3. (8 pts) (Based on 13.58) In the figure, the left sphere has mass M and the ri

Question

3. (8 pts) (Based on 13.58) In the figure, the left sphere has mass M and the right sphere has mass 5M. The middle sphere has mass and is released from rest at the position shown, with its center located a distance d from the center of the left sphere and a distance 2d from the center of the right sphere. Assume that the only forces on the middle sphere are the gravitational forces exerted by the other two spheres and that the left and right spheres are held in place at their original positions. Find an expression for the speed of the middle sphere when it has moved a distance d to the right from its original position d to the right from i 5M O2016 Pearson Education, Inc.

Explanation / Answer

conservation of energy

initial potential energy = final potential energy + KE

-GMm/d -G5Mm/2d = -GMm/2d -G5Mm/d + 0.5mv^2

-7GM/2d =-11GM/2d + 0.5V^2

2GM/d = 0.5V^2

V = sqrt (4GM/d)      m/sec

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