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 = 3.40 m. The mass of one of the passengers (including the chair he is sitting on) is 69 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

So on your free body diagram you have two forces: gravity pointing downward and tension (by the cable on the chair) pointing 30 degrees left of the vertical. The centripetal force is done by the cable's horizontal component because the circle is horizontal. so Tsin(30) = mv2/R. to solve for T, the upwards component of the tension must be equal to the force of gravity; the person doesn't move up or down. So mg = Tcos(30).

R = 2.8 + 3.4sin(30) because that is the total distance from the chair to the circle's center. Plug and chug once you solve for T!

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