On the ride "Spindletop" at the amusement park Six Flags Over Texas, people stood against the inner wall of a hollow vertical cylinder with radius 2.5 m. The cylinder started to rotate, and when it reached a constant rotation rate of 0.60 rev/s, the floor on which the people were standing dropped about 0.5 m. The people remained pinned against the wall.

a) Draw a force diagram for a person on this ride, after the floor has dropped.
b) What minimum coefficient of static friction is required if the person on the ride is not to slide downward to the new position of the floor?
c) Does your answer in part b) depend on the mass of the passenger? (NOTE: When the ride is over, the cylinder is slowly brought to rest. As it slows down, people slide down the walls to the floor.)

You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. you will have no access to any electricity, but you must be able to illuminate the entire grounds. you know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. suppose the intensity is 90 when the distance is 5 m. a. write an equation to model the situation. b. solve for the constant of variation. c. write the equation to model the situation using the constant () of variation. d. you have been given lanterns with 40 light intensity. use your equation to solve for the distance from the lantern. e. you need to illuminate 225 km. how many meters do you need to light? f. how many lanterns will you need?