Consider two masses connected by a string over a pulley, like so:

enter image description here

Where mass $M$ is held in place by a hand.

I'm asked to draw free-body diagrams for mass $m$ and $M$ individually, and identify third-law pairs in the two diagrams. I'm then asked to consider when the hand moves and mass $m$ begins accelerating downwards.

We can assume the surface to be frictionless and the pulley to be massless.

It doesn't seem to me that there are any third-law pairs. The only third-law pairs I can identify in the diagram are the normal forces between the hand and the block (in the first case).

Am I thinking about this wrong?

  • $\begingroup$ yes, you are wrong, cant you think of any other forces acting on each mass? $\endgroup$
    – user65081
    Oct 29 '20 at 22:41
  • $\begingroup$ @Wolphramjonny In what way? Third-law pairs must a) act on two objects and b) be of the same type and magnitude. I see no such pairs here? $\endgroup$ Oct 29 '20 at 22:42
  • $\begingroup$ each force you can identify will have a pair. Can you find any other forces other than the ones between the hand and the mass on the table? $\endgroup$
    – user65081
    Oct 29 '20 at 22:43
  • $\begingroup$ Mass $m$ will have two forces, the tension $T$ of the rope, and the force of gravity $F_g$. Mass $M$ will have the normal force from the hand, $F_g$ and the normal force between the surface and the mass, and $T$ the tension. $\endgroup$ Oct 29 '20 at 22:48
  • $\begingroup$ good!!! now find the reaction (pair) of each one, which is the force that the masses do to the objects that make a force on them $\endgroup$
    – user65081
    Oct 29 '20 at 23:44

It doesn't seem to me that there are any third-law pairs.

Every force has its third law pair, but indeed you are correct that none of the forces acting on m form a third law pair with any of the forces acting on M.

For M there are four forces: weight, tension, contact force from the ground and the contact force from the hand. The third law pairs act on the earth, the string, the ground, and the hand respectively. None of them act on m.

Similarly for m there are two forces: weight and tension. The third law pairs of those forces act on the earth and the string respectively. None of them act on M


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