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Help in strain energy calculation

by Stefenng
Tags: calculation, energy, strain
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May13-09, 11:03 PM
P: 10
1. The problem statement, all variables and given/known data
When a spring fixed at one end is pulled by a force of 8N, the extension is 40mm. Two such springs are joined in series and is pulled to produce a total extension of 40mm. What is the strain energy in the springs.

2. Relevant equations
strain energy, U = Fe / 2 or
U = F2/2k

*e is the extension while k is the spring constant.

( I found this equation online, correct me if this is wrong. )

3. The attempt at a solution
I calculate the strain energy of 1 spring first, which is
8 x 0.04m / 2 = 0.16J

for one spring, the spring constant should be
F = ke
8 = 0.04k
k = 200

For two spring, the spring constant is
1/k = 1/k1 + 1/k2
1/k = 1/100
k = 100

hence, the force used to made an extension of 0.04m is
F = 100 x 0.04
= 4N

Thus, the strain energy is
U = F2 / 2k
= 16 / 200
= 0.08J


U = Fe /2
= 4 x 0.04 / 2
= 0.08J

The answer provided by the book is 0.32J, which is differ with the answer I calculated, either one string or two strings. Can anyone correct the mistakes I made while doing calculation? Or the answer given is incorrect?
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May14-09, 07:49 AM
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Mapes's Avatar
P: 2,532
Given the conditions you've described, the book answers seems to be incorrect.
May14-09, 08:04 AM
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tiny-tim's Avatar
P: 26,160
Hi Stefenng! Welcome to PF!

Yes, your answer looks right

(though it would have been easier if you'd also used the equation U = ke2/2, and just added the energies in the two halves )

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