Need to find the spring constant

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SUMMARY

The discussion focuses on calculating the spring constant (k) using the provided data of mass versus spring length. The relevant equation is Fs = k |l - l0|, where Fs is the spring force, l is the measured length of the spring, and l0 is the initial length. The user correctly identifies that the force due to gravity (Fg) can be expressed as mass multiplied by the acceleration due to gravity (10 N/kg). The key insight is that the spring constant can be determined from the slope of a graph plotting force against the extension of the spring, regardless of the initial length.

PREREQUISITES
  • Understanding of Hooke's Law and spring mechanics
  • Familiarity with basic physics concepts such as force and mass
  • Ability to interpret and create graphs
  • Knowledge of units of measurement (grams to Newtons conversion)
NEXT STEPS
  • Learn how to plot force versus extension graphs for springs
  • Study the relationship between slope and spring constant in Hooke's Law
  • Explore the concept of initial spring length and its effect on calculations
  • Investigate different methods for measuring spring constants experimentally
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and spring dynamics, as well as educators seeking to enhance their teaching methods for spring-related topics.

christianhood
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Homework Statement


A series of masses are hung from a vertical spring and the length is measured in each case to the nearest milimeter. Data below:

Mass : Spring Length
050g : 40.2cm
100g : 45.8cm
150g : 50.9cm
200g : 56.4cm
250g : 61.4cm
300g : 66.9cm
350g : 73.7cm
400g : 81.2cm

I need to find the spring constant.

Homework Equations



Fs = k | l - l0| ,
where
Fs = Spring Force
k = spring constant
l = length of spring
l0 = initial length of spring

The Attempt at a Solution


I know that Fs = Fg = mass / 100 (using g = 10 N/kg).
I just don't know how to get the constant because I don't know what the initial spring length is (it's not 0).
 
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Think about the equation F = kX for a moment. What kind of graph does that make? What one of those letters represents the slope of that graph?

Can you put those hints together to figure out a way to determine the spring constant?
 
AEM said:
Think about the equation F = kX for a moment. What kind of graph does that make? What one of those letters represents the slope of that graph?

Can you put those hints together to figure out a way to determine the spring constant?

Oh, okay. It's the same for any initial length. Thanks :)
 

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