Two identical, uniform and frictionless spheres, each of mass m, rest in a rigid

Question

Two identical, uniform and frictionless spheres, each of mass m, rest in a rigid rectangular container as shown in the figure. A line connecting their centers is at 45° to the horizontal. Find, in terms of a ratio to the weight (mg), the magnitude of the forces on the spheres from the left side of the container?

And what is the magnitude of the forces on the spheres from the right side of the container?

And what is the magnitude of the forces on the spheres from the bottom of the container?

And what is the magnitude of the forces on the spheres from each other?

If the angle is increased to 90.° think about what happens to the forces. Now consider another angle, 21°.

What is now the magnitude of the forces on the spheres from the left side of the container?

And what is now the magnitude of the forces on the spheres from the right side of the container?

And what is now the magnitude of the forces on the spheres from the bottom of the container?

And what is now the magnitude of the forces on the spheres from each other?

Explanation / Answer

The contact force exerted by the lower sphere on the upper is along that is 45o and the forces exerted by the wall and floors are normal.

Equilibrium force on the top sphere leads to Fwall = F cos 45 and F sin 45 = m g

According to newtons third law the equilibrium of forces on the bottom sphere leads to F'wall = F cos 45 and F'floor = F sin 45 +mg

a)
magnitudes of the forces on the spheres from the left side of the container F'wall = mg

b)
magnitudes of the forces on the spheres from the right side of the container F'wall = mg

c)
magnitudes of the forces on the spheres from the bottom of the container F'floor = mg +mg = 2mg

d) magnitudes of the forces on the spheres from each other F = mg / sin 45 = mg * 2

No figure is provided for me to proceed with other part.

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