Perhaps the most-common gravitational calculation is to determine the "weight" of an object of mass mo sitting on the surface of the earth (i. e., the size of the gravitational attraction between the earth and the object). according to newton's law of universal gravitation, the gravitational force on the object is

fg=g(memo r2e)=(gme r2e)mo,

where me is the mass of the earth and re is the distance between the object and the center of the earth(i. e., re = radius of the earth = 6.38

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)

The mass of the sun is 1.99×1030kg and its distance to the earth is 1.50×1011m. what is the gravitational force of the sun on the earth?

Estimate the change in the gibbs energy and molar gibbs energy of 1.0dm3 of octane when the pressure acting on it is increased from 1.0 atm to 100 atm. the mass density of octane is 0.703 g cm−3