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Classical Mechanics

Potential Energy

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 is at rest on a frictionless surface is attached to the wall by an elastic spring of strength \(\SI[per-mode=symbol]{10}{\newton\per\meter}.\)

A force of strength \(F=40\text{ N}\) pulls the object toward the right.

What is the elastic potential energy of the spring at equilibrium?

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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