CALC A thin, uniform rod has length L and mass M . A small
Chapter 13, Problem 32E(choose chapter or problem)
CALC A thin, uniform rod has length L and mass M . A small uniform sphere of mass ?m is placed a distance x from one end of the rod, along the axis of the rod (?Fig. E13.34?). (a) Calculate the gravitational potential energy of the rod–sphere system. Take the potential energy to be zero when the rod and sphere are infinitely far apart. Show that your answer reduces to the expected result when x is much larger than L. (?Hint: Use the power series expansion for ln (1 + x) given in Appendix B.) (b) Use Fx = -dU/dx to find the magnitude and direction of the gravitational force exerted on the sphere by the rod (see Section 7.4). Show that your answer reduces to the expected result when x is much larger than L.
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