Work on a Block Sliding Up a Frictionless Incline

Part A = 0J

Part B = -19.9J

Part C = 19.9J

Part D = 0J

A block of weight w = 15.0 N sits on a frictionless inclined plane, which makes an angle θ = 23.0° with respect to the horizontal, as shown in the figure. A force of magnitude F = 5.86 N, applied parallel to the incline, is just sufficient to pull the block up the plane at constant speed.

Part A

The block moves up an incline with constant speed. What is the total work W

Express your answer numerically in joules.

_{Total}done on the block by all forces as the block moves a distance L = 3.40 m up the incline? Include only the work done after the block has started moving at constant speed, not the work needed to start the block moving from rest.Express your answer numerically in joules.

Since the block is moving at a constant speed there is no change in kinetic energy. Since work is the change in kinetic energy and there is no change, the net work on the block is zero.

0 J

Part B

What is W

_{g}, the work done on the block by the force of gravity w as the block moves a distance L = 3.40 m up the incline?

W_{g} = -mgy = -15.0N*3.40m*sin(23.0) = -19.9 J

-19.9 J

Part C

What is W

_{F}, the work done on the block by the applied force as the block moves a distance = 3.40m up the incline?

Since we found the net work to be zero (in Part A), the work done by the applied force has to offset the work done by gravity:

19.9 J

Part D

What is W

_{N},the work done on the block by the normal force as the block moves a distance = 3.40 up the inclined plane?

The normal force is perpendicular to the direction of motion, therefore it does no work on the block:

0 J

“What is Wg, the work done on the block by the force of gravity w as the block moves a distance L = 3.40 m up the incline?”

I think there’s a typo here. “force of gravity w”

What’s “gravity w” ? Did you mean the force of gravity due to weight of the box? Or the force of gravity times w? Or did you include w by accident?

That’s correct, ‘w’ is just the force due to gravity. Some versions of this question leave out ‘w’. Definitely confusing.