A woman rides a carnival Ferris wheel at radius 15 m,completing five turns about its horizontal axis every minute.What are (a) the period of the motion, the (b) magnitude and(c) direction of her centripetal acceleration at the highest point,and the (d) magnitude and (e) direction of her centripetal accel-eration at the lowest point?
Question
A woman rides a carnival Ferris wheel at radius 15 m,completing five turns about its horizontal axis every minute.What are (a) the period of the motion, the (b) magnitude and(c) direction of her centripetal acceleration at the highest point,and the (d) magnitude and (e) direction of her centripetal accel-eration at the lowest point?
Solution
(a) The period of the motion is the time it takes for one complete rotation. Since the Ferris wheel completes 5 turns every minute, the period is 1/5 of a minute or 12 seconds.
(b) The magnitude of her centripetal acceleration at the highest point can be calculated using the formula for centripetal acceleration: a = v^2/r. The velocity (v) can be found by dividing the circumference of the Ferris wheel (2πr) by the period. Substituting the given values, we get v = 2π(15 m)/12 s = 7.85 m/s. Therefore, a = (7.85 m/s)^2 / 15 m = 4.09 m/s^2.
(c) The direction of her centripetal acceleration at the highest point is downwards towards the center of the Ferris wheel.
(d) The magnitude of her centripetal acceleration at the lowest point is the same as at the highest point, 4.09 m/s^2, because the speed and radius are the same.
(e) The direction of her centripetal acceleration at the lowest point is upwards towards the center of the Ferris wheel.
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