Law of the lever without (infinitesimal) displacements

In summary, the conversation discusses the possibility of deriving the law of the lever without using any displacements or the concept of work or torque. It is suggested that a 3 node truss model could be used to determine static equilibrium in a lever system.
  • #1
greypilgrim
506
36
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.
 
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  • #2
For a static scenario you could easily derive it from torque
 
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Likes CWatters and russ_watters
  • #3
Let's take a block and tackle system then.
 
  • #4
greypilgrim said:
Let's take a block and tackle system then.
Take it where? What are you asking?
 
  • #5
greypilgrim said:
Let's take a block and tackle system then.
Do a free body diagram at each pulley assuming uniform tension.
 
  • #6
greypilgrim said:
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.
 
Last edited:

1. What is the law of the lever without infinitesimal displacements?

The law of the lever without infinitesimal displacements is a principle in physics that states the equilibrium condition for a lever is achieved when the product of the force and its distance from the fulcrum on one side is equal to the product of the force and its distance from the fulcrum on the other side.

2. How is the law of the lever without infinitesimal displacements different from the regular law of the lever?

The regular law of the lever only applies to situations where the lever is in a state of equilibrium with infinitesimal displacements, while the law of the lever without infinitesimal displacements takes into account larger displacements and the effect of these displacements on the equilibrium of the lever.

3. What is the significance of the law of the lever without infinitesimal displacements?

The law of the lever without infinitesimal displacements allows scientists and engineers to analyze and design lever systems with larger displacements and greater accuracy. It is also a fundamental principle in mechanics and is used in many different applications, such as in construction and engineering.

4. Can the law of the lever without infinitesimal displacements be applied to other systems besides levers?

Yes, the principle behind the law of the lever without infinitesimal displacements, which is the conservation of energy, can be applied to other systems as well. For example, it can be used to analyze the equilibrium of pulley systems or any other simple machines.

5. How does the law of the lever without infinitesimal displacements relate to real-world scenarios?

The law of the lever without infinitesimal displacements is applicable to many real-world scenarios, such as determining the appropriate balance between weight and distance in see-saws or the positioning of weights on a lever to achieve equilibrium in a weighing scale. It is also used in designing and analyzing various mechanical systems, such as cranes and forklifts.

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