Question

A student of weight 667 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the magnitude of the normal force F_n on the student from the seat is 556 N. 

(a) Does the student feel "light" or "heavy" there?  (b) What is the magnitude of F_n at the lowest point? If the wheel's speed is doubled, what is the magnitude F_n at the (c) highest and (d) lowest point?

Answer 1

a. Since normal force at the highest point is less than the

weight of student, he must feel lighter

b. Net force \(F=\) weight \((W)+\) centripetal force \(\left(F_{c}\right)\)

At the highest point \(F=556 \mathrm{~N}\)

\(\therefore 556 \mathrm{~N}=667 \mathrm{~N}+F_{c}\)

\(F_{c}=-667 \mathrm{~N}+556 \mathrm{~N}\)

\(=-111 \mathrm{~N}\)

Negative sign indicates that the force is directed upwards.

At the lowest point, \(F_{c}=+111 \mathrm{~N}\)

Hence normal force \(F_{n}=667 \mathrm{~N}+111 \mathrm{~N}\)

$$ =778 \mathrm{~N} $$

c. Centripetal force \(F_{c}=111 \mathrm{~N}=m r \omega^{2}\) On doubling the speed, \(\omega^{\prime}=2 \omega\)

\(F_{c}^{\prime}=m r(2 \omega)^{2}\)

\(=4 m r \omega^{2}\)

\(=4 \times 111 \mathrm{~N}\)

\(=444 \mathrm{~N}\)

Force at the highest point \(F_{n}^{\prime}=W-F_{c}^{\prime}\) \(=667 \mathrm{~N}-444 \mathrm{~N}\)

\(=223 \mathrm{~N}\)

d. Force at the lowest point \(F_{n}{ }^{\prime}=W+F_{c}{ }^{\prime}\) \(=667 \mathrm{~N}+444 \mathrm{~N}\)

\(=1111 \mathrm{~N}\)