Calculating the potential energy of a spring

[bobsmith76]

Homework Statement

A force of 18 N compresses a spring by 15 cm. By how much does the spring’s potential energy change?

Homework Equations

E_e = .5kx²

The Attempt at a Solution

Why doesn't .5 * 18 * .15^{2p/sup] do it? Seems pretty obvious. My answer is .2 J, the book's answer is 1.4J}

 

[VulcanWong]

Actually,the k in your equation is not the force applied on the spring,it is a spring constant(force/compressed length).If you insist on using force(18N) to calculate,you can rewrite your equation to 0.5Fx^2 by Hooke's Law(F=kx).Then you should get your answer

 

[bobsmith76]

Ok, but I find distinguishing those two to be rather hard.

 

[VulcanWong]

I think F=kx (Hooke's Law) is a great way to distinguish these 2 variables,I don't know whether it works on you,but that's my way^^(P.S It is always easier to distinguish similar variable by understanding the underlying principle of the equations)
Hope this helps

 

[bobsmith76]

But I don't understand the difference between force compressed and force Newtons.

To me they both measure the same thing. They both measure the force needed to compress a spring.

 

[VulcanWong]

That k is not force compressed,it is a quantity called spring constant or force constant.i think you really don't understand what Hooke law means.Here is the meaning,Hooke's Law states that the tension of the spring is proportional to is extension or compression from its natural length.That k is a proportionality constant which means how many Newton is needed to compress or extend 1 meter of the spring.

 

[SHISHKABOB]

when talking about springs, k is the spring constant. The spring constant of some spring is a ratio of Force required to compress or stretch it some distance x.

Or: k = $\frac{F}{x}$

The potential energy of a spring is given in terms of its spring constant times the square of the distance compressed or stretched, like you've got it

E = $\frac{1}{2}$kx²

so plug and chug



so remember: k = spring constant = N/m

while: F = force = N

that's the difference