What tangential speed, v, must the bob have so that it moves in a horizontal circle with the string always making an angle θ from the vertical? express your answer in terms of some or all of the variables m, l, and θ, as well as the acceleration due to gravity g?

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.

The heliocentric and the geocentric models of the solar system included these central principles

Most of the volume of an atom is occupied by the