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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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References:

1. Philosophiæ Naturalis Principia Mathematica’ (book, English translation published 1728), Isaac Newton, 1st ed., vol. 1, 1687, en.wikisource.org/wiki/Page:Newton%27s_Principia_(1846).djvu/89 (accessed Sep. 27th, 2019)
2. Historical development of Newton’s laws of motion and suggestions for teaching content’ (article), Wheijen Chang, Beverley Bell and others, Asia-Pacific Forum on Science Learning and Teaching, vol. 15, issue 1, article 4, 2014, www.eduhk.hk/apfslt/download/v15_issue1_files/changwj.pdf
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