8/8/2011 Physics 111 Practice Problem Statements 13 Universal Gravitation SJ 8th Ed.: Chap 13.1 – 13.6 Overview - Gravitation Newton’s Law of Gravitation.

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8/8/2011 Physics 111 Practice Problem Statements 13 Universal Gravitation SJ 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

8/8/2011 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?

8/8/2011 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 = m. What is the magnitude of the gravitational force on a 20 kg sphere located at the origin due to the other spheres?

8/8/2011 Problem 14-15: At what altitude above Earth's surface would the gravitational acceleration be 4.9 m/s 2 ?

8/8/2011 Problem 14-41: The Martian satellite Phobos travels in an approximately circular orbit of radius 9.4x10 6 m with a period of 7 h 39 min. Calculate the mass of Mars from this information.

8/8/2011 Problem 14-42: Determine the mass of Earth from the period T = 27.3 days and the radius r = 3.82x 10 5 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.

8/8/2011 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.)