## Main Question or Discussion Point

I believe I might have a fundamental misconception about work. Please correct me where my reasoning is wrong so I can improve my conceptualization.

Let's say there is a block of mass M being raised. The gravitational acceleration is assumed to be a constant, g. Thus, the weight of the block is Mg.

Let's say that two forces are acting on the block, both of which are constant:
- The external force, F, which causes the block to rise.
- Gravity, Mg, which tends to cause the block to fall.

Assume that F > Mg. Thus, a resultant force of magnitude (F-Mg) causes the block to accelerate upwards.

If the block travels an upward distance of magnitude D, then am I correct in saying that the work done on the block by the applied force is MgD ? This should be a positive number, right? Since the applied force is in the same direction as the displacement of the block?

On the other hand, the work done on the block by gravity should be equal to -MgD right? Since gravity and the block's displacement are in opposite directions, this quantity should be negative?

Also, can we conclude that the net work done on the block is equal to (F-Mg)*D. In other words, can we say that the net work done on any object equals the dot product of the net force acting on it (assuming the net force is constant) and its displacement.

Now comes the difficult part...

Does the block do work on the agent of the applied force? So if I am the agent that is raising the block with my upward force F on the block, can I say that the block is exerting a downward force of F on me? And since the block's displacement is D directed upwards relative to me, can I say that my displacement relative to the block must be D directed downards? Thus, can I say that the block did some work on me? Will this work be equal to the work I did on the block?

Similarly, does the block do any work on the Earth? After all, the block exerts an equal and opposite force Mg on the Earth causing it to slightly push downwards?

Wherever I am wrong, please provide a reason where my reasoning is flawed.

Thanks! All help is appreciated!

BiP

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russ_watters
Mentor

I don't see anything you've gotten wrong with anything you said.

Andrew Mason
Homework Helper

Assume that F > Mg. Thus, a resultant force of magnitude (F-Mg) causes the block to accelerate upwards.

If the block travels an upward distance of magnitude D, then am I correct in saying that the work done on the block by the applied force is MgD ?
The work done by the applied force is FD, not MgD.

This should be a positive number, right? Since the applied force is in the same direction as the displacement of the block?
Correct.

On the other hand, the work done on the block by gravity should be equal to -MgD right? Since gravity and the block's displacement are in opposite directions, this quantity should be negative?
Correct.

Also, can we conclude that the net work done on the block is equal to (F-Mg)*D. In other words, can we say that the net work done on any object equals the dot product of the net force acting on it (assuming the net force is constant) and its displacement.
Correct.

Now comes the difficult part...

Does the block do work on the agent of the applied force? So if I am the agent that is raising the block with my upward force F on the block, can I say that the block is exerting a downward force of F on me? And since the block's displacement is D directed upwards relative to me, can I say that my displacement relative to the block must be D directed downards? Thus, can I say that the block did some work on me? Will this work be equal to the work I did on the block?

Similarly, does the block do any work on the Earth? After all, the block exerts an equal and opposite force Mg on the Earth causing it to slightly push downwards?
A block falling toward the earth under gravity force Mg exerts an equal and opposite force on the earth of Mg = Mea (where a is a very small acceleration of the earth toward the centre of mass of the earth/M system). The work done by the block on the earth would be Mgd where d is the distance the earth moves toward the centre of mass - an extremely small distance. So, in the frame of reference of the earth/M centre of mass, the work done by the block on the earth is insignificant compared to the work done by the earth on the block.

In the case where you apply the upward force F to the block, you have to define a frame of reference. Are you asking whether there is work done to you in the frame of reference of the earth?

AM

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