5.2 The spring constant and combinations of springs — Practise
Work independently. The questions and answers are shown together at the end.
For every combination, check your answer against the size of the individual spring constants before you write it down: a series answer must be smaller than the smallest, and a parallel answer larger than the largest.
- Two springs of spring constant 60 N/m and 30 N/m are joined end to end. Calculate the spring constant of the combination.
- Two springs of spring constant 60 N/m and 30 N/m are joined side by side so that they stretch together. Calculate the spring constant of the combination.
- H Explain why the spring constant of two springs in series is smaller than either spring constant, while in parallel it is larger.
Answers and concise solutions
1. Spring constant of the combination
Answer: , so . A combination in series is easier to stretch than either spring, so the answer is smaller than both.
2. Spring constant of the combination
Answer: . Two springs sharing the load need less force each for the same extension, so the combination is stiffer than either spring and the answer is larger than both.
3. Series compared with parallel
- in series the same force acts on each spring, so the extensions add
- in parallel the load is shared, so each spring carries only part of the force and stretches less
- by k = F / x, a larger extension for the same force means a smaller spring constant, and a smaller extension means a larger one
Answer: In series the same force acts on each spring, and the extensions add. So the combination stretches further than either spring alone for that force, which by means a smaller spring constant. In parallel the load is shared, so each spring carries only part of the force and each stretches less. The combination stretches less than either spring alone for the same total force, which means a larger spring constant.