Force on Series of Springs: Does It Equal Sum?

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Homework Help Overview

The discussion revolves around the behavior of springs in series, specifically examining the relationship between the force applied and the spring constants of the individual springs. Participants are exploring the principles of spring mechanics within the context of Hooke's Law.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning whether the force applied to a series of springs can be expressed as the sum of the spring constants multiplied by the distance stretched. There is a focus on the implications of applying the same force to both springs and how this relates to their individual spring constants.

Discussion Status

The discussion is active, with participants providing insights into the mechanics of springs in series. Some have offered clarifications regarding the application of force and the calculation of equivalent spring constants, while others are exploring the implications of these relationships.

Contextual Notes

There appears to be some confusion regarding the application of Hooke's Law to springs in series, particularly in how the force relates to the individual spring constants and the overall system behavior.

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If two springs, having different spring constants, are in a series (lined up, NOT parrallel): is the Force pulling the spring = (sum of spring constants)*(distance stretched) ?
 
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No, no. If the force apply to the [tex]1^{st}[/tex] spring, the equation will be

[tex]F=k_1\Delta l_1[/tex][/color]
 
so the same force is applied to both springs?
 
in other words, if F = kx:
F=(k1)(x1)
and
F=(k2)(x2)

but not F=(k1+k2)(x1+x2)
 
That's right, and the equivalent constant is

[tex]\frac{1}{k}=\frac{1}{k_1}+\frac{1}{k_2}+...+\frac{1}{k_n}[/tex][/color]
 

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