# Tension on the string is doing work

1. Aug 4, 2009

### BlueOwl

1. The problem statement, all variables and given/known data

When someone ties a string to a ball and swings it in a circular motion is the string doing work on the ball?

2. Relevant equations

3. The attempt at a solution

Ok I am a little bit lost here it does seem that the tension on the string is doing work on the ball but again there is no change in kinetic energy(constant rotation) so could there be no work at all? I am totally lost here .

2. Aug 4, 2009

### kuruman

Re: Work

Write down the expression for the work done by a force on an object (Hint: It is not "force times distance") and apply it to this situation.

3. Aug 4, 2009

### prob_solv

Re: Work

The tension force of the string which coincide with the length of the string. It didn't make any difference of distance with the axis, so, it didn't loss any energy.

4. Aug 4, 2009

### rock.freak667

Re: Work

In theory yes the mechanical energy of the system stays constant i.e. KE+PE=constant.

But does if work is said to be done when a force F moves it point of application through a displacement s in the direction of the force, would the string do work on the ball?

5. Aug 4, 2009

### prob_solv

Re: Work

The tension force is perpendicular with the movement of s. You may not just multiply it without seeing the vector.

6. Aug 4, 2009

### RoyalCat

Re: Work

prob_solv, that's a dead give-away, I think you should edit it out and let the thread starter reach that conclusion by himself.

As the others have pointed out here, work is not just the force times the distance over which it is exerted on the mass. If you're more of a maths guy, this exact definition should help you:

$$W \equiv \vec F \cdot d \equiv |F||d|\cos{\theta}$$
Work is defined as the dot product of the force vector and the displacement vector. The dot product:
$$\vec A\cdot\vec B\equiv |A||B|\cos{\theta}$$ where $$\theta$$ is the angle between the two vectors.