Two identical, uniform, frictionless spheres, each of weight W , rest in a rigid
ID: 1264354 • Letter: T
Question
Two identical, uniform, frictionless spheres, each of weight W , rest in a rigid rectangular container as shown in the figure. Find, in terms of a ratio to W, the forces acting on the spheres due to the container surfaces and one another, if the line of centers of the spheres makes an angle of 45
Two identical, uniform, frictionless spheres, each of weight W , rest in a rigid rectangular container as shown in the figure. Find, in terms of a ratio to W, the forces acting on the spheres due to the container surfaces and one another, if the line of centers of the spheres makes an angle of 45 degree with the horizontal. Normal force from the left side of the container? Normal force from the right side of the container? Normal force from the bottom of the container? Force of contact between the spheres? If the angle is increased to 90.degree think about what happens to the forces. Now consider another angle, 31 degree. Normal force from the left side of the container? Normal force from the right side of the container? Normal force from the bottom of the container? Force of contact between the spheres?Explanation / Answer
The contact force exerted by the lower sphere on the upper is along that is 45o and the forces exerted by the walla 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 bottom of the container F'floor = mg +mg = 2mg
b) magnitudes of the forces on the spheres from the left side of the container F'wall = mg
c) magnitudes of the forces on the spheres from the right side of the container F'wall = mg
d) magnitudes of the forces on the spheres from each other F = mg / sin 45 = mg * ?2
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