Concept explainers
A Ferris wheel 22.0 m in diameter rotates once every 12.5 s (see Fig. 5-9). What is the ratio of a person's apparent weight to her real weight at (a) the top, and (b) the bottom?
Part (a)
The ratio of apparent weight to the real weight at the top of a Ferris wheel.
Answer to Problem 53P
Solution:
0.717.
Explanation of Solution
Given:
The diameter of the Ferris wheel,
The radiusof the Ferris wheel,
Period,
Formula Used:
Angular velocity can be obtained by:
Where, T is the period.
Acceleration can be obtained by:
Calculation:
The angular velocitycan be calculated as follows:
The acceleration can be calculated as follows:
Apparent weight at the top of the Ferris wheel
The ratio of apparent weight to the real weight at the top of a Ferris wheel
Conclusion:
Therefore, the ratio of apparent weight to the real weight at the top of a Ferris wheel is 0.717.
Part (b)
The ratio of apparent weight to the real weight at the bottom of a Ferris wheel.
Answer to Problem 53P
Solution:
1.283
Explanation of Solution
Given:
The diameter of the Ferris wheel,
The radius of the Ferris wheel,
Period,
Formula Used:
Angular velocity can be obtained by:
Where, T is the period.
Acceleration can be obtained by:
Calculation:
The angular velocity can be calculated as follows:
The acceleration can be calculated as follows:
Apparent weight at the top of the Ferris wheel
The ratio of apparent weight to the real weight at the top of a Ferris wheel
Conclusion:
Therefore, the ratio of apparent weight to the real weight at the bottom of a Ferris wheel is 1.283.
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