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)If the angle is increased to 90° think about what happens to the forces. This can help provide a check to your answers as we make a change to the problem. For all of the following questions, the configuration is now changed such that the line connecting their centers is at an angle 29.6° to the horizontal. At this new angle, what is the magnitude of the force on the spheres from the left side of the container? b) What is the magnitude of the force on the spheres from the right side of the container? c) What is the magnitude of the force on the spheres from the bottom of the container? d) What is the magnitude of the force of the top sphere on the bottom sphere? Hint: b,c,d are depends on part (a).

Explanation / Answer

Solution :-

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

Equilibrium force on the top sphere leads to

     Fwall = F cos 45and    F sin 45 = m g

According to newtons third law the equilibrium of forceson 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 thebottom of the container

       F'floor = mg+mg = 2mg

b)magnitudes of the forces on the spheres from the leftside of the container

        F'wall = mg

c))magnitudes of the forces on the spheres fromthe right side of the container

        F'wall = mg

d)  magnitudes of the forces on the spheresfrom  each other

         F = mg / sin45 = mg* ?2

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