A carnival Ferris wheel has a 15-m radius and completes five turns about its horizontal axis every minute. What is the acceleration of a passenger at his lowest point during ride?
14 m/s
To find the acceleration of a passenger at the lowest point during the ride, we can use the formula for centripetal acceleration:
a = (v^2) / r
Where:
a = acceleration
v = velocity
r = radius
First, let's find the velocity of the passenger at the lowest point.
The Ferris wheel completes 5 turns in one minute, which means it completes 5 cycles in 60 seconds. Therefore, the time taken for one complete cycle is:
T = 60 s / 5 = 12 s
The formula to find the velocity is:
v = (2πr) / T
Substituting the given values:
v = (2π * 15) / 12
v ≈ 7.85 m/s
Now, we can calculate the acceleration using the centripetal acceleration formula:
a = (v^2) / r
Substituting the given values:
a = (7.85^2) / 15
a ≈ 4.09 m/s^2
Therefore, the acceleration of a passenger at the lowest point during the ride is approximately 4.09 m/s^2.
To find the acceleration of a passenger at the lowest point during the ride, we can use the formula for centripetal acceleration.
Centripetal acceleration (a) is given by the equation:
a = (v^2) / r
Where:
a = acceleration
v = velocity
r = radius
First, we need to find the velocity of the passenger at the lowest point. Since the Ferris wheel completes five turns about its axis every minute, we can calculate the angular velocity (ω) using the equation:
ω = (2π * n) / t
Where:
ω = angular velocity
n = number of turns
t = time in seconds
Since the Ferris wheel completes five turns in one minute (60 seconds), we can substitute the values in the equation:
ω = (2π * 5) / 60
Now, we can calculate the velocity (v) using the formula:
v = ω * r
Substituting the values:
v = [(2π * 5) / 60] * 15
Finally, we can calculate the acceleration (a) using the formula for centripetal acceleration:
a = (v^2) / r
Substituting the values:
a = [([(2π * 5) / 60] * 15)^2] / 15
Simplifying the equation further will give you the numerical value for acceleration.
Please note that the result will depend on the units used.