Question

While at the country fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephants ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 15 cm, and you use your watch to find that each loop around takes 25 s.

a. What are your speed and magnitude of your acceleration?
b. What is the ratio of your apparent weight to your true weight at the top of the ride?
c. What is the ratio of your apparent weight to your true weight at the bottom?

Answer 1

0.038 m/s, 0.0096 m/s²

0.101

0.103

Step-by-step explanation:

The speed is given by

v = 2πr / T

v = (2 * π * 0.15) / 25

v = 0.9426 / 25

v = 0.038 m/s

Acceleration, a is given by

a = v² / r =

a = 0.038² / 0.15

a = 0.001444 / 0.15

a = 0.0096 m/s²

Ratio of apparent weight to true weight at the top

w = m (g - a) / (m g)

w = 1 - a/g

w = 1 - 0.0096 / 9.81

w = 0.9904 / 9.81

w = 0.101

Ratio of apparent weight to true weight at bottom

w = m (g+a)/ (m g)

w = 1 + a/g

w = 1 + 0.0096 / 9.81

w = 1.0096 / 9.81

w = 0.103