Question

A spring is compressed through a distance 'x'. Which of the following is the correct expression for the energy stored in it?
PE=1/2kx^2
PE=1/2kx
PE=1/2x^2
PE=(1/2)(x^2/k)

Answer 1

a

Answer 2

more correctly, if the springs original length is \[d_{0}\] and the spring was compressed or stretched by a factor of x the the energy that is stored in the spring is \[\frac{ 1 }{ 2 }*k*(x-d_{0})^{2}\]
in your case i guess that \[d_{0}=0\]

Answer 3

why is kx squared?

Answer 4

the work it takes to compress the spring is calculated using the hook law. if you have the work than the energy is the integral of the work. considering that the work is a function of x of a first order the integral should look something like \[\frac{ 1 }{ 2 }*x^{2}\]

Answer 5

I can write the calculation for you if you really really want

Answer 6

so wouldnt the answer be c?

Answer 7

nope. half x squared +a const. is the overall form of the integral of x. in other words: \[\int\limits_{}^{}x dx = \frac{ 1 }{ 2 }*x + const.\]
as I said I didn't write the entire calculation only the main idea. plus this is a known formula, if your in high school I don't think you really need to know the whole math around it.

only maybe the physics which is that energy is the integral of the work it took to take the spring from one situation to another and maybe also hook's law which is\[F=-k \Delta x\]

Answer 8

You have have been a big help btw thanks!

Answer 9

oh i understand now

Answer 10

thanks!

Answer 11

any time :)