Fundamental Forces: Spring Question

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Homework Help Overview

The discussion revolves around a problem related to the forces acting on a spring, specifically focusing on the equations of motion and the directionality of forces involved. Participants are examining the relationship between mass, spring constants, and displacement.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are analyzing the formulation of the equation of motion for a spring and questioning the signs associated with the forces. There is a discussion about whether both forces should be considered in the same direction and how this affects the resulting equations.

Discussion Status

Some participants have offered guidance on the interpretation of force directions and the definition of positive and negative axes. There is ongoing exploration of the implications of these definitions on the calculations being performed, with no explicit consensus reached yet.

Contextual Notes

Participants are navigating potential misunderstandings regarding the direction of forces and the absolute value of displacement in the context of spring forces, as well as the implications of their assumptions on the problem setup.

JoeyBob
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Homework Statement
See attached
Relevant Equations
F=lk
ma=-k2l+k1l

(ma-k1l)/l=-k

(-65.12-35.7)/0.51=-k

k=197.69, but answer should be 57.7
 

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Sorry i had some wrong posts here which i deleted... Your mistake is in first line, you take one force as positive and the other as negative. Aren't both forces towards the same direction at position l?
 
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Delta2 said:
Sorry i had some wrong posts here which i deleted... Your mistake is in first line, you take one force as positive and the other as negative. Aren't both forces towards the same direction at position l?

Okay I found out how to do it but am a bit confused. To get the right answer it needs to be

(-ma-lk)/l

This would mean the equation is ma=-k1l-k2l

But doesn't this imply the forces are in the negative i hat direction when they should be in the positive direction??
 
On your picture which is the positive i hat direction? Is that the direction of the force when l is positive?
 
hutchphd said:
On your picture which is the positive i hat direction? Is that the direction of the force when l is positive?
It would be to the right, no?
 
So you have to define positive x (you have called it l) in that direction also. Going to the left is negative.
 
hutchphd said:
So you have to define positive x (you have called it l) in that direction also. Going to the left is negative.

Isnt the change in length an absolute value though when calculating the force?
 
No. The force from a spring is opposite from displacement. Hence the minus sign in ##F_x=-kx##.
 
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