A bob of mass m is suspended from a fixed point with a massless string of length L (i. e., it is a pendulum). You are to investigate the motion in which the string moves in a cone with half-angle θ.What tangential speed, v, must the bob have so that it moves in a horizontal circle with the string always maintaining an angle θ from the vertical? Express your answer in terms of some or all of the variables m, L, and θ and the acceleration due to gravity, g.

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?