Solving Spring Problems: Finding Total Force

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Homework Help Overview

The discussion revolves around a problem involving the calculation of total force exerted by a spring as it extends from 400mm to 0. Participants are exploring the application of work done through force and distance, particularly in the context of integrating variable forces.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand how to calculate the total force exerted by the spring and whether to use the dot product in their calculations. Questions about the nature of the force and its variation with direction are raised, along with considerations for using integrals to account for changing forces.

Discussion Status

The discussion is active, with participants providing guidance on setting up integrals and addressing the complexities of variable forces. There is an acknowledgment of confusion regarding calculus concepts, and multiple interpretations of the problem are being explored without a clear consensus.

Contextual Notes

Participants express uncertainty about the integration process and the assumption of constant force over small distances, highlighting the challenges posed by the variable nature of the force in this scenario.

spaceshipone
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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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