A Ferris wheel rotates 4 times each minute and has a diameter of 17 m.
The acceleration of gravity is 9.8 m/s2. What is the centripetal acceleration of a rider?
Answer in units of m/s2
Thank You!!!
To find the centripetal acceleration of a rider on the Ferris wheel, we first need to calculate the angular velocity of the wheel.
The Ferris wheel rotates 4 times per minute, which means it completes 4 * 2π = 8π radians per minute.
To convert this to radians per second, we divide by 60 (since there are 60 seconds in a minute):
8π radians/min ÷ 60 min/s = 8π/60 radians/s.
Now, we can calculate the angular velocity as the rate of change of angle over time:
ω = 8π/60 radians/s.
The centripetal acceleration can be calculated using the formula:
a = ω² * R,
where ω is the angular velocity and R is the radius of the Ferris wheel, which is half of its diameter.
The diameter of the Ferris wheel is 17 m, so the radius is 17/2 = 8.5 m.
Plugging in the values, we get:
a = (8π/60)² * 8.5 m.
Now we can calculate the centripetal acceleration:
To find the centripetal acceleration of a rider on a Ferris wheel, we need to use the formula for centripetal acceleration:
a = (v^2) / r
where:
a is the centripetal acceleration
v is the linear velocity of the rider
r is the radius of the Ferris wheel
First, we need to find the linear velocity of the rider. Since we are given the number of rotations per minute, we can calculate the number of seconds it takes for one rotation:
Time for one rotation = 60 seconds / 4 rotations = 15 seconds
The linear velocity of the rider is given by:
v = 2πr / t
where:
r is the radius of the Ferris wheel (which is half the diameter, so r = 17 / 2 = 8.5 m)
t is the time for one rotation in seconds
Substituting the values into the formula:
v = 2π(8.5) / 15 ≈ 3.56 m/s
Now, we can calculate the centripetal acceleration using the formula mentioned earlier:
a = (v^2) / r
Substituting the values:
a = (3.56^2) / 8.5 ≈ 1.49 m/s^2
Therefore, the centripetal acceleration of a rider on the Ferris wheel is approximately 1.49 m/s^2.
The centripetal acceleration does not depend upon g or the position on the wheel (top, bottom side etc.)
It equals V^2/R
In this case,
V = pi*17m/15s = 3.56 m/s
R = 17/2 = 8.5 m
Now compute V^2/R for the answer.