A child having a mass of 45 kg sits 0.5 m from the center of a merry-go-round that is rotating with a period of 23 s. What is the centripetal force acting on the child?
To determine the centripetal force acting on the child, we need to use the formula for centripetal force:
F = m * a
Where:
F = centripetal force (in Newtons)
m = mass of the child (in kilograms)
a = centripetal acceleration
To find the centripetal acceleration, we can use the formula:
a = (4 * π^2 * r) / T^2
Where:
a = centripetal acceleration (in meters per second squared)
π = pi (approximately 3.14159)
r = radius (distance of the child from the center of the merry-go-round) in meters
T = period of the merry-go-round's rotation in seconds
Given:
m = 45 kg
r = 0.5 m
T = 23 s
First, let's calculate the centripetal acceleration:
a = (4 * π^2 * r) / T^2
= (4 * 3.14159^2 * 0.5) / (23^2)
Using a calculator, we can evaluate this expression:
a ≈ 0.68 m/s^2
Now, we can calculate the centripetal force:
F = m * a
= 45 kg * 0.68 m/s^2
Again, using a calculator, we can determine the centripetal force:
F ≈ 30.6 N
Therefore, the centripetal force acting on the child is approximately 30.6 Newtons.