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So I came across this picture on facebook enter image description here

My logic says it should show 200N, because you are pulling it with 100N on each side. On the other hand (as one of the facebook comments also stated, also saying is he is wrong he wasted 20k$ on physics degree), if you replace the right side with a wall you get this situation:

enter image description here

In this case I guess everyone agrees that the dynamometer would show 100N force. But if you isolate the dynamometer and "cut" the ropes on either picture, you would get the same thing. Because the system needs to be balanced, there would be 100N on each side. enter image description here

And I study engineering too but I am confused by this. Why do we get the same distribution of forces, but dynamometer shows a different force?

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  • $\begingroup$ When you cut the rope on one side, what's preventing the dynamometer from being pulled off the table? $\endgroup$
    – probably_someone
    Commented Aug 10, 2018 at 21:42
  • $\begingroup$ "My logic says it should show 200N, because you are pulling it with 100N on each side." What do you think pulling on only one side would look like? Have you ever seen a spring balance only pulled on one side? (This would mean, for the scales you see at grocery stores that hang from the ceiling, that the top could not be attached to the ceiling.) $\endgroup$
    – knzhou
    Commented Aug 10, 2018 at 21:50
  • $\begingroup$ Maybe you think that's different, because no person is pulling on the top. Instead the top is "just where it attaches to the ceiling" so there is "no force" there. Well, if you've managed to invent a material that somehow attaches things to a ceiling without exerting any force, tell me so we can get rich! $\endgroup$
    – knzhou
    Commented Aug 10, 2018 at 21:51
  • $\begingroup$ "Why do we get the same distribution of forces, but dynamometer shows a different force?" Rather than merely trusting your logic you should definitely put this to the test... $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Aug 10, 2018 at 23:08

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If I pull a dynamometer on the left side with a force of $100N$, which I intend to measure, it'll obviously start acclerating to the left and will hardly indicate any force.

What force do I need to apply to the right side of the dynamometer, say, with my hand, in order to prevent the dynamometer from accelrating away in the first place? It is, obviously, $100N$.

When such force is applied, instead of accelrating, the dynamometer will stretch a bit and then stop, indicating some force.

Since, my intend was to measure $100N$ force acting on the dynamometer from the left side, I, naturally, expect that the dynamometer shows $100N$ - despite the fact that $100N$ forces are applied to both sides.

So, no matter who supplies the force to the right side, a hand, a weight or a wall, it has to be there to keep the dynamometer in place, and, in each case, the dynamometer will show the same force value.

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