Consider the ring-shaped object in Fig. E13.39. A particle with mass m is placed a distance x from the ing, along the line through the center of the ring and perpendicular to its plane. (a) Calculate the gravitational gy U of this system. Take the potential energy to be zero when the two objects are far apart. (b) Show that o part (a) reduces to the expected result when x is much larger than the radius a of the ring. (c) Use

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13.39 • CALC Consider the ring- shaped object in Fig. E13.39 D. 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. (a) Calculate the gravitational
potential energy U of this system. Take the potential energy to be zero when the two objects are far apart. (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. (c) Use
F. = -dU/dx to find the magnitude and direction of the force on the particle (see Section 7.4 9). (d) Show that your
answer to part (c) reduces to the expected result when x is much larger than a. (e) What are the values of U and F, when
x = 0? Explain why these results make sense.
Figure E13.39
т
M
Transcribed Image Text:13.39 • CALC Consider the ring- shaped object in Fig. E13.39 D. 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. (a) Calculate the gravitational potential energy U of this system. Take the potential energy to be zero when the two objects are far apart. (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. (c) Use F. = -dU/dx to find the magnitude and direction of the force on the particle (see Section 7.4 9). (d) Show that your answer to part (c) reduces to the expected result when x is much larger than a. (e) What are the values of U and F, when x = 0? Explain why these results make sense. Figure E13.39 т M
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