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**Summary:**I am confused in when to use 1/2 e squared k

we studied in class that normally, the extension of the spring is directly proportional to the tension applied

and we did this question :

what is the work that has to be done for a spring to have an extension of length e

as the area of the force extension graph gives the work done, we get the formula as 1/2ke

^{2}.

but in the next question :

A weightless spring is attached to a ceiling and a weight of 20 N is applied. Here the spring extend for 5cm. Calculate the spring constant.

solution1:

f= ek

k= 20 / 0.05

=400 N m

^{-1}

solution 2

according to the energy conservation theorum,

mgh = 1/2 e

^{2}k

20* 0.05=1/2 * 0.05 * 0.05 *k

k=800 N m

^{-1}

why am i getting two different answers? It will help if anyone explains. Also please don't use derivatives. I cannot understand them.