Discussion
A spring of spring constant k is cut into n pieces of equal length. The force constant of any one of the pieces is
Answer: E
The force constant of each piece is \(nk\).
For a spring of given material and coil, the spring constant is inversely proportional to its length: \(k \propto \frac{1}{L}\). Each piece is \(\frac{L}{n}\) long, so its constant is \(n\) times larger.
A check: the n pieces joined end to end in series must give back the original spring, and \(n\) springs of constant \(nk\) in series give \(\frac{nk}{n} = k\).
\(\frac{k}{n}\) has the proportion the wrong way round; a shorter spring is stiffer, not softer. \(nk^{2}\), \(\frac{n^{2}}{k}\) and \(\frac{n}{k}\) do not even have the units of a spring constant.
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