Spring constant

Spring-mass system is extensively discussed while teaching simple harmonic motion. The quantity, tension/extension is called spring constant of the spring and relates to how soft or hard is the spring. To get familiarity with springs, we propose that each group of teachers makes two springs of different lengths and find their spring constants by doing the experiment described.

You need copper-wire, weight, stand, pipe, stop watch, nut or a weight, threads, scale, weighing balance.

1. You are given a pipe and some copper wire. You have to make two springs from this wire with approximate length ratio 1:2. Cut the wire in that ratio. Wrap the smaller piece of the wire on the given pipe to make a helical structure. Gently remove it from the pipe. Bend the ends so that it can be hanged on a support at a point on the axis and also a weight can be hanged from it at the lower end at a point on the axis.
2. Make another spring from the other part of the wire. Find masses \(m_1\) and \(m_2\) of the springs. Find the mass \(m_3\) of the given nut. Now hang the smaller spring on the stand. Tie the given weight (nut) to a small length of thread and hang it at the lower end of the spring.
3. Measure the extension of the spring using the scale given. Get spring constant \(k_1\) from the masses and the extension. Which equation will you use?
4. Similarly measure the spring constant \(k_2\) of the other spring. What are the values of \(k_1/k_2\) and \(l_1/l_2\).
5. How does spring constant depend on the length of the spring?

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1. Experiments

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