What's wrong with my definition of work?

[WindScars]

Please look this configuration:

The image explains itself. It's a block an a ramp at A with an initial velocity v0, kinetic coefficient of friction u, there's gravity and an extra unknown force, F, acting parallel to the ramp. The block travels a distance of d and stops at B. The question asked the total work done by all the forces on the block.

The answer is equal to "minus" the kinetic energy of the block (because the block stopped). But stopping the block wasn't the only thing that changed. It was lifted! If my definition of work were right, the energy required to lift it from A to B would have to be included on the total work done on it, but just the kinetic is. What is wrong?

Note: I didn't post this on the homework section because it's not my homework, it's an example I used to ask why energy required to lift the block doesn't count when calculing the total work done by the forces. Fell free to move the topic if it belongs there, though.

 

[DiracRules]

I'm still a bit sleepy now, so I may be wrong.
Perhaps the problem is in the question: The question asked the total work done by all the forces on the block.

Considering an energetic approach,
$K_{beginning}+U_{beginning}+W_{F}=K_{end}+U_{end}+W_{friction}$ where W is work.
If you want to know the work of all the forces, then you must include in W all the works:
$W=W_{F}-W_{friction}+W_{gravitational}$, where $W_{gravitational}=U_{beginning}-U_{end}$
then you have
$W=K_{end}-K_{beginning}=-K_{beginning}$

Your definition of work wasn't wrong (though you had to take in account also the work done by the friction force), it was only that the question asked something different.

 

[Doc Al]

The answer is equal to "minus" the kinetic energy of the block (because the block stopped). But stopping the block wasn't the only thing that changed. It was lifted! If my definition of work were right, the energy required to lift it from A to B would have to be included on the total work done on it, but just the kinetic is. What is wrong?

To amplify what DiracRules explained, it depends on how you choose to represent gravity.

The Work-KE theorem states that the net work done on an object due to all forces (including gravity) equals the change in KE. This is what the question is looking for.

But it's common to represent the effect of gravity as a potential energy term, in which case the net work done on an object due to all forces except gravity equals the change in KE + PE. This is what you are thinking of.

 

[D H]

To amplify what DiracRules explained, it depends on how you choose to represent gravity.

The Work-KE theorem states that the net work done on an object due to all forces (including gravity) equals the change in KE. This is what the question is looking for.

TO amplify what both DiracRules and Doc al explained, suppose the block is not on a ramp. It is instead on a rough but horizontal floor. Your goal is to push the block across the floor. You are doing work on the block. So is the floor, but the work done by the floor is negative. The total work done on the block: Zero, assuming it starts and ends at rest. You don't need to know the magnitudes of the force exerted by the pusher and that exerted by the floor.

 

[PJC01]

Your definition of work is incomplete. In order to accurately calculate the total work done on the block, you must consider all the forces acting on it, as well as the distance it travels. In this case, the force of gravity and the unknown force F are both doing work on the block as it moves up the ramp, in addition to the work done by the force of friction as it slows the block down.

When the block is lifted from A to B, work is done against the force of gravity, which requires energy. This energy is not accounted for in your definition of work, which only considers the kinetic energy of the block. Therefore, in order to accurately calculate the total work done on the block, you must also include the work done against gravity in lifting the block from A to B.

In summary, your definition of work must consider all forces acting on an object, as well as the distance it travels, in order to accurately calculate the total work done.