Hooke's Law: Mass vs. Length Data Analysis

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    Hooke's law Law
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Discussion Overview

The discussion revolves around analyzing a set of data to determine whether a spring obeys Hooke's Law. Participants explore the relationship between mass and spring length, considering the implications of equilibrium and the spring constant.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to determine if the spring obeys Hooke's Law and whether the initial length of 15.7 cm represents the equilibrium position.
  • Another participant suggests that if the force is zero, the displacement should also be zero, indicating that 15.7 cm is the equilibrium position. They propose checking how well the force scales linearly with displacement.
  • A different participant provides a modified equation for the scenario where mass is hung vertically, introducing variables for equilibrium and gravitational force, and suggests checking for consistency with the values of mass and length.
  • One participant recommends plotting mass against extension on a graph, stating that a straight line would indicate compliance with Hooke's Law, with the gradient representing the spring constant, k.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of equilibrium and the application of Hooke's Law. There is no consensus on the best approach to analyze the data or the definition of equilibrium in this context.

Contextual Notes

Participants have not fully resolved the assumptions regarding the equilibrium position and the method for determining the spring constant. The discussion includes various interpretations of the data and the mathematical relationships involved.

audreylynn
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If I'm given a set of data such as...

Mass(kg) Spring Length(cm)
0.0 15.7
1.0 16.5
2.0 17.8
3.0 19.3
and so on...

How do I determine whether or not the spring is obeying Hooke's law?
I'm not sure what k is equal too.
And is 15.7 the equilibrium?
 
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F = kx. If the force is zero, then the displacement should be zero, so you should take 15.7 cm as your equilibrium position. From there, it is simply seeing how well the force scales linearly with displacement. The force here being provided by the attached masses.
 
You are hanging the mass from the spring vertically? If so, the equation is

[tex]F=k(y_{0}-y)-mg[/tex]

Where y_{0} is the point of equilibrium. g= 9.8 m/sec^2 (gravitational constant), m is the mass
, and y is the measured length of the spring.

If the force is zero, i.e., the mass is in equilibrium,
[tex]k(y_{0}-y)-mg=0[/tex]

Plug in the possible values for m and and y and if the equations are consistent(with y_{0}, and k being the unknowns), then hook's law is obeyed.
 
From the data, draw a graph of mass of spring (horizontal axis) against extension (vertical).
If it is a straight line then Hooke's Law is obeyed. The gradient is equal to the elastic constant, k.
 

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