# Work and displacement of the point of application

1. Jun 16, 2011

### iampaul

I have this example from my physics books which says:
If a skater pushes against the wall and the skater moves, the wall does no work and the motion of the skater only results from the internal work of the skater. It also says that the wall does no work because there is no motion of its point of application, and this part is what i don't understand.
I am thinking that if the force from the wall acts on the skater, then the point of application of the force exerted by the wall is the skater. Since the skater did move, then there is motion of the point of application of the force from the wall.
Although I agree that the wall must have done no work, what confuses me is the reason why, which is about the motion of the point of application as the book tells.

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2. Jun 16, 2011

### iampaul

work and displacement of the point of application
I have this example from my physics books which says:
If a skater pushes against the wall and the skater moves, the wall does no work and the motion of the skater only results from the internal work of the skater. It also says that the wall does no work because there is no motion of its point of application, and this part is what i don't understand.
I am thinking that if the force from the wall acts on the skater, then the point of application of the force exerted by the wall is the skater. Since the skater did move, then there is motion of the point of application of the force from the wall.
Although I agree that the wall must have done no work, what confuses me is the reason why, which is about the motion of the point of application as the book tells.

3. Jun 16, 2011

### Pengwuino

In general, the work done by a force is given by

$$W = \int \vec{F} \cdot d\vec{x}$$

If you're in a non-calculus based course, you typically have constant forces and this boils down to

$$W = F\Delta x$$

If the wall did not move, the wall could not have done work, even if a force was applied. If this is confusing, think of yourself standing on the ground. The Earth is exerting a force on you and you on it, but just by standing there no work is done because no displacements occur vertically.

4. Jun 16, 2011

### iampaul

"If the wall did not move, the wall could not have done work,..."
What I only understand is that if the wall didn't move then the skater did no work to the wall, but i can't still understand why the wall couldn't have done work to the skater based on the reason that there is no motion of its point of application which is the skater and the skater moved so there is displacement.

5. Jun 16, 2011

### rcgldr

Since the point of contact of force between the skaters hands and the wall doesn't move, then the wall does no work. The skater's arms are acting similar to a spring and that is the source of the work.

6. Jun 16, 2011

### Pengwuino

I'm not entirely sure what you mean "there is no motion of its point of applications", but the skater did move so work was done, but it was only done by the skater.

7. Jun 16, 2011

### iampaul

thanks a lot!! now i get it!!

8. Jun 16, 2011

### Redbelly98

Staff Emeritus
Last edited by a moderator: Apr 26, 2017