A pendulum bob of mass m is set into motion in a circular path in a horizontal plane as show in the figure. The square of the angular momentum of the bob about the vertical axis through the point P is

Apositive rod is placed to the left of sphere a, and the spheres are separated. which best describes the spheres? sphere a is negative and sphere b is positive because protons from sphere a are attracted to the rod and move to sphere b. sphere a is negative and sphere b is positive because electrons from sphere b are attracted to the rod and move to sphere a. sphere a is positive and sphere b is negative because electrons from the rod move to sphere b and protons then move to sphere a. sphere a is positive and sphere b is negative because protons move from sphere b to the rod and also to sphere a.

Which explanation describes the forces involved for a person to walk down the sidewalk? a. the person's feet push backward on the sidewalk; the sidewalk pushes backward on the person. b. the person's feet push forward on the sidewalk; the sidewalk does not push on the person. c. the person's feet push backward on the sidewalk; the sidewalk pushes forward on the person. d. the person's feet push forward on the sidewalk; the sidewalk pushes forward on the person.

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.)