Question

newton 3rd law mathemitacally prove

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Answer 1

Answer:

Newton's third law is often considered "trivial", but it's more subtle than most students realize. It asserts that "If body A exerts a force on body B, then B exerts a force of equal size and opposite direction on A." It can be written: FAB = – FBA. The pair of forces in this law are often called an "action-reaction pair." Each force is said to be a "reaction" force of the other, though this language is mere window dressing. The terms "action" and "reaction" are often misleading to students and are best avoided in these discussions, for they aren't necessary.

Explanation:

Let's first consider the case of two bodies in contact. Each exerts a force on the other at the interface, or point of contact, where the bodies touch. If that point or interface is treated as a "body" of mass zero, then Newton's second law tells us that Fnet = 0a, so Fnet = 0. So the net force on a body of zero mass is always zero, whatever forces act upon it. Therefore if only two forces act on a body of mass zero, they must add to zero, and therefore must be equal size and oppositely directed. This establishes Newton's third law.

Answer 2

Answer:

It asserts that "If body A exerts a force on body B, then B exerts a force of equal size and opposite direction on A." It can be written: FAB = – FBA. ... If that point or interface is treated as a "body" of mass zero, then Newton's second law tells us that Fnet = 0a, so Fnet = 0.