A rope exerts an 18-N force while lowering a 20-kg crate down a plane inclined a

Question

A rope exerts an 18-N force while lowering a 20-kg crate down a plane inclined at 20 (the rope is parallel to the plane). A 24-N friction force opposes the motion. The crate starts at rest and moves 11 m down the plane.

Part A:  Determine the final speed of the crate. The system consists of the crate, the surface of the incline and Earth.

Part B: Determine the change in gravitational energy.

Part C: Determine the change in kinetic energy.

Part D: Determine the change in internal energy.

Part E: Determine the work done by the rope.

Explanation / Answer

acceleration= (18 + 20x9.8xsin20-24)/20=3.05 m/s^2

final speed = sqrt( 2x 3.05 x 11)=8.19 m/s

b. change in gravitational energy = 20 x9.8 x 11 sin 20=737.35 j

c. change in kinetic energy= 1/2 x 20 x 8.19^2= 670.76 j

d. change in internal energy = 737.35 -670.76= 66.58j

e. work done by rope= 18 x 11=198 j

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