How Does the Ceiling Exert Force on a Pulley System?

[J89]

Homework Statement

Two weights are connected by a very light flexible cord that passes over a 50 N frictionless pulley of radius .300 m. Pulley is a solid uniform disk and is supported by a hook connected to a ceiling. What force does the ceiling exert on the hook? There are two weights around each side of the disk, one is 75 N and the other is 125 N. Answer is 249 N.

Homework Equations

I = 1/2 MR^2
F=ma

The Attempt at a Solution

 

[tiny-tim]

Two weights are connected by a very light flexible cord that passes over a 50 N frictionless pulley of radius .300 m. Pulley is a solid uniform disk and is supported by a hook connected to a ceiling. What force does the ceiling exert on the hook? There are two weights around each side of the disk, one is 75 N and the other is 125 N. Answer is 249 N.

Hi J89!

(I assume that "frictionless pulley" means that there is friction between the pulley and the rope, with no slipping)

The tension in the two sections of rope will be different … call them T_m and T_M, and call the linear acceleration a …

then apply good ol' Newton's second law three times, ie to each of the weights and the pulley (separately), to get T_m + T_M