Question

(a) Show that the potential energy stored in a spring is kx, where k is the force constant of the spring and x is the change in length of spring​

Answer 1

Solution -

Suppose that there is a compressible spring of length k units .

Now, when a force F is applied on it , it is compressed to a new length k` .

So , the length of compression becomes : ( k - k` ) .

Let this be equal to x .

Here, we can observe that the force , F is proportional to the change in length of the spring. ]

So, F $\propto$ x

The proportionality constant is k

So, it becomes, F = | -kx |

The modulus is because we need to find the magnitude of the force exerted .

This is the general formula for spring force .

k is known as the spring constant.

-------------------------------------------------------------------------------------