# Work

Discussion in 'Physics & Math' started by Nivvedan, Sep 30, 2007.

1. ### NivvedanRegistered Senior Member

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Work = Force x Displacement. Right?
Let’s consider a frictionless space. Here I apply 100N force to a body and it moves with a constant velocity to another point 10 m from the starting position. Then work done = 100 x 10 = 1000J.
If I apply a force of 10N to the same body then too it moves with a constant velocity and reaches the same point, it takes more time but definitely reaches it. Since Work is independent of time, work done now is 10 x 10 = 100J. But how come, to move a same body first 1000J work was done and then now only 100J work is done?
Some people claim work is done only when there is a change in energy, But the formula is Force x Displacement. If a body at rest is accelerated by a force some people say that the work done is exqual to the change in kinetic energy of the body. But the formula is F x s. It is independent of the kinetic energy. It only depends on the displacement.
A force can cause a body to move with a constant velocity, thereby the body will go on and on and on. So the displacement is infinite. So the work done must also be infinite. I thought about it and concluded that only the power of two forces is different but the work done by the two forces is infinite. It’s altogether confusing to me.
Can you please tell me if I have got something wrong and explain this to me?

3. ### NasorValued Senior Member

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6,221
Because the 100J job took longer.
Only if you apply the force for an infinitly long time.

5. ### andbnaRegistered Senior Member

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316
You are using the formula wrong, the displacement means the amount of ditance it travelled while an unballanced net force is applied.

For how long?
Once again, for how long?

Answer those two questions and you can calculate the work done, but based on the information provided above, it is not 100 x 10 = 1000J or 10 x 10 = 100J There isn't eanough info provided for us to know.
Which is 100% correct by definition, anyone who tells you otherwise is wrong.

If you are applying a force, the object will not move at a constant velocity. You will never find a scenario in which work done=infinite, as either the force would need to be infinite, or the duration of the event (and therby distance travelled) would also be infinite, which would make for a completely bogus question.

-Andrew

7. ### James RJust this guy, you know?Staff Member

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30,644
Nivvedan:

Only for a constant force and displacement in a straight line.

Note that this is the word done by a particular force.

It will not move with constant velocity if the applied force is the only force acting. F=ma, so the body will accelerate.

If you want it to move with constant velocity, you will need zero net force.

Your assumption of constant velocity is incorrect.

The reason more work is done in the first case, as compared to the second, is that the object ends up going at a faster speed in the first case.

The Work-kinetic energy theorem says that the (net) work done on an object is always equal to the change in its kinetic energy. It is relatively easy to prove that from the definition of force as F=ma.

Doing (net) work always changes the kinetic energy.

No. A force causes an acceleration. F=ma.

8. ### cosmictravelerBe kind to yourself always.Valued Senior Member

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But what happens when there's a "change order" and everything must be done all over again plus what was done must be "undone".

9. ### James RJust this guy, you know?Staff Member

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30,644
I have no idea what you're asking, cosmictraveler. Want to try again?

10. ### cosmictravelerBe kind to yourself always.Valued Senior Member

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33,264
A little humor. I was in construction many years and whenever there was a large project and everything was finalized and construction started the developers would find something new that they wanted to use instead of what was already planned upon. They then put in "change orders" to update the plans to use those new things which really causes allot of delays and problems. The developers think that it's easy just to switch things around but they have have no iseds as to how much more work it takes to get er done.

11. ### NivvedanRegistered Senior Member

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Thanks I got it now.

12. ### NivvedanRegistered Senior Member

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There's something I don't understand though. Please go to the thread on Work against gravity if you could help me.