Question

A spring of spring constant 'k' cut into n pieces. What is the spring constant of each piece?

• A. $\frac{k}{n}$
• B. $\frac{n}{k}$
• C. $\frac{n^2}{k}$
• D. $nk$

Hint:

Intuitively, making a spring shorter drastically reduces the amount of elastic material available to stretch, rendering it much stiffer and significantly harder to pull!

Answer 1

The Correct Option is D

To determine the spring constant of each piece when a spring with an original spring constant \(k\) is cut into \(n\) equal parts, we need to understand how the spring constant changes when the length of a spring is altered.

The spring constant, often denoted as \(k\), is a measure of a spring's stiffness. It is inversely proportional to the length of the spring. Mathematically, this is expressed as:

\(k' \propto \frac{1}{L}\)

where \(k'\) is the spring constant of a segment of the spring, and \(L\) is the length of this segment.

If the original spring is cut into \(n\) pieces, each piece is \(\frac{1}{n}\) of the original length. Since the original spring constant \(k\) corresponds to the full length, the spring constant for each piece (with the reduced length) will be:

\(k' = n \times k\)

This is because the spring constant is inversely proportional to the length of the spring segment.

Conclusion: The spring constant of each piece after cutting the spring into \(n\) equal parts is \(nk\). Therefore, the correct answer is \(nk\).