# DW = F * dr Derivative

1. Dec 7, 2013

### Miraj Kayastha

dW = F * dr

in this equation why is the derivative of distance r taken and not of the force?

2. Dec 7, 2013

### Simon Bridge

Because the equation is answering the question: how much work is done by force F(x) in moving an object from x=r to x=r+dr.

3. Dec 7, 2013

### voko

This equation is a definition. We define work that way because it is useful for us, specifically, it leads to the work/energy theorem.

4. Dec 8, 2013

### Miraj Kayastha

Changing force

But in a case where F changes as r changes shouldn't there be dF. For example shouldn't there be dF in gravitational potential energy derivation?

5. Dec 8, 2013

### Simon Bridge

I'm wondering about the context - i.e. why presume the relation was arrived at by taking the derivative of work with distance? One could start with the work and take the derivative with force as suggested, and still keep the same definition. Perhaps there has been a lesson that presented the relation as coming from the derivative?

6. Dec 8, 2013