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> **Context**: I have no background in physics, and I'm trying to understand the role of the concepts of energy, momentum and other invariants/symmetries in physics. In particular, I'm trying to get a feel for why reasoning based on forces is/can be less powerful than reasoning based on invariants like energy.
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In the [Feynman lectures](http://www.feynmanlectures.caltech.edu/I_04.html), he gives an example of a lever problem where it is helpful to solve it with the principle of conservation of energy:

[![enter image description here](https://i.stack.imgur.com/CrudP.png)](https://i.stack.imgur.com/CrudP.png)

The problem is to find a weight $W$ that would keep the rod horizontal. He uses the definition of the potential energy of the three weights, and the condition that energy is conserved which implies that the potential energy must not change by a rotation of the rod.

Generalizing this, we can derive the general rule "the law of the lever" from energy conservation. **I am wondering whether we can find the solution merely using Newton's laws, without the concept of energy** (and of course without already using the law of the lever).