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 acceleration at the lowest point?

Answer 1

Given:

$R=15\;\rm m,$

$N=5\;\rm rev,$

$t=60\;\rm s.$

(a) the period of motion

$$T=\frac{t}{N}=\frac{60}{5}=12\:\rm s.$$

(b) the magnitude of the woman centripetal acceleration at the highest point

$$a=\frac{4\pi^2}{T^2}R=\frac{4\pi^2}{12^2}\times 15=4.1\:\rm m/s^2.$$

(c) the acceleration of the woman at the highest point is directed vertically down to the center of wheel.

(d) the magnitude of the woman centripetal acceleration at the lowest point

$$a=\frac{4\pi^2}{T^2}R=\frac{4\pi^2}{12^2}\times 15=4.1\:\rm m/s^2.$$

(e) the acceleration of the woman at the lowest point is directed vertically up to the center of wheel.