Spring Potential Energy

Before I forget, let me say something quickly about spring potential energy.

I don’t think this is in my book, but you will need to know about it.  First, there is Hooke’s law.  This is a model for the force a spring exerts on something when it is compressed or stretched.  The magnitude of this force is:

Here k is the spring constant.  It basically tells you how stiff the spring is.  The “s” is the distance the spring is either compressed or stretched.

Normally, problems with springs can be seemingly difficult.  You can’t use the momentum principle very easily because the force is not constant.  However, if you were to determine the amount of energy needed to compress a spring an amount s, you would find that it would be:

If this is the amount of work that goes into compressing a spring, that must be the amount of energy stored in a spring. So, I can write the spring potential energy as:

Notice that it has positive potential energy no matter if the spring is compressed or stretched.

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