why is both kinetic energy and potential energy of a spring

equal to

1/2 kx^2??


also what sign is used for the force of the spring, F = kx for spring stretching and shrinking?

Opposite of the direction you chose as positive..

but how can it be on the opposite direciton of the datum... the spring cant go below the datum

i meant to set my datum where the horizontal line of 20 degree is, but it still doesnt change how it can be negative

This post was edited by FamilyGuyViewer on Oct 11 2015 10:38pm

Because you're looking at compression. Since for part 2, x is representing additional compression, you're going to have to multiply by a negative x quantity.

hmm still dont really get it, how else can u represent x in this problem or is this the only way to represent it...

signs always confuse me when it comes to springs

Work =Froce *Displacement

common work against gravity is =mgh ,mg=force ,h=displacement

in a spring force= kx
intergal of (kx) dx
(1/2)kxx

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energy is energy when it's all expended/transfered

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the sign doesn't matter as long as you keep everything straight in your problem
it's either absorbing or releasing

This post was edited by saber_x3 on Oct 12 2015 12:52pm

so the x in both Kinetic and Potential Energy is the same? which is the change in length?

A classical spring,mass-less, has no kinetic energy
it only has potential

but...kinetic and potential can be used interchangeably i guess
in the end, keep your track of your signs and everything will be ok. energy is energy

This post was edited by saber_x3 on Oct 14 2015 12:43am