State Newton’s second law of motion. Show that Newton’s first and third laws of motion are contained in the second law

Every physics student learns Newton's three laws of motion. It's tempting to consider that these are three separate and independent laws. That's not so. Both the first and third laws may be mathematically derived from the second law, as we will show.

The fact that the first law may be derived from the second has long been known. The second law,Fnet=ma, tells us that the net (vector sum) of all forces acting on a body is equal to the product of the body's mass and its vector acceleration. When the acceleration is zero, the net force must be zero. This is exactly the content of the first law.

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 thatFnet=0a, soFnet= 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, they must add to zero, and therefore must be equal size and oppositely directed. This establishes Newton's third law.

Explanation:

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