What Speed Keeps the Cylinder Stationary in the Puck-Cylinder System?

[raptik]

Homework Statement

A puck of mass m = 1.10 kg slides in a circle of radius r = 18.0 cm on a frictionless table while attached to a hanging cylinder of mass M = 3.00 kg by a cord through a hole in the table. What speed (in m/s) keeps the cylinder at rest?

Homework Equations

F = ma

The Attempt at a Solution

I know the F_net,y for the hanging cylinder is zero because it does not move, so I deduced that T - F_g = 0.
On the puck the 2 things I looked at was the a moving towards the hole and the tension which I am also deducing is moving towards the hole, away from the puck. (Note: I left out F_N and F_g because I didn't see how they would apply in the equation for the puck.) I thus got the equation T = ma.

I then plugged in the in this T into the previous equation to get: ma - F_g = 0
I then simplified the equation to a = g. Knowing that a in circular motion with constant velocity is a = v²/R, so the equation I ended up with was v = √Rg. This came out to 1.328 ms^-1, which is wrong. Could somebody tell me where my thinking went astray and how I can fix this.

 

[Delphi51]

There are TWO different masses, so you need to keep two different m's in your equation or replace them with the two different numbers. Your solution will be more elegant if you write Fc = Fg first (centripetal force is provided by the gravitational force), then replace them both with their detailed formulas.

 

[raptik]

Thank you very much. I overlooked that there were two different masses involved in the equation and just worked them out of my problem by mistake.

 

[Delphi51]

Most welcome! It is a pleasure to save you the frustration of a tiny mistake after you demonstrate your mastery of the whole problem.