Help using Hooke's law to find work

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SUMMARY

This discussion focuses on applying Hooke's Law to calculate the work done in stretching a spring. The problem states that 18 foot-pounds of work is needed to stretch a spring 4 inches, and the goal is to find the work required to stretch it an additional 3 inches. The solution involves integrating the force function derived from Hooke's Law, resulting in an expression for work that requires careful evaluation of limits and constants. The final calculation yields a work value of 74.25 foot-pounds, emphasizing the importance of correctly setting up the integral.

PREREQUISITES
  • Understanding of Hooke's Law and its formula, f = kx
  • Knowledge of integral calculus, specifically the Fundamental Theorem of Calculus
  • Familiarity with units of work, particularly foot-pounds
  • Ability to manipulate algebraic expressions and solve for constants
NEXT STEPS
  • Review the application of Hooke's Law in various spring problems
  • Study integration techniques in calculus, focusing on definite integrals
  • Explore the relationship between force, work, and energy in physics
  • Practice solving similar problems involving variable forces and work calculations
USEFUL FOR

This discussion is beneficial for physics students, educators teaching mechanics, and anyone interested in understanding the practical applications of Hooke's Law in real-world scenarios.

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Homework Statement


Use Hooke's Law to determine the variable force in spring problem.

Eighteen foot-pounds of work is required to stretch a spring 4 inches from it's natural length. Find the work required to stretch the spring an additional 3 inches.


Homework Equations


W=∫f(x)dx
f=kd


The Attempt at a Solution



I set the work equal to 18 and the distance equal to 4.
so 18=4K, K=18/4
with this knowledge I set my function is (18/4)X
integrating
∫(18x/4)dx from 4 to 7
I get 9x(^2)/4
using the fundamental theorum of Calculus from 4 to 7
I get 74 1/4 (not sure of units, is it inches-pound)
 
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You need to start off recognizing that

W - W(t) = ∫0df(x) dx = ∫0d kx dx

If you will re-work the problem with this beginning, I think you will get a totally different outcome.
 

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