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Potential Energy

Potential energy lets us do work in the present to change things in the future. If energy is currency, then potential energy is money in the bank.

Potential Energy of Springs

         

A spring is shortened by \(2\text{ m}\) from its original length. If the elastic potential energy of the spring is \(10\text{ J},\) what is the value of the spring constant?

A spring hanging from the ceiling has a length of \(4\text{ m},\) and its spring constant is \(k=20\text{ N/m}.\) If the spring is pulled so that its length gets doubled, what is the elastic potential energy in the spring?

An object attached to a spring lies on a frictionless horizontal floor. A force \(F=40\text{ N}\) is applied on the object towards the right. If the spring constant is \(k=10\text{ N/m},\) what is the elastic potential energy of the spring when it reaches its maximum length?

In the figure above, an object of mass \(m=4\text{ kg}\) is sliding towards a spring with a speed of \(v=6\text{ m/s}\) on a frictionless horizontal floor. If the spring constant is \(k=1\text{ N/m},\) what is the maximal change in the spring's length?

The spring in a monster truck's suspension is shortened by \(4\text{ m}\) from its original length. If the spring constant is \(k=2\text{ N/m},\) what is the elastic potential energy of the spring?

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