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 = F^{2}/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/k_{1} + 1/k_{2} 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 = F^{2} / 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?
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 = ke^{2}/2, and just added the energies in the two halves )