Help in strain energy calculation

[Stefenng]

Homework Statement

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.

Homework 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. )

The Attempt at a Solution

I calculate the strain energy of 1 spring first, which is
8 x 0.04m / 2 = 0.16J

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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

or

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?

 

[Mapes]

Given the conditions you've described, the book answers seems to be incorrect.

 

[tiny-tim]

Welcome to PF!

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 )