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Physics 111 Practice Problem Statements 13Universal GravitationSJ 8th Ed.: Chap 13.1 – 13.6

• Overview - Gravitation

• Newton’s Law of Gravitation

• Free Fall – Acceleration = Field

• Gravitational Potential Energy

• Kepler’s Laws of Planetary Motion

• Satellite Orbits and Energy

Contents

14-5, 14-11, 14-15, 14-41, 14-42, 14-44

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Problem 14-5: A mass M is split into two parts, m and M - m, which are then separated by a certain distance. What ratio m/M maximizes the magnitude of the gravitational force between the parts?

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Problem 14-11:The masses and coordinates of three spheres are as follows: 20 kg, x = 0.50 m, y = 1.0 m; 40 kg, x = -1.0 m, y = -1.0 m; 60 kg, x = 0 m, y = -0.50 m. What is the magnitude of the gravitational force on a 20 kg sphere located at the origin due to the other spheres?

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Problem 14-15: At what altitude above Earth's surface would the gravitational acceleration be 4.9 m/s2?

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Problem 14-41: The Martian satellite Phobos travels in an approximately circular orbit of radius 9.4x106 m with a period of 7 h 39 min. Calculate the mass of Mars from this information.

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Problem 14-42: Determine the mass of Earth from the period T = 27.3 days and the radius r = 3.82x 105 km of the Moon's orbit about Earth. Assume the Moon orbits the center of Earth rather than the center of mass of the Earth–Moon system.

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Problem 14-44: A satellite is placed in a circular orbit about Earth with a radius equal to one-half the radius of the Moon's orbit. What is its period of revolution in lunar months? (A lunar month is the period of revolution of the Moon.)