# What would the tension in the cable be?

A subsequent question stemming from here A massless motor is attached to a massless pulley(the blue circle) with a fixed rotational inertia and they are all attached to a mass X (the green platform). A cable (in orange) with spring constant K is attached to the pulley from the black rigid ceiling, the cable could be at the top of the pulley at t=0, or it could be at the side as shown in the picture.

Assume it is a motor supplying the torque to the pulley. What torque should the motor (assume it has the same outer diameter with the pulley) output to move the mass up? Should the torque produce a force that is the same as the weight of the platform and the cable would experience a tension two times the weight of the platform? If this is so, it could be said that it is the tension from the cable that is pulling up the mass with an acceleration of g, right? But if the motor rpm is constant, then why would there be acceleration?

– Fred
Feb 21, 2021 at 4:49