A common amusement park ride has a circular platform with swings hanging from it

Question

A common amusement park ride has a circular platform with swings hanging from it. Riders get in and the platform begins to rotate, causing the riders to also begin rotating and swing outward, eventually maintaining a constant angle with respect to the vertical. If a rider is a distance of 12 m from the axis of rotation and moving with a speed of 12 m/s what is (a) the radial accelerating of the rider. (b) What is the angle ? the supporting wires make with the vertical? (c) Did either of your answers depend on the mass of the rider? Explain. (d) If you were asked to solve for the tension in the wires, what additional information would you need to answer that question.

Explanation / Answer

(a) radial acceleration = v^2/R = 12 x 12/12 = 12 rad/s^2 Ans (b) let angle be q. T = tension. Tcos q = mg, Tsin q = mv^2/R. so tan q = v^2/gR = 12 x 12/(9.8 x 12) = 1.2244. so q = tan inverse 1.2244 = 50.76 degrees. Ans (c) no, mass is not required. (d) T = mg/cos q or mv^2/Rsin q. we cannot find tension unless mass is provided.

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