A popular carnival ride consists of seats attached to a central disk through cab

Question

A popular carnival ride consists of seats attached to a central disk through cables. The passengers travel in uniform circular motion. As shown in the figure, the radius of the central disk is R0 = 2.80 m, and the length of the cable is L = 3.00 m. The mass of one of the passengers (including the chair he is sitting on) is 51 kg. (a) If the angle ? that the cable makes with respect to the vertical is 30?, what is the speed, v, of this passenger? (b) What is the magnitude of the force exerted by the cable on the chair?

Explanation / Answer

90 - 30 = 60 degrees from horizontal g = 9.8 m/s^2 (a) If the angle theta that the cable makes with respect to the vertical is 30 degrees, what is the speed, v , of this passenger. 9.8/tan(60) = centripetal acceleration = 5.658 m/s^2 radius = Lcos(60)+R=(3cos(60)) +2.8= 4.3 m centripetal acceleration formula = v^2/r 5.658 x 4.3 = v^2 = 24.3294, sqrt(24.3294) = v = 4.93 m/s (answer) (b) What is the magnitude of the force exerted by the cable on the chair. 51x 4.93^2/4.3 = 288.267 N 288.267 /cos(60) = 576.534 N (answer)

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