If the distance from the center of a merry-go-round to the edge is 1.2m, what centripetal acceleration does a passenger experience when the merry go round rotates with a frequency of 0.08 hz?
Centripetal acceleration = (2π x 0.08 hz)^2 x 1.2m
= 0.0048 m/s^2
To find the centripetal acceleration experienced by a passenger on the merry-go-round, we can use the formula:
ac = 4π^2f^2r
where:
ac = centripetal acceleration
f = frequency of rotation (in Hz)
r = radius of the merry-go-round
Given:
Frequency (f) = 0.08 Hz
Radius (r) = 1.2 m
Substituting the values into the formula:
ac = 4π^2(0.08)^2(1.2)
Calculating:
ac = 4π^2(0.0064)(1.2)
ac = 0.0768π^2
The centripetal acceleration experienced by the passenger is approximately 0.0768π^2 m/s^2 (or you can use a calculator for the numerical approximation).
To calculate the centripetal acceleration experienced by a passenger on a merry-go-round, you can use the formula:
Centripetal acceleration (a) = (2πf)^2 * r
where:
- a is the centripetal acceleration
- f is the frequency of rotation in hertz (Hz)
- r is the radius of the merry-go-round
In your case, the frequency (f) is given as 0.08 Hz, and the radius (r) is given as 1.2 meters.
Let's plug these values into the formula:
a = (2π * 0.08)^2 * 1.2
First, calculate 2π * 0.08:
2π * 0.08 = 0.5034
Next, square the result:
0.5034^2 = 0.2534
Finally, multiply the squared value by the radius:
a = 0.2534 * 1.2
a ≈ 0.3041 m/s^2
Therefore, the passenger on the merry-go-round experiences a centripetal acceleration of approximately 0.3041 m/s^2.