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Ok so I know that the (simplified) equation for force is $F=ma$, but here is what I don't grasp. If given that to get more $F$ you need either more $m$ or more $a$, then how come, if I'm pushing something e.g.: let's say I'm arm wrestling with someone, and I "lock" my arm, meaning that I'm not pushing forward just staying in place, how come I can resist his force, if I'm not increasing either my mass or my acceleration?

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  • $\begingroup$ What does "simplified" refer to? As the answer below points out, $F=ma$ is not a simplified equation; it's a wrong equation. The correct one is $\sum F=ma$. $\endgroup$ – Steeven Sep 8 '16 at 7:24
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    $\begingroup$ thx, I've been corrected and do apologize for the mistake $\endgroup$ – Bruno Sebastian Messeguer Cobo Sep 8 '16 at 11:21
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$F=ma$ is a little too simplified. It's really $\sum F=ma$: the sum of the forces acting on an object is equal to its mass times its acceleration. You have to account for all of the forces involved.

You can resist someone who is arm wrestling you because you are using your arms to apply a force to your hand in one direction, and your opponent is using their arms (and hand) to apply a force to your hand in the opposite direction. If the forces happen to be exactly equal in magnitude, then the sum of the forces is 0, and you have no acceleration.

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  • $\begingroup$ Ok, that explains the lack of movement, now I get it, but then, how come we are able to "lock" the arm in place without moving it? is it cuz the muscle is applying force on a different direction (towards my arm itself but I don't see the movement cuz the rest of my body has more M) and that force is enough to stop a force in a different direction to alter the trajectory that arm is supposed to go, even tho it's not moving anywhere? again I do apologize for the very unorganized examples, but without diagrams or pictures I find it hard to explain $\endgroup$ – Bruno Sebastian Messeguer Cobo Sep 8 '16 at 11:30
  • $\begingroup$ @BrunoSebastianMesseguerCobo I'm not entirely sure where the issue is. Unfortunately, as many of these things go, once they make sense they make sense, so in my mind there's no issue ;-) As it turns out, the human body is a very difficult place to learn basic physics, because it has a large number of control loops that are constantly changing how much force it applies in order to accomplish its goals. Also, in the human body, the acceleration periods are often very short, making it harder to see what is happening. However, if an object is "held still," it will not be accelerating... $\endgroup$ – Cort Ammon - Reinstate Monica Sep 8 '16 at 14:30
  • $\begingroup$ ... and thus will always have a balanced set of forces acting upon it. It might help to work backwards and try to identify where those forces can come from. In your arm wrestling case, the 3 primary sources of force are your own muscles (acting on your body which eventually acts on the ground in a chain of balanced forces), your opponent's muscles, and the table itself (which is pushing upwards on your elbows). $\endgroup$ – Cort Ammon - Reinstate Monica Sep 8 '16 at 14:31
  • $\begingroup$ That helped me alot, thank you kindly. going a it backwards solved it. thank you kindly $\endgroup$ – Bruno Sebastian Messeguer Cobo Sep 9 '16 at 2:42

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