What is the influence of a lever arm's flexibility on torque?

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Discussion Overview

The discussion revolves around the influence of a lever arm's flexibility on torque generation, exploring how elastic deformation may affect the relationship between applied force and torque. Participants examine theoretical implications and practical applications related to this concept.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • Some participants propose that flexing a lever arm, such as a pipe, stores energy as elastic potential energy, which could influence the torque generated.
  • Others argue that while some energy may be lost during deformation, the torque remains constant once the lever reaches its maximum bend, assuming the geometry does not change significantly.
  • One participant asserts that force and energy are distinct, suggesting that at low accelerations, the flexibility of the lever does not affect the relationship between applied force and torque, although it may impact the ability to apply force and the work done.

Areas of Agreement / Disagreement

Participants express differing views on the impact of lever arm flexibility on torque, with no consensus reached regarding the extent of this influence or the implications for torque calculations.

Contextual Notes

Assumptions about the extent of deformation, the geometry of the lever, and the conditions under which torque is measured remain unresolved. The discussion also highlights the distinction between force and energy in the context of elastic deformation.

Connordzg
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If you flex a pipe, the energy is stored in it (assuming it returns to its original state). If that pipe were being used as a lever, wouldn't the torque it can generate be influenced by the flexibility of the lever? Why doesn't the equation T=Fd take this into account? Would all of the applied force be transferred to the torque?
 
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What I mean by this, is that wouldn't some of the applied force be stored as elastic energy in the lever arm? If yes, wouldn't this result in a discrepancy between the magnitude of the applied force and the magnitude of torque it generates?
 
Connordzg said:
If you flex a pipe, the energy is stored in it (assuming it returns to its original state). If that pipe were being used as a lever, wouldn't the torque it can generate be influenced by the flexibility of the lever? Why doesn't the equation T=Fd take this into account? Would all of the applied force be transferred to the torque?

Connordzg said:
What I mean by this, is that wouldn't some of the applied force be stored as elastic energy in the lever arm? If yes, wouldn't this result in a discrepancy between the magnitude of the applied force and the magnitude of torque it generates?

I believe that is correct. Just as if you had a spring that you were applying the force to the end of the lever through. That's why torque wrenches are usually made with very strong and stiff lever arms... :smile:
 
I'm not sure I agree. I'm assuming for a second the deformation is not so large that the geometry of the wrench would cause a different torque equation. In that case, once the wrench has reached its maximum bend, it will essentially behave like a completely solid wrench again.
So, while a certain amount of energy will have been lost, the torque, once the wrench is fully deformed, will stay the same. One during the deformation will it be lower.
 
Didn't read the whole post I responded to.
 
Connordzg said:
wouldn't some of the applied force be stored as elastic energy
No, force is not energy. At low accelerations, you can ignore the inertia of the lever and propagation velocity within the material. Then flexibility doesn't affect the relation between applied force and created torque. But a flexible lever might affect your ability to apply the force in the first place, and it affects the work you have to do, which will be stored as elastic energy.
 

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