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43. Problem 13.20P (HRW) Two identical, uniform, frictionless spheres, each of weight
W, rest in a rigid rectangular container. We have to find in terms of W, the
forces acting on the spheres due to (a) the container surfaces and (b)
one another, if the line of centres of the spheres makes an angle of
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with
the horizontal.
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Solution: Click For PDF Version We will first draw the free-body diagram of the ball 1. In this diagram F is the force on the ball exerted
by the wall, and T is the force exerted by the ball 2 on the ball 1.
As the spheres are frictionless, force T will be along their line of
contact, which is at an angle of
As the ball is in equilibrium, the vector sum of forces has to be zero. Adding the vertical component of forces, we get
Adding the horizontal component of forces acting on ball 1, we get
We will consider next the free-body diagram of ball 2. It is as shown on the line diagram.
N is the force exerted by the base of the box on the ball 2. F is the force exerted by the side on the ball and T is the force exerted by the ball 1 on ball 2. Applying the conditions of static equilibrium, we get the following two equations:
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