# Work done when point of application of force remains fixed

1. Mar 24, 2015

If an object moves in such a way that the point of application remains fixed then what can be commented on the work done by the force? (only qualitative analysis required)

2. Mar 24, 2015

### Staff: Mentor

Welcome to PF! Do you have an example in mind? This is typically a misunderstanding of the system definition and how the force is applied.

3. Mar 24, 2015

No I don't. I was reading conceptual problems of a book when I got this TRUE/FALSE question "work done by a force on an object is zero, if the object moves in such a way that the point of application of the force remains fixed."
According to the answers this statement is False. I cannot think about any example or explanation for this.

4. Mar 24, 2015

### Staff: Mentor

Hmm. That doesn't sound right to me, but maybe it is just because I can't think of a good example. One common one is a person jumping up. The force is applied between the persons' feet and the ground and doesn't move. The earth does no work, but it is a bit of a trick question because the person "deforms", releasing internal energy.

Maybe someone else can weigh-in...

5. Mar 24, 2015

### Staff: Mentor

That doesn't sound right to me either. What book is this question from?

6. Mar 24, 2015

### CWatters

Badly worded? Fixed relative to what?

If you push a book across a desk against friction the "point of application of the force" can remain fixed relative to the book but move relative to the table.

7. Mar 24, 2015

Doesn't sound right to be either. It is from a famous book in my country for preparation of admission to college. The name is "practice book of physics by DC Pandey". I don't think you would have heard of it.

I agree with you, the point of reference must be stated.

After thinking about the problem again I could think of one example that ought to satisfy the condition but proves the answer wrong: Consider a wheel fixed and hinged about its center, now if we bring it into contact with a conveyor belt then it would start rotating. Now since the point of application of force remains fixed and the center of mass does not move, we can say that the work done by that force is equal to zero.
Do you people agree with this explanation or something to add?

8. Mar 24, 2015

### Staff: Mentor

Isn't the conveyor belt moving? And if the wheel starts rotating, something must have done work on it.

9. Mar 24, 2015

The conveyor belt is moving but the point of application of force i.e the point of contact between the wheel and belt isn't.
I could be wrong about the work, but according to me since there is no net displacement of the wheel therefore work done is zero.

10. Mar 24, 2015

### jbriggs444

I am a little surprised not to see Doc Al jump all over this.

A wheel on a conveyer belt is an excellent example of a point of application remaining fixed while non-zero work is done. Work is being done on the wheel because the material at the point of application is moving in the direction of the force applied to that material. Work is being extracted from the conveyer because the material at the point of application is moving in the opposite direction of the force applied to that material.

The position of the point of application is not directly relevant to the work done. It is the motion of the material to which the force is applied that matters.

11. Mar 24, 2015

That answers my question to satisfaction. Thank you.

PS. if a moderator sees this then you may close the thread.

12. Mar 24, 2015

### Staff: Mentor

Sure it is! The point of contact between wheel and belt does move (with respect to the room). I think what you're thinking is that, ignoring slipping between the surfaces, the relative motion of wheel and belt is zero. That's certainly true, and it just tells you that the "real" source of the work is whatever is moving the belt.

You are probably thinking of center of mass "work" (or pseudowork).

13. Mar 24, 2015

### Staff: Mentor

I'm getting there... slowly. (Multi-tasking, and not very well.) :)

14. Mar 24, 2015

I don't get it, how is the point of contact moving with respect to the room?
The real source of the work was not the problem, however I agree with you that the thing that is actually doing work is the motor that is moving the belt.
Yes earlier I was considering only the pseudowork (thanks for giving me the correct term) but i believe that jbriggs444 explained it clearly.

15. Mar 24, 2015

### Staff: Mentor

Isn't the conveyor belt moving?

Contrast this with an example of a wheel rolling on the ground. In that case, the point of contact of the wheel is (momentarily) stationary. Not so with the conveyor belt.

16. Mar 24, 2015

### jbriggs444

There is a distinction that can be drawn between the material at the point of contact and the point of contact itself. In the case of a car rolling along the road, the point of contact is moving but the material (both road and tread) is at least momentarily at rest. In the case of a wheel riding along a conveyer belt, the point of contact is stationary but the material (both belt and tread) is moving.

Which one of these situations applies is, of course, purely a matter of one's choice of reference frame. Regardless of that choice, it remains true that the motion of the material and of the point of contact are not identical.

17. Mar 24, 2015

### Staff: Mentor

I'm not quite clear what distinction you are making. When I speak of the "point of contact" of the wheel with the surface, I mean that physical portion of the wheel that is in momentary contact with the surface. What do you mean by "point of contact"?

18. Mar 24, 2015

### jbriggs444

The point where contact is being made. The position of that point will be a function of time and might even be differentiable.

19. Mar 24, 2015

### Staff: Mentor

Ah, now I see what you were saying. I was using "point of contact" as a shorthand way of referring to the physical portion of the wheel that is instantaneously in contact with the surface. And I see where my use of that term could lead to confusion. Thanks!