A1.6 kg ball at the end of a 1.1 m string swings in a vertical plane. at its lowest point the ball is moving with a speed of 17 m/: s (a) what is its speed (in m/s) at the top of its path? 4.64 xm/s (b) what is the tension (in n) in the string when the ball is at the bottom and at the top of its path? bottom of its path 436.04 top of its path

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.)

Apulley system is used to lift a 2,000 newton engine up a distance of 3 meters. the operator must apply a force of 250 newtons to the chain of the pulley system to lift the motor. to lift the engine 3 meters, the operator must pull a total of 30 meters of chain through the pulley system. what is the value of di?

Four point charges each having charge q are located at the corners of a square having sides of length a. find symbolic expressions for the following. (a) the total electric potential at the center of the square due to the four charges (use any variable or symbol stated above along with the following as necessary: ke.) vtotal= (b) the work required to bring a fifth charge p from infinity to the center of the square (use any variable or symbol stated above along with the following as necessary: w=