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I've been told by my professor that the restoring force (a reaction force) is always equal to the deforming force due to Newton's third law, and this is why stress is calculated using deforming force.

My understanding is that in the case of elastic objects like a spring, the restoring force = the deforming force at equilibrium position. But before that, the deforming force will be greater than the restoring force, which is when deformation occurs. Once the equilibrium is reached, no more deformation occurs. This restoring force drives the spring back to its original position once the deforming force is removed. Is this correct?

Also, if restoring force (which must be generated due to Newton's third law) = deforming force at equilibrium for plastic objects like mud, why don't they attain their original dimensions after the deforming force is removed? Is it that plastic objects never attain equilibrium (i.e. the object goes on deforming until the object physically separates) and then fracture at some point? But that would mean that the two forces are unequal.

Apologies for the silly question, and my sincere thanks for any help.

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The confusion arises from conflating Newton's reaction forces with the various forces acting on a single object.

Newton's reaction forces act on different objects: When I bend a paper clip, the force I exert on the paper clip is the same as the force the paper clip exerts on me. These are reaction forces, and they're equal and opposite, as specified by Newton's third law. They can't be legitimately added together because they don't act on the same object.

The paper clip bends because the force I exert is greater than its internal resistance. These are not reaction forces, and they can differ. They are correctly added together to determine how the paper clip dynamically responds to the load (e.g., through translational or rotational acceleration or deformation).

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    $\begingroup$ Thank you very much sir:) $\endgroup$ Commented Jan 12, 2023 at 5:08

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