Question

Two springs have different spring constants. How could you identify the spring with the greater spring constant value?

Answer 1

Hint:In this question, we have two springs having different spring constants. We want to know which one has more spring and will have more spring constant. For that use the Hooke’s law, which tells that the spring constant depends inversely on the distance of compression of the spring. Hence, the spring which stretches less has more spring constant.

Complete answer:
Before knowing about the spring constant, we have to know from where it is being originated. It is being introduced from Hooke's law which states that the force applied to the spring to revert its size is proportional to the distance of the compression of the spring. To remove the proportionality, we had introduced the term spring constant.Hooke’s law: $F = - kx$ where $k$ is the spring constant.

Now in the question, we are provided with the two springs with two different spring constants. Now to check which spring will have more spring constant for that we are performing an experiment:Hang the two springs to the ceiling with the same mass on both the springs. The one which stretches less will have the larger spring constant.The explanation for this is that the spring constant is inversely proportional to the displacement of the spring. Hence, the spring whose x is less will have more spring constant.

Note:Hooke’s law shows a negative sign which tells that the force applied to the spring is always on the opposite side of the load applied by the load. This is because the spring always tries to come to its original position. Spring constant represents the stiffness of the spring.