Prooving a system will travel up to 180 degrees

[physicsodyssey]

Homework Statement

To prove that system will travel freely upto 180 degree
m2 is counterweight and m1 is mass of pan (=3kg)
i have attched the fbd or another link http://www.imagebam.com/image/54bb5a394377595

Homework Equations

m1(h + a sin θ) g x = m2 y h g
m2 = 9.13 kg

The Attempt at a Solution

we are stuck at the following equation
Pwg ≥( m1 x^2 + m2 y^2) sin2 θ / [ x(h-xsin2 θ)]
LHS is weight of pan and arm and if LHS>RHS, system will rotate freely
is this correct? can you pls explain it properly because it will clear my concepts.
Thanks.

 

[BvU]

Hello, welcome to PF

Could you clarify the problem statement a bit more? The diagram is difficult to read, I see no forces, what is what, what is the pivot point, what is a, what is P w (pr Pw ?), etc.

 

[physicsodyssey]

a is the length of bearing housing(the middle block which is the reference axis) hence a sin θ is added to h for balancing. my issue is the second equation. i cannot understand the RHS side.LHS is simply the wt of pan and tray.(ρwg).
can you help me with the equation on RHS
( m1 x^2 + m2 y^2) sin2 θ / [ x(h-xsin2 θ)]
Thanks a lot for a warm welcome in this wonderful community.

 

[BvU]

Still lost -- or rather not "in":

The thing on the right is a pan. What is a pan ? The thing in the middle is a bearing housing. Interesting. Does it pivot around some axis ? What axis ?

If the LHS was the weight of the pan and arm and now is the weight of the pan and tray, how come m1 doesn't feature in it ? What tray ?
What is s ?

What does the equation m1(h + a sin θ) g x = m2 y h g represent ? I see something in kg m³ /s²

What is $\theta$ ? What's the blue horizontal line ? And the black sloping line just underneath ?

THe fat black lines to L and R ? The thin black lines (where the h are mentionsed) ?

What is dangling from the bearing housing ? Where is the reference point for a ?

Are lengths measured in meters ?

What has to rotate 180 degrees ? Doesn't it bum into the fat line on the left ?