Gravitation

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Gravitation

  1. 1. Problem Exercises GRAVITATION Here are some additional problems that you can work out. These are about gravitational force, gravitational field, satellite motion,and Kepler’sLaws. If you haveconcernsand difficultyin solving problems,do nothesitateto consult. 01. A coordinate system (in meters) is constructed on the surface of a pool table, the three objects are placed on the table as follows: a 2.0-kg object at the origin of the coordinate system, a 3.0-kg object at (-2.0, 0), and a 4.0-kg object at (4.0, 0). (a) What is the force (magnitude and direction) by the 3.0-kg object on the 2.0-kg object? (b) What is the force (magnitude and direction) by the 4.0-kg object on the 2.0-kg object? (c) What is the net force (magnitude and direction) by the two objects on the 2.0-kg object? 02. A man is standing on the surface of a hypothetical X-planet with a radius of 𝑅 𝑥 = 7.12 𝑥 103 km. He drops a rock from a height of 9.0 m. It takes 5.09 s to hit the ground. (a) Calculate the acceleration due to gravity (gravitational field) of the planet? (b) Find the mass of the X-planet given the said data. (c) Calculate the acceleration due to gravity 50.0 km from the surface of the X-planet. 03. A certain satellite is launched and moves in a circular orbit around the Earth. The speed of the satellite is 5000 m/s. (a) What is the orbital radius of the satellite? (b) What is the satellites altitude above the Earth’s surface? (c) What are the period and frequency of the satellite’s orbit? The mass of the Earth is 5.98 𝑥 1024 kg. 04. The mean distances of Venus from Sun and Mars from Sun are 𝑟𝑉𝑆 = 1.08 𝑥 1011 m and 𝑟 𝑀𝑆 = 2.28 𝑥 1011 m, respectively. If Mars has 687.5 days to complete one revolution around the Sun, what is the period of Venus’ orbit? 05. Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22 x 105 km. From these data, determine the mass of the Jupiter. -Sir Bernard L. -Sir Darwin Q. For 3RD Years… 

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