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We are supposing in my mechanics course that forces add as vectors. But why, philosophically, should this be the case?

Qmechanic
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  • Possible duplicate of Why does force add like a vector? – Kyle Kanos Aug 23 '19 at 18:08
  • Possible duplicate of Why is force a vector? – Thomas Fritsch Aug 23 '19 at 18:09
  • Hi The question is duplicate, but here a little answer: A force has always a direction: if you are pushing me backwards, and I am pushing you backwards (fighting as sumo for example): if we add the force, we are suppose to move twice as fast as if I was only pushing you. In reality, one force is substracted to the other and we are not moving, because of the opposite direction. So if you want to add forces, you need to consider their direction, (modelize them as vector is an easy tool), otherwise you are not speaking of physics – totalMongot Aug 23 '19 at 18:22
  • I see that this means that their direction should be taken into account, but is there any proof that they have the same properties as vectors, then? –  Aug 23 '19 at 18:31
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    There is nothing philosophical about this. It is a physical observation. – G. Smith Aug 23 '19 at 18:41
  • @G.Smith, I agree. Physics is based on mathematical models that more or less accurately reproduce observations of the physical world in a mathematical way, whether or not those observations seem to make intuitive or philosophical sense. – David White Aug 23 '19 at 21:14
  • @DavidWhite Yes, but it is hard to imagine anything more intuitive than vectors. Their law of addition is defined to match how displacements are observed to work. If I walk a mile north and a mile east, I end up at the same point as when I walk 1.414 miles northeast. I cannot understand how physics courses can leave students puzzled over something so basic. – G. Smith Aug 24 '19 at 00:38
  • @G.Smith, I agree. Note that I taught high school physics for 13 years, and over time, I noted that students became much more dependent on technology to give them the answer, they became much more comfortable with copying other student's homework to minimize the amount of work that they had to do, they used cell phone apps to give them the answer to their math problems, etc. Once students get accustomed to these methods, they avoid any original thought, and they can't deal with a course that requires thinking rather than memorizing the answer. – David White Aug 24 '19 at 01:29
  • Interesting discussion, although I note you focus on the idea of displacement vectors, which I was not asking about. –  Aug 24 '19 at 19:15
  • @Phys1, a vector is a vector. All vectors have the same properties of direction and magnitude. All vectors can be broken down into orthogonal components, and the orthogonal components are mathematically independent from each other. – David White Aug 26 '19 at 02:29

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