# What is wrong in this pulley diagram?

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.

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?

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.
• But aren't $T_1$ and $T_2$ the same in magnitude? Nov 20 '19 at 13:11