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.

(a)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?

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

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

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

(e)If the angle is increased to 90.° think about what happens to the forces. Now consider another angle, 29°. What is now the magnitude of the forces on the spheres from the left side of the container?

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

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

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

Explanation / Answer

Given that

A line connecting their centers is at 45° to the horizontal.Therefore the contact force exerted by the wall and the floor are normal

The equilibrium force on the top of the sphere leads to

Fwall =Fcos45 anf F sin45 =mg

According to the newtons third lwa the equilibrium forces on the bottom pshere leads to

F'wall =Focs45 and F'loor =Fsin45+mg

The magnitude of thr forces on the spheres from the bottom of the container is

F'lorr =mg+mg =2mg

The magnitudes of the forces on the spheres from the leftside of the container is

F'wall =mg

Magnitude of the forces on the spheres from the right side of the container is

F'wall =mg

Magnitudes of the fores on the spheres from each other is

F =mg/sin45 =mg/Sqrt(2)

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