# Varying angle for work

1. Dec 23, 2012

### autodidude

When you calculate the work done by a force on a particle, you multiply the magnitude of the force by the displacement and the cosine of the angle between them. If it's a varying force, in one dimension, you take the integral from the initial position to final position. Does this integral assume that the angle of the force is constant? What if it varies?

2. Dec 23, 2012

### Staff: Mentor

Take the integral of the scalar product, this includes the angle between force and displacement.

3. Dec 24, 2012

### autodidude

So if a CONSTANT force of 10N acts on a body for 10m but the angle changes from 0 to 45 degrees then to compute it, that's all you would have to do?

If the angle of changing, the scalar (dot?) product is always changing isn't it? I can't see how this is taken into account

4. Dec 24, 2012

### sophiecentaur

You need to Integrate over the path of the action, as stated above. This involves adding the work done over infinitessimal portions of the path. If the path shape makes it hard to integrate analytically then you can do it numerically, breaking the path down into small straight lines.

5. Dec 24, 2012

### autodidude

Does this have to do with line integrals?

6. Dec 25, 2012

### sophiecentaur

Sure does. Merry Christmas.

7. Dec 25, 2012

### autodidude

Thanks, you too. I'll work out things from here xD