You are explaining why astronauts feel weightless while orbiting in the space shuttle. your friends respond that they thought gravity was just a lot weaker up there. convince them and yourself that it isn't so by calculating the acceleration of gravity 248 km above the earth's surface in terms of g. (the mass of the earth is 5.97 1024 kg, and the radius of the earth is 6380 km.)

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.)

Amoving electron has kinetic energy k1. after a net amount of work w has been done on it, the electron is moving one-quarter as fast in the opposite direction. (a) find w in terms of k1. (b) does your answer depend on the final direction of the electron's motion?

Greg drew a diagram to compare two of the fundamental forces. which labels belong in the areas marked x, y and z? gravitational force electromagnetic force x. attractive y repulsive z: infinite range x: infinite range y attractive z. repulsive x. always attractive y: infinite range z: attractive or repulsive x. attractive or repulsive y infinite range z: always attractive