A passenger with mass 85 kg rides in a Ferris wheel. The seats travel in a circl

Question

A passenger with mass 85 kg rides in a Ferris wheel. The seats travel in a circle of radius 35 m. The Ferris wheel rotates at constant speed and makes one complete revolution every 25 s. A) Calculate the magnitude of the net force exerted on the passenger by the seat when she is one-quarter revolution past her highest point. B) Calculate the direction of the net force exerted on the passenger by the seat when she is one-quarter revolution past her highest point. (Directon of net force exerted on the passenger by the seat when she is one-quarter revolution past her lowest point = 77.3 degrees above the horizontal. The magnitude of the net force exerted on the passenger by the seat when she is one-quarter revoltion past her lowest point= 854 N.)

Explanation / Answer

time period T = 25 s

angular speed w = 2pi/T = 2pi/25 = 0.251

at one quarter position

along horizontal

force exerted by seat Fx = Fc = m*R*w^2

Fx = 85*35*0.251^2 = 187.4 N

along vertical

n - Fg = 0

n = mg = 85*9.8 = 833 N

net force = sqrt(187.4^2+833^2) = 854 N <<----------ANSWER

direction = tan^-1(n/Fx) = tan^-1(833/187.4) = 77.3 degrees above horizontal <---------ANSWER

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