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

AI Thread Summary
The flexibility of a lever arm, such as a pipe, can influence the torque it generates by storing energy as elastic potential when flexed. The equation T=Fd does not account for this energy storage, leading to potential discrepancies between applied force and resulting torque. While some argue that once a lever reaches its maximum bend, it behaves like a solid object, others highlight that flexibility can affect the ability to apply force effectively. Additionally, at low accelerations, the inertia of the lever can be ignored, making flexibility less significant in torque calculations. Ultimately, the relationship between applied force and torque is complex and influenced by the lever's material properties.
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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