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Free-body diagrams for uniform circular motion


In the amusement park ride shown below, riders stand along the outside wall of a circular platform. As the ride begins to spin and speed up, the riders are “pinned” against the wall. The floor drops away, and the riders, to their amazement, are stuck to the wall and do not slide down off the ride.
A diagram shows a person standing against the inner wall of a cylinder. A straight line, labeled R, extends from the center of the bottom of the cylinder to the bottom edge of the cylinder. A vertical axis goes through the center of the top and bottom of the cylinder. A counterclockwise arrow is drawn around the axis.
The free body diagram for a rider of mass m is given below. The force Fg is the gravitational force exerted on the rider by the Earth, and the centripetal acceleration on the rider is 3g.
A diagram includes a grid with three arrows extending from a central dot. Two vertical arrows of the same length extend from the dot. One goes straight up, and the other, labeled F sub G, extends straight down. A horizontal arrow three times the length of one of the vertical arrows extends to the right.
Determine the minimum coefficient of friction required to prevent the rider from sliding off the ride when the floor drops away.
Write your answer to 2 significant figures.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi