# Symbols in the equation relating work, force, and distance moved

1. Oct 15, 2012

### Dr Moriarty

I have been taught that work = force x distance moved in direction of force, or

W=Fd

However, should this not be W=Fs, as what is really meant is displacement (s), not distance (d)?

Thank you - I sense that this is something the real Dr Moriarty would have known....

2. Oct 15, 2012

### lendav_rott

If you move in a circular trajectory on your bicycle. Do you mean to say that the total energy you have spent is 0?

I have been taught that A = Fs aswell, s is the distance travelled by the influence of the Force, so it would make no sense if the summarum is 0.

3. Oct 15, 2012

### Dr Moriarty

My question is less about the actual physics, and more about the convention - it seems to me that writing W=Fd is inaccurate, as d represents distance, not displacement (s).

4. Oct 15, 2012

### tiny-tim

Welcome to PF!

Hi Dr Moriarty! Welcome to PF!
The correct equation is W = ∫ F · ds

(since neither the force nor the direction of motion need be constant).

W = Fd is just a simplification which applies in some circumstances.