Work-Energy Theorem – Detailed Explanation and Applications

kinematicsnewtonian-mechanicspotential energywork

The Work Energy theorem states that work $W$ done is equal to the change in kinetic energy $KE$.

$$
W= Δ{KE}
$$

But say some work I do is stored as Potential Energy, in this case, the some work done is used as potential energy and all work isn't converted to kinetic energy. How does this statement remain true in the case of work being stored as Potential Energy?

Best Answer

Potential energies come from work done by conservative forces. The work-energy theorem includes all work done by all (mechanical) forces, so:

$$\underbrace{W_\text{conservative}+W_\text{other}}_W=\Delta K.$$

Remember that work can be negative, such as when gravity pulls downwards while you lift something up.

Sometimes, instead of referring to the work done by conservative forces we rather want to consider the potential energy that they store due to their conservative nature, and then $W_\text{conservative}=-\Delta U.$ Then the energy-work theorem is written as:

$$W_\text{other}=\Delta K+\Delta U,$$

and this is actually the general energy conservation law (for mechanical forces). To avoid confusion remember that potential energy and work by a conservative force are two sides of the same coin - we use the terms more or less interchangable depending on scenario, and you can invoke the work-energy theorem or the general energy conservation law when you feel for it.

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