As a student in a physics lab, you are asked to classify two springs. Right away

Question

As a student in a physics lab, you are asked to classify two springs. Right away you notice some differences. The first spring, spring 1, is very easy to compress and pliable. The second spring, spring 2, is stiffer and more difficult to deform. What qualitative statement can you make about their spring constants? Now you want to understand the springs quantitatively. You find that it takes 6.00 J of work to stretch spring 1 by 11.0 cm. 12.0 J is required to displace the second spring 2.75 cm. What is the ratio of the two spring constants, k2/k1? k1 is the spring constant of spring 1 and k2 is the spring constant of spring 2.

Explanation / Answer

Use E = ½kx² ==> k = 2E/x²
#1: k1 = 2 * 6J / (0.11m)² = 991.735 N/m
#2: k2 = 2 * 12J / (0.0275m)² = 31735.53 N/m

k2 / k1 = 31735.53/991.735= 32

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