Forces on spheres in a cylinder

[emmettfoner]

Homework Statement

Two solid smooth (frictionless) spheres of radius r and mass m are
placed inside a cylinder of radius R. Find the force exerted by the cylinder
on each ball where they make contact with the cylinder (2 points on the
lower sphere, one on the upper) and the force each ball exerts on the
other. Express all forces in terms of m, R and r.

Relevant Equations

No relevant equations

I literally don't know where to start with this, i drew a free body diagram to try and understand where the cylinder was affecting them, but it didn't get me anywhere

 

[emmettfoner]

Also here is the solution, I don't know how to get to it.
Fbottom = 2mg, Fball-ball = mgr/[R(2r – R)] 1/2 , Fwall-ball = mg(R- r)/[R(2r – R)] 1/2

 

[Gaussian97]

I drew a free body diagram to try and understand where the cylinder was affecting them, but it didn't get me anywhere

Show us your diagram, also try to think of some equation you know that you think could be helpful.

 

[Lnewqban]

Can you understand what is happening in this problem?
Those spheres act as two wedges jamming each other in between two walls by the action of their own weights.
They make those spheres, so there is no wedge angle to talk about, giving infinite possibilities of angles formed between both spheres.
The solution equations clearly show that they are valid only for R<2r, since beyond that, there is no more jamming effect.
Same applies for the case of R=r.

 

[Chestermiller]

Also here is the solution, I don't know how to get to it.
Fbottom = 2mg, Fball-ball = mgr/[R(2r – R)] 1/2 , Fwall-ball = mg(R- r)/[R(2r – R)] 1/2

The force on the bottom is easy to get since it is the only upward force that the cylinder exerts on the balls (and they are in equilibrium). From the geometry, what is the angle that the line between the centers of the two balls makes with the vertical?