Spring 1 has a force constant of k, and spring 2 has a force constant of 2k. Bot

Question

Spring 1 has a force constant of k, and spring 2 has a force constant of 2k. Both springs are attached to the ceiling, identical weights are hooked to their ends, and the weights are allowed to stretch the springs. The ratio of the energy stored by spring 1 to that stored by spring 2 is... My initial answer was 1:2 because spring 1 has an equation of U=1/2kx^2 and spring 2 has an equation of U=kx^2. Spirng 2 has two times the energy of spring 1. Why am I wrong? The correct answer, according to the book, is B.

(A) ?2:1

(B)2:1

(C) 1:2

(D) 1:1

(E) 1:?2

Explanation / Answer

m g = k1 x1 m g = k2 x2 so k1 x1 = k2 x2 >>>> x1/x2 = k2/k1 U1/U2 = (0.5 k1 x1^2)/(0.5 k2 x2^2) = (k1/k2)(x1/x2)^2 = (k1/k2)(k2/k1)^2 = k2/k1 = 2 So correct answer is 2:1

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