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# Newton’s 2nd law with momentum

The carried tomato and the falling tomato both weigh the same. Carrying the tomato means that your hand is doing the tough task of counteracting that weight. If it is even tougher to catch a tomato than to carry one, doesn’t that mean that there is more to counteract than just the weight?

Yes, indeed. Apart from balancing out the weight, your hand must also slow the tomato down to no speed. It must be given a (negative) acceleration. This brings up Newton’s 2nd law: $\sum \vec F=m\vec a$.

We just invented momentum to include both mass and speed. Causing an acceleration means changing the speed; which thus must mean changing the momentum. Momentum $\vec p$ must be involved with acceleration, and thus in Newton’s 2nd law, in some way:

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