Lever rotating around an axis.

clicwar

1. The problem statement, all variables and given/known data

A lever of length 3L can rotate freely around a horizontal axis O.
The end of each arm "2L" and "L" of the lever has one mass : "4m" and "9m" , respectively.

Find the velocity of mass "9m" at the bottom.
Consider that the lever was initially at rest in the horizontal position.

2. Relevant equations
The problem is in a chapter of work and energy, before the conceps of torque and moment of inercia, so i guess that only energy and work can solve this.
But any solution/hint with any method will be welcome.

3. The attempt at a solution
I'm trying to apply conservation of energy, but i'm confused if the whole system is conservating energy or only part of it.

I really need a hint of how start this problem or if possible a solution of it.

Thanks in advance!

Attached Thumbnails

 

andrevdh

What forces are acting on the system?

clicwar

I believe that only the gravitational forces are acting on the system "lever+masses". I can't see any other possible force able to do work.

Doc Al

Since everything is connected, treat the system as a whole. How does the mechanical energy change as the system rotates?

clicwar

The mechanical energy of the system as whole is doesn't changing ... right?
(Does the support O of the lever is doing work?) .

Doc Al

Right.
I interpret "rotate freely" as saying that there is no friction, and thus no mechanical energy lost to friction. The support O does no work, since it doesn't move.

clicwar

Thank you very much for the help DocAl. The sentence quoted above is exactly what i was looking for.