Explanation:
To determine the apparent weight of a passenger at the lowest point of the circle, we need to consider the gravitational force and the centripetal force acting on the passenger.
At the lowest point of the circle, the passenger is experiencing both the gravitational force and the centripetal force acting towards the center of the Ferris wheel.
The gravitational force acting on the passenger is given by the formula:
F_gravity = m * g
Where:
m = mass of the passenger (70 kg)
g = acceleration due to gravity (9.8 m/s^2)
F_gravity = 70 kg * 9.8 m/s^2
F_gravity = 686 N
The centripetal force acting on the passenger is given by the formula:
F_centripetal = m * (v^2/r)
Where:
m = mass of the passenger (70 kg)
v = linear velocity of the passenger
r = radius of the Ferris wheel (40 ft or 12.192 m)
To find the linear velocity, we need to convert the rotational speed of the Ferris wheel into linear speed. Since the Ferris wheel completes one revolution in 24 seconds, the angular velocity can be calculated as:
angular velocity = 2π / time period
angular velocity = 2π / 24 s
angular velocity = π/12 rad/s
The linear speed can be calculated by multiplying the angular velocity by the radius:
linear velocity = angular velocity * radius
linear velocity = (π/12 rad/s) * 12.192 m
linear velocity = π m/s
Now we can calculate the centripetal force:
F_centripetal = 70 kg * (π m/s)^2 / 12.192 m
F_centripetal = 70 kg * (π^2 / 12.192) m/s^2
F_centripetal ≈ 70 kg * 8.165 m/s^2
F_centripetal ≈ 571.55 N
The apparent weight of the passenger at the lowest point of the circle is the sum of the gravitational force and the centripetal force:
Apparent weight = F_gravity + F_centripetal
Apparent weight = 686 N + 571.55 N
Apparent weight ≈ 1257.55 N
Therefore, the apparent weight of the 70 kg passenger at the lowest point of the circle is approximately 1257.55 Newtons.
