Answer:
a
![F_A =425.42 \ N](https://tex.z-dn.net/?f=F_A%20%20%3D425.42%20%5C%20N)
b
![F_A_H = 358.58 \ N](https://tex.z-dn.net/?f=F_A_H%20%20%3D%20358.58%20%5C%20N)
Explanation:
From the question we are told that
The diameter of the Ferris wheel is ![d = 80 \ ft = \frac{80}{3.281} = 24.383](https://tex.z-dn.net/?f=d%20%20%3D%20%2080%20%5C%20ft%20%3D%20%20%5Cfrac%7B80%7D%7B3.281%7D%20%3D%20%2024.383)
The period of the Ferris wheel is ![T = 24 \ s](https://tex.z-dn.net/?f=T%20%20%3D%20%2024%20%5C%20s)
The mass of the passenger is ![m_g = 40 \ kg](https://tex.z-dn.net/?f=m_g%20%20%3D%20%2040%20%5C%20kg)
The apparent weight of the passenger at the lowest point is mathematically represented as
![F_A_L = F_c + W](https://tex.z-dn.net/?f=F_A_L%20%20%3D%20%20F_c%20%20%2B%20W)
Where
is the centripetal force on the passenger, which is mathematically represented as
![F_c =m * r * w^2](https://tex.z-dn.net/?f=F_c%20%20%3Dm%20%2A%20%20r%20%2A%20%20w%5E2)
Where
is the angular velocity which is mathematically represented as
![w = \frac{2* \pi }{T}](https://tex.z-dn.net/?f=w%20%3D%20%20%5Cfrac%7B2%2A%20%5Cpi%20%20%20%7D%7BT%7D)
substituting values
![w = \frac{2* 3.142 }{24}](https://tex.z-dn.net/?f=w%20%3D%20%20%5Cfrac%7B2%2A%203.142%20%7D%7B24%7D)
![w = 0.2618 \ rad/s](https://tex.z-dn.net/?f=w%20%3D%20%200.2618%20%5C%20rad%2Fs)
and r is the radius which is evaluated as ![r = \frac{d}{2}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7Bd%7D%7B2%7D)
substituting values
![r = \frac{24.383}{2}](https://tex.z-dn.net/?f=r%20%3D%20%20%5Cfrac%7B24.383%7D%7B2%7D)
![r = 12.19 \ ft](https://tex.z-dn.net/?f=r%20%3D%2012.19%20%5C%20ft)
So
![F_c = 40 * 12.19* (0.2618)^2](https://tex.z-dn.net/?f=F_c%20%20%3D%2040%20%2A%2012.19%2A%20%280.2618%29%5E2)
![F_c = 33.42 \ N](https://tex.z-dn.net/?f=F_c%20%20%3D%20%2033.42%20%5C%20N)
W is the weight which is mathematically represented as
![W = 40 * 9.8](https://tex.z-dn.net/?f=W%20%3D%20%2040%20%2A%209.8)
![W = 392 \ N](https://tex.z-dn.net/?f=W%20%3D%20%20392%20%5C%20N)
So
![F_A = 33.42 + 392](https://tex.z-dn.net/?f=F_A%20%20%20%20%3D%20%2033.42%20%2B%20392)
![F_A =425.42 \ N](https://tex.z-dn.net/?f=F_A%20%20%3D425.42%20%5C%20N)
The apparent weight of the passenger at the highest point is mathematically represented as
![F_A_H = W- F_c](https://tex.z-dn.net/?f=F_A_H%20%20%3D%20%20W-%20F_c)
substituting values
![F_A_H = 392 - 33.42](https://tex.z-dn.net/?f=F_A_H%20%20%3D%20392%20-%20%2033.42)
![F_A_H = 358.58 \ N](https://tex.z-dn.net/?f=F_A_H%20%20%3D%20358.58%20%5C%20N)