Question

What is the difference between the energy of spring A, stretched 0.6 meters, and spring B, stretched 0.3 meters, if they have the same spring constant?

Answer 1

the energy W of a spring, is given by the subsequent formula:
\[W=\frac{ 1 }{ 2 }k \Delta ^{2}\]
where k is the spring constant and \[\Delta \] is the spring stretch.
So if we have the same spring (namely the same value of k) we can write:
\[W _{2}-W _{1}=\frac{ 1 }{ 2 }k*(\Delta _{2}^{2}-\Delta _{1}^{2})\].
Substituting, your values, you get the answer. What is the value for k?

Answer 2

But you know that k is the same so:

\[\frac{ W _{1} }{W _{2}}= \frac{(\Delta _{1})^{2} }{(\Delta _{2} )^{2}}\]

So the ratio of the energy in the springs in independent of k

I think that the ratio is what is required for the answer to this question

Answer 3

@MrNood you are right, I also thought the same thing, nevertheless from the text of the problem it is required a difference, not a ratio.

Answer 4

The question does not give enough information to solve a numeric value.

(As you point out - you need k to solve that)

The answer in my opinion is

"The difference is that the energy in one is 4 times that in the other"