Work done to move spring displacement

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SUMMARY

The discussion focuses on calculating the work done to change the length of a spring from 2 cm to 10 cm, given a spring stiffness of 95 N/m and a relaxed length of 5 cm. The correct approach involves recognizing that the force exerted by the spring is not constant and requires integration to determine the work done. The relevant equations include Hooke's Law (F = -kx) and the work integral W = ∫ F(x) dx. The user initially attempted to apply the work formula incorrectly, leading to confusion about the direction of force and displacement.

PREREQUISITES
  • Understanding of Hooke's Law (F = -kx)
  • Basic knowledge of calculus, specifically integration
  • Familiarity with the concept of work in physics (W = Fdcostheta)
  • Ability to analyze variable forces in mechanical systems
NEXT STEPS
  • Study the principles of integration in physics for variable forces
  • Learn how to apply Hooke's Law in different scenarios
  • Explore energy conservation methods in spring systems
  • Review examples of work done on non-constant forces
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and spring dynamics, as well as educators looking for examples of work calculations involving variable forces.

gunster
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Homework Statement


A spring has a relaxed length of 5 cm and a
stiffness of 95 N/m. How much work must you
do to change its length from 2 cm to 10 cm?

k=95
Lnull=0.05
delta x = .1-.02 = 0.08


Homework Equations



F=-kx
W=Fdcostheta


The Attempt at a Solution



I honestly have tried everything and am beginning to think I am way off the mark and missed something. But what i tried was

W = Fdcostheta where F = -kx

Therefore, since force changes direction after the displacement is past the relaxed spring length, i used:

W = -95 * (0.05-0.02) * (0.05-0.02) cos 0 + -95 * (0.1-0.5) * (0.1-0.5) cos 180


But that was apparently completely wrong. any help please?
 
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[itex]F = F d \cos \theta[/itex] is only valid if the force is constant over the distance (not a function of x in this case). Your force is a function of x, so you will have to integrate to get the work. It's possible you can solve the problem with a energy approach if integrals are beyond your course material.

[tex]W = \int F(x) dx[/tex]
 
EDIT: nvm realized my mistake was suppose to subtract

Thanks a lot for reminding me force is not constant XD
 
Last edited:

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