Solving Spring Problems: Finding Total Force

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The discussion focuses on calculating the total force exerted by a spring as it compresses from 400mm to 0. Participants emphasize the importance of using the work-energy principle, specifically the dot product of force and distance, to find the work done. There is a debate about whether the force can be treated as constant during small intervals, with suggestions to set up an integral for varying forces. The complexity of integrating due to changing angles and force magnitudes is acknowledged, highlighting the need for a careful approach to calculus. Overall, the conversation centers on the correct application of physics principles to solve the spring problem effectively.
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Welcome to PF!

Hi spaceshipone! Welcome to PF! :smile:
spaceshipone said:
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! :wink:

(how would you work out the total force, anyway? :confused:)
 
How would you calculate extension?
 
Last edited:
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:
spaceshipone said:
… you'd also need to set up some type of integral. Doing any of the calculus part always starts to confuse me.

Hi spaceshipone! :smile:

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. :smile:

(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 :wink:)
 
I don't understand. The force for this problem isn't constant. It varies as the direction changes.
 
spaceshipone said:
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 :smile:
 

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