In the following setup, a free-hanging weight of mass $m$ is attached to a rope which passes over a pulley. I assume that the system is in equilibrium, so the sum of the forces is equal to zero.

enter image description here My question is: is this diagram wrong and why? I think it's wrong because if we consider the vector sum of the forces shown, and knowing it must be zero, we find that the magnitude of $T_1$ has to be in general different from that of $T_2$ and should depend on the angles involved in the setup. But we know that $||T_1||=||T_2||$. So what's happening? I think I am missing some force, maybe that exerted by the pulley rod on the base?

Would it change anything if instead of having a pulley the rope would be fixed to the rod?


1 Answer 1


The assumption that the force $R$ is in the direction of the rod is false. In fact, the direction of $R$ is exactly what you need to compensate the forces $T_1$ and $T_2$ with, which will produce some nonzero torque on the rod for general angles.

Simple experiment with your hand and some rope (and with a pulley if you have one) can give you an idea what kind of force your hand needs to generate to compensate forces coming from the rope.

  • $\begingroup$ But aren't $T_1$ and $T_2$ the same in magnitude? $\endgroup$ Nov 20, 2019 at 13:11
  • $\begingroup$ @marco trevi yes, they are.. $\endgroup$
    – Umaxo
    Nov 20, 2019 at 13:43

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