# Spring Problem, Work

1. Mar 23, 2009

### spaceshipone

2. Mar 23, 2009

### tiny-tim

Welcome to PF!

Hi spaceshipone! Welcome to PF!
work done = force "dot" distance …

stop trying to take short-cuts!

(how would you work out the total force, anyway? )

3. Mar 23, 2009

### sArGe99

How would you calculate extension?

Last edited: Mar 23, 2009
4. Mar 23, 2009

### spaceshipone

Hi,

Thanks for all the replies. If I used the dot product here is what I've come up with

W = F dot dr
so
W = fs dot <.4 , 0>
W = <40(l - .2), angle 221.4 degrees> dot <0 ,0.4>

So I'm not sure where to go from here. I know the distance part is straightforward. It's just straight up.
The force part goes varies as l goes from .3m to .1m and actually doesn't the degrees vary also from 221.4 degrees to 270 degrees initial to final? So I would imagine along with the dot product you'd also need to set up some type of integral. Doing any of the calculus part always starts to confuse me.

Thanks again for all the relies.

Last edited: Mar 23, 2009
5. Mar 24, 2009

### tiny-tim

Hi spaceshipone!

To set up an integral:

General method:

choose a very short distance (or time or whatever), in this case from x to x + dx,

and then you can assume that the force is constant over that distance,

so you "dot" that "constant" force with dx, and integrate.

(similar to getting the volume of a solid: choose a slice from z to z + dz, assume the area of that slice is constant, and integrate that "constant" area times dz )

6. Mar 24, 2009

### spaceshipone

I don't understand. The force for this problem isn't constant. It varies as the direction changes.

7. Mar 24, 2009

### tiny-tim

Yes, but you can assume it's constant, over the very short distance dx …

that's how integration works