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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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