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

here diagram is not apeared

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 45o and Fsin45o = mg

According to newtons 3rd law the equilibrium of forces on the bottom sphere leads to Fwall= Fcos45o and Ffloor = F sin45o+mg

a)      The magnitude of the forces on the spheres from the left side of the container is Fwall = mg

b)      The magnitude of the forces on the spheres from the right side of the container is Fwall = mg

c)     The magnitude of the forces on the spheres from the bottom of the container is Ffloor = mg+mg =2mg

d)    The magnitude of the forces on the spheres from each other is F = (mg)/Sin45o =(2)mg

As per the above solution please plug in the values for 90o and 21o

Please post the questions as per the chegg rules

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