Answer :
Final answer:
The net force (centripetal force) acting on the child on the merry-go-round is approximately 315 N, which is calculated using the child's mass, the radius of the merry-go-round, and the frequency of rotation. The correct option is(A).
Explanation:
To calculate the net force acting on the child on the merry-go-round, also referred to as centripetal force, we can use the following formula: F = m imes r imes
(2 π ν)2,
where m is the mass of the child (24.5 kg), r is the distance from the center of the merry-go-round (1.05 m), and ν is the frequency of rotation in revolutions per second. Since the merry-go-round rotates at 37.9 rev/min, we need to convert this to rev/s by dividing by 60:
ν = 37.9 rev/min imes (1 min / 60 s) = 0.6317 rev/s
Plugging the values into the formula, we get: F = 24.5 kg imes 1.05 m imes (2π imes 0.6317 rev/s)2
F ≈ 315 N, So, the net force acting on the child is approximately 315 N (Option A).
