Solving Spring Problems: Finding Total Force

[spaceshipone]

I've been trying for a while to solve this problem

http://www.flickr.com/photos/36633646@N03/3379407472/

Do I just find the total force the spring exerts from 400mm to 0 and multiply it by distance b?

 

[tiny-tim]

Welcome to PF!

Hi spaceshipone! Welcome to PF!

Do I just find the total force the spring exerts from 400mm to 0 and multiply it by distance b?

work done = force "dot" distance …

stop trying to take short-cuts!

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

 

[sArGe99]

How would you calculate extension?

 

[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.

 

[tiny-tim]

… you'd also need to set up some type of integral. Doing any of the calculus part always starts to confuse me.

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 )

 

[spaceshipone]

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

 

[tiny-tim]

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

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

that's how integration works