to the plane, that will prevent the sled from slipping down the plane = Wsin() - s*Wcos()

b)

friction acts downwards

friction force =  s*Wcos()

minimum magnitude F that will start the sled moving up the plane = Wsin() + s*Wcos()

c)

as it is moving we have to take kinetic friction

value of F that is required to move the sled up the plane at constant velocity = Wsin() + k*Wcos()

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