Work done by friction on an incline plane

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SUMMARY

The discussion focuses on calculating the work done by a rope on a block of mass M being pulled up an inclined plane at a constant speed. The inclined plane has an angle θ and a coefficient of kinetic friction μk. Key calculations include the work done by the rope, total work done on the block (Wtot = Wcons + Wnoncons), and verification of Wtot equating to the change in kinetic energy (ΔKE). Additionally, the scenario of pulling the block down the incline is analyzed, emphasizing the relationship between work done, potential energy (ΔPE), and kinetic energy (ΔKE).

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with concepts of work and energy in physics
  • Knowledge of inclined plane mechanics
  • Basic understanding of frictional forces and coefficients
NEXT STEPS
  • Study the equations of motion for objects on inclined planes
  • Learn about the work-energy theorem in classical mechanics
  • Explore the effects of friction on motion in detail
  • Investigate the relationship between potential energy and kinetic energy in various scenarios
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Students of physics, educators teaching mechanics, and anyone interested in understanding the dynamics of forces on inclined planes and the work-energy principle.

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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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