A child having a mass of 37 kg sits 0.2 m from the center of a merry-go-round that is rotating with a period of 36 s. What is the centripetal force acting on the child?
on the child: 37*w^2 r
w=2PI/Period
To solve this problem, we need to use the formula for centripetal force:
F = (m * v^2) / r
Where F is the centripetal force, m is the mass of the child, v is the velocity of the child, and r is the radius of the merry-go-round.
To find the velocity of the child, we can use the formula for linear velocity:
v = 2πr / T
Where v is the velocity, r is the radius of the merry-go-round, and T is the period.
Given that the period is 36 s and the child sits 0.2 m from the center, we can substitute these values into the formula to find the velocity:
v = (2 * π * 0.2) / 36
Now we can calculate the velocity:
v ≈ 0.0349 m/s
Next, we can substitute the values of the mass (37 kg), velocity (0.0349 m/s), and radius (0.2 m) into the formula for centripetal force:
F = (37 * (0.0349)^2) / 0.2
Now we can calculate the centripetal force:
F ≈ 2.501 N
Therefore, the centripetal force acting on the child is approximately 2.501 Newtons.