Solving the Pulley Problem: Calculating Ceiling Force

[negatifzeo]

Homework Statement

Two weights are connected by a very light flexible cord that passes over a 50.0 N frictionless pully of radius .300 m. The pulley is a solid uniform disc connected by a hook to the ceiling. What force does the ceiling exert on the hook?

(In the picture shown is the pulley and two weights hanging on each side. One weight is 75 N, on the other side the weight is 125 N)

Homework Equations

t=FL?

The Attempt at a Solution

I know the force exerted on the hook will be the total net downward force (or the opposite of it). I also understand that the 125 n wieght on one end of the pulley "makes lighter" the 75 n weight, and vice versa. What I'm not sure of is the relationship how.

 

[bucher]

Try by first drawing a free body diagram of the pulley and the weights. If I'm thinking correctly, you would subtract the 75 N from the 125 N and the remaining 50 N would act on the pulley. I'm assuming, of course, that this system is not in equilibrium.

 

[negatifzeo]

I know from the back of the book that the answer is 239 N. I'm just puzzled as to how the solution was reached.

 

[bucher]

Oh, I was just re-reading what I just wrote. Forget my previous post. I was thinking of a different scenario.

 

[LowlyPion]

I know from the back of the book that the answer is 239 N. I'm just puzzled as to how the solution was reached.

Look at the pulley.

You have the weight of the pulley and what other forces acting on it?

If you are thinking it is the sum of the tensions in the cable that would be a good place to start.

Since the weights are accelerating, one up and the other down, then you need to determine the acceleration. Of course this involves not only the difference in weight, but also the moment of inertia of the pulley itself.