# Work is done?

1. Jun 2, 2013

Wikipedia defines work as:
What if in space,where there is no external force acting,Someone applies a force and the object will move on to a infinite displacement forever(Newton's first law).Is work done?

Another question is from that wikipedia:
Work done=Energy transfered . That means in circular motion no energy is transfered to the object ,not even kinetic.Then how can it move?

2. Jun 2, 2013

### tiny-tim

work is done is getting the object moving

once it is moving, it carries on in a straight line at the same speed (newton's first law of motion) without any more force

"its work is done!"
work was done to get it moving

the string keeps it in a circle, but doesn't reduce its speed

no further work is neeeded

3. Jun 2, 2013

How can I calculate the work done then?
W=FS
It moves to an infinite distance,Meaning work done is infinite?

4. Jun 2, 2013

We need centripetal force all the time it is moving in a circle,meaning work is done always?

5. Jun 2, 2013

### tiny-tim

no, S is the displacement of the point of application of the force

the force is only applied at the start (to get it going)

after that, there is no force (so zero displacement)
the displacement (of the point of application of the force) is tangential, the force is radial

so the displacement "in the direction of the force" (see wikipedia) is zero

the full formula is the dot product, W = F·S

6. Jun 2, 2013

But displacement is defined as the distance travelled in a stated direction.No force is needed.
Or do you mean S is the displacement(in the direction of force) covered when the force is still there?

Again
We still apply a force and get tired why?If no work is done,then we would not get tired?

Last edited: Jun 2, 2013
7. Jun 2, 2013

### tiny-tim

yes

the displacement is of the point of application of the force

when the force is no longer applied, it no longer has a point of application!
stand between two doorposts, and push apart

the doorposts don't move, but parts of your body do move, and work is done

now relax your arms … if they were made of elastic, you would get all the energy back, and then do the same again without getting tired

but they're not made of elastic, so the energy is wasted, and if you do it again, you have do work all over again

8. Jun 2, 2013

### Octans

Think of it this way: work is only done when a force is applied. Imagine you and an object are the only two things in the whole universe. Start with the object at rest (relative to you) and push on it. You apply a force and the object accelerates from rest to some velocity in a certain distance while you push on it. Because you're applying a force and the object is moving, you're doing work. $F$ isn't 0 and $s$ isn't 0 in the $W = F \cdot s$ equation, so $W$ also isn't 0.

But once you let go of the object, it no longer accelerates. It travels at constant velocity and it does have a displacement, however you're no longer applying a force. Now $W = 0 \cdot s = 0$. So you can see that no work is done even though the object moves.

That was an ideal situation where the only force was your pushing. So that you could see the concept clearly, I neglected an important fact: just by having mass you would be attracting the object gravitationally and the object would be attracting you. So even once you let go of the object and you're not pushing on it, there would still be a gravitational force pulling it back toward you. Does this force do work?

9. Jun 2, 2013

### Staff: Mentor

We are inefficient, 0% efficiency in some circumstances. You get tired, not because you are doing external work, but because you are wasting lots of energy generating heat by using your muscles inefficiently.