Question

You compress a spring by x, and then release it. Next you compress the spring by 2x. How much more work did you do the second time than the first

Answer 1

Answer:

Work done is $\frac{3}{2}$k$x^{2}$.

Explanation:

The work done by the spring is the same as the potential energy stored in the spring.

So that,

work done = potential energy = $\frac{1}{2}$ k$x^{2}$

where k is the spring constant of the material of the spring, and x is the compression.

When the spring is compressed by x;

work done = $\frac{1}{2}$ k$x^{2}$

When the spring is compressed by 2x;

work done = $\frac{1}{2}$ k$(2x)^{2}$

                  = $\frac{1}{2}$ k(4$x^{2}$)

                  = 2k$x^{2}$

Therefore,

The work done the second time more than the first = 2k$x^{2}$ - $\frac{1}{2}$ k$x^{2}$

                                                                                = $\frac{3}{2}$k$x^{2}$

The work done the second time more than the first is $\frac{3}{2}$k$x^{2}$.