Law of the lever without (infinitesimal) displacements

[greypilgrim]

Hi.

Usually the law of the lever or similar force laws for simple machines are derived using
$$W_1=F_1\cdot s_1=F_2\cdot s_2=W_2\enspace,$$
sometimes called "Golden Rule of Mechanics". However, these force laws also hold in the static case where no work is done. Is it possible to derive the law of the lever without using any displacements, not even infinitesimal or virtual ones? As far as I can see, such a derivation would have to be independent of conservation of energy, as mechanical work is defined in terms of displacements.

 

[Dale]

For a static scenario you could easily derive it from torque

 

[greypilgrim]

Let's take a block and tackle system then.

 

[russ_watters]

Let's take a block and tackle system then.

Take it where? What are you asking?

 

[Dale]

Let's take a block and tackle system then.

Do a free body diagram at each pulley assuming uniform tension.

 

[A.T.]

Is it possible to derive the law of the lever without using any displacements, not even infinitesimal or virtual ones?

You can model the lever as a 3 node truss (triangle as the simplest rigid structure) to derive the static equilibrium, without any mention of work or torque.