Please show all work and equations and calculations :) A loaded penguin sled wei

Question

Please show all work and equations and calculations :)

A loaded penguin sled weighing 82 N rests on a plane inclined at angle theta = 19 degree to the horizontal (see the figure). Between the sled and the plane, the coefficient of static friction is 0.28, and the coefficient of kinetic friction is 0.19. (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? Number Units Number Units Number Units

Explanation / Answer

a) F + friction - m g sin theta = 0

friction = u N = u m g cos theta

F = 82*sin(19) -0.28*82*cos(19)=4.99 N

b) now friction will oppose F

F - friction - mg sin theta = 0

F = 82*sin(19)+0.28*82*cos(19)

F=48.41 N

c) now use kinetic friction

F=82*sin(19) +0.19*82*cos(19)=41.43 N

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