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Tyrannosaurus_
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Homework Statement
GIVEN: Force constant (k) = 170N/m. Displaced 10cm (0.1m) from equilibrium position.
REQUIRED: Find the work done on the spring.
Homework Equations
Solution 1 uses: W = ΔE, & (elastic energy} Ee = 0.5(k)x2, where k is the constant, and x is displacement from equilibrium position.
Solution 2 uses: W = F(Δd), & (elastic/spring force} Fe = kx, where k is the constant, and x is the displacement from the equilibrium position.
The Attempt at a Solution
Please evaluate these solutions & choose the best. Please tell me why. Please correct my misunderstandings. Thanks!
SOLUTION 1.
w = ΔE
w = Eefinal - Eeinitial
w = 0.5(k)xfinal2 - 0 {because initial the spring is at the eq. position.)
w = 0.5(170N/m)(0.1m)2
w = 0.85J
SOLUTION 2.
w = F(Δd)
w = Fe(Δd)
w = kx(Δd)
w = (170N/m)(0.1m)(0.1m)
w = 1.7J
Which solution is better, and why? (It's obvious why the values are different.)
Please help me understand why/where these approaches are best. (I understand calculus, but I need to understand these concepts, before I use calculus to evaluate.)