Work done by friction on an incline plane

AI Thread Summary
The discussion focuses on calculating the work done by a rope pulling a block up and down an inclined plane at constant speed, considering the effects of friction. The work done by the rope is determined by the tension in the rope and the distance moved, while also accounting for the forces of gravity and friction acting on the block. Participants emphasize the importance of drawing a force diagram to visualize the forces at play, including the gravitational force and the frictional force, which is influenced by the coefficient of kinetic friction. The total work done on the block is analyzed in relation to changes in kinetic and potential energy, confirming that the work done aligns with the principles of energy conservation. Overall, the discussion highlights the relationship between work, energy, and forces in the context of motion on an incline.
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A block of mass M is being pulled up an inclined plane at a constant speed, by an attached rope that exerts a tension T. The block is pulled a distance L. The plane makes an angle θ with the horizontal, and the coefficient of kinetic friction between the block and the incline is μk.
a.) What is the work done by the rope?

b.) Find the total work done on the block, Wtot = Wcons + Wnoncons. Verify that Wtot = ΔKE.

Suppose that the rope is attached to the downward side of the block, and it is pulled down the plane, a distance L. The tension in the rope again has magnitude T. Assume once again that the sled is pulled at a constant speed.
a.) What is the work done by the rope?

b.)Verify that Wnon-cons = ΔPE + ΔKE by first calculating the change in kinetic energy.
I know work is equal to Force times the distance the object moved and that frictional force is equal to mgcos(theta)
 
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Start by drawing a force diagram.

What forces is the rope working against? Over what distance.
 
The tension force in the rope is working against the force of gravity as well as the force of friction on the block
 
So maybe if you reduce this to an equation ...?
 
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