A 22 kg child is riding a playground merry-go-round that makes 40 revolutions in 60 seconds. Determine the magnitude of force (in Newtons) necessary to make the child stay on the merry-go-round if she is 1.25m from its center.
To determine the magnitude of force required to make the child stay on the merry-go-round, we need to consider the centripetal force acting on the child.
The centripetal force is given by the formula:
F = m * ω^2 * r
Where:
F is the centripetal force (in Newtons),
m is the mass of the child (in kilograms),
ω is the angular velocity (in radians per second),
and r is the radius (in meters).
First, let's calculate the angular velocity (ω):
The problem tells us that the merry-go-round makes 40 revolutions in 60 seconds. Since one revolution is equal to 2π radians, we can convert the number of revolutions to radians:
ω = (40 * 2π) / 60
Next, let's calculate the centripetal force (F):
F = m * ω^2 * r
Given:
m = 22 kg (mass of the child),
r = 1.25 m (radius from the center of the merry-go-round).
Now we can substitute the values into the equation and calculate the centripetal force:
ω = (40 * 2π) / 60
≈ 4.18879 rad/s
F = 22 kg * (4.18879 rad/s)^2 * 1.25 m
≈ 357.98 N
Therefore, the magnitude of force necessary to make the child stay on the merry-go-round is approximately 357.98 Newtons.