Just before finals you decide to visit an amusement park set up in the Metrodome

Question

1. Just before finals you decide to visit an amusement park set up in the Metrodome. Since it is a weekend, you invite your favorite niece along. She loves to ride on a Ferris wheel, and there is one at the amusement park. The Ferris wheel has seats on the rim of a circle with a radius of 25 m. The Ferris wheel rotates at a constant speed and makes one complete revolution every 20 seconds. While you wait, your niece who has a mass of 42 kg, rides the Ferris wheel. To kill time you decide to calculate the total force (both magnitude and direction) on her when she is one quarter revolution past the highest point. Because the Ferris wheel can be run at different speeds, you also decide to make a graph which gives the magnitude of the force on her at that point as a function of the period of the Ferris wheel.

Explanation / Answer

angular velocity of the ferris wheel w = 2*3.14/20 = 0.314 rad/s

tangential speed of, v = r*w = 25*0.314 = 7.85 m/s

centripetal acceleration a = v^2/r = 2.45 m/s^2

centripetal force Fc = m*v^2/r = 103.53 N

weight of the person Fg = m*g = 411.6 N

the net force acting on the person Fnet = sqrt(Fc^2 + Fg^2) = 424.42 N

direction theta = tan^-1(103.53/411.6) = 14.12 degreees with vertical axis

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