Consider the ring-shaped body of the figure. A particle with mass m is placed a distance x from the center of the ring, along the line through the center of the ring and perpendicular to its plane.
Part A
Calculate the gravitational potential energy U of this system. Take the potential energy to be zero when the two objects are far apart.
Part B
Show that your answer to part (a) reduces to the expected result when x is much larger than the radius a of the ring.
Part C
Use Fx=-dU/dx to find the magnitude and direction of the force on the particle.
Part D
Show that your answer to part (c) reduces to the expected result when x is much larger than a.
Part E
What is the value of U when x=0?
Part F
What is the value Fx when x=0?
Part G
Explain why the results for Fx(0) and U(0) make sense.