Calculating the potential energy of a spring

In summary, the potential energy of a spring is calculated by using the equation Ee = .5kx2, where k is the spring constant and x is the distance compressed or stretched. The spring constant is a proportionality constant that measures how many Newtons are needed to compress or extend 1 meter of the spring. The distinction between force compressed and force Newtons is important to understand in order to correctly use Hooke's Law and calculate the potential energy of a spring.
  • #1
bobsmith76
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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



Ee = .5kx2

The Attempt at a Solution



Why doesn't .5 * 18 * .152p/sup] do it? Seems pretty obvious. My answer is .2 J, the book's answer is 1.4J
 
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  • #2
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
 
  • #3
Ok, but I find distinguishing those two to be rather hard.
 
  • #4
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
 
Last edited:
  • #5
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.
 
  • #6
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.
 
  • #7
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 = [itex]\frac{F}{x}[/itex]

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 = [itex]\frac{1}{2}[/itex]kx2

so plug and chug



so remember: k = spring constant = N/m

while: F = force = N

that's the difference
 

What is potential energy?

Potential energy is the energy stored in an object or system due to its position or configuration.

How do you calculate the potential energy of a spring?

The potential energy of a spring can be calculated using the equation U = 1/2kx^2, where U is the potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

What is the spring constant and how do you determine it?

The spring constant, represented by the variable k, is a measure of the stiffness of a spring. It can be determined by dividing the force applied to the spring by the displacement it causes.

Can potential energy of a spring be negative?

Yes, the potential energy of a spring can be negative. This occurs when the spring is compressed or stretched beyond its natural length, resulting in a negative value for displacement in the equation U = 1/2kx^2.

How does the potential energy of a spring change with displacement?

The potential energy of a spring is directly proportional to the square of its displacement. As the displacement increases, the potential energy also increases. However, if the spring is stretched or compressed beyond its natural length, the potential energy may decrease or become negative.

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