Spring problem. I thought I had it

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SUMMARY

The discussion focuses on solving a spring mechanics problem involving work, force, and the spring constant. The work done to stretch a spring 3.30 cm is 12.5 J, leading to the need to calculate the spring constant (k) using the formula for elastic potential energy. The correct approach involves using the equation for energy stored in a spring, E = (1/2)kx², to derive k. The user initially misapplied the force equation, leading to incorrect calculations.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Knowledge of elastic potential energy in springs (E = (1/2)kx²)
  • Basic algebra for solving equations
  • Familiarity with units of measurement (Joules, Newtons, centimeters)
NEXT STEPS
  • Calculate the spring constant using the formula k = (2E)/x²
  • Determine the force required to stretch the spring 3.30 cm using F = kx
  • Calculate the work done to compress the spring 4.35 cm using E = (1/2)kx²
  • Find the force needed to stretch the spring 4.35 cm using F = kx
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and spring dynamics, as well as educators looking for practical examples of applying Hooke's Law and energy concepts.

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Homework Statement



To stretch a spring 3.30 cm from its unstretched length, 12.5 J of work must be done.
(a) What is the force constant of this spring?
(b) What magnitude force is needed to stretch the spring 3.30 cm from its unstretched length?
(c) How much work must be done to compress this spring 4.35 cm from its unstretched length?
(d) What force is needed to stretch it this distance?

Homework Equations



F = -kx


The Attempt at a Solution



Pre note: I feel as though if I can find part a I can find B-D without much trouble as it seems to be just plug and chug. Am I right to assume this?

I did the F =-kx (Where F = 12.5 and x = .033) and I got 378.7878... N/m which was wrong. Did I do anything wrong?
 
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12.5 J is the work done, not the force applied.
Use the expression for the energy stored in a spring to find k.
 

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