Problem1 : What is the force exerted by Big Ben on the Empire State building? Assume that Big Ben has a mass of 108 kilograms and the Empire State building109 kilograms. The distance between them is about 5000 kilometers and Big Ben is due east of the Empire State building.The direction of the force clearly attracts the Empire State towards Big Ben. So the direction is a vector pointing due east from New York. The magnitude is given by Newton's Law:
|F === 2.67×10-7 N|
Problem 2: What is the gravitational force that the sun exerts on the earth? The earth on the sun? In what direction do these act? ( M e = 5.98×1024 and M s = 1.99×1030 and the earth-sun distance is 150×109 meters).First, consider the directions. The force acts along the direction such that it attracts each body radially along a line towards their common center of mass. For most practical purposes, this means a line connecting the center of the sun to the center of the earth. The magnitude of both forces is the same, as we would expect from Newton's Third Law, and they act in opposite directions, both attracting each other mutually. The magnitude is given by:
|F === 3.53×1022|
Figure %: alignment of Mercury, Venus and the Sun.
|F s == 5.54×1022|
|F m == 9.19×1015|
Problem 4: It is possible to simulate "weightless" conditions by flying a plane in an arc such that the centripetal acceleration exactly cancels the acceleration due to gravity. Such a plane was used by NASA when training astronauts. What would be the required speed at the top of an arc of radius 1000 metres?We require an acceleration that exactly cancels that due to gravity -- that is, exactly 9.8 m/sec 2 . Centripetal acceleration is given by a c =. We have been given r = 1000 meters, so v ==99 m/s.
Problem5 : Show using Newton's Universal Law of Gravitation that the period of orbit of a binary star system is given by:
|T 2 =|
|T 2 ==d 3 =|