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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.

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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?

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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?

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