A child sitting 1.39 m from the center of a merry-go-round moves with a speed of 1.21 m/s. Calculate the centripetal acceleration of the child.
(in m/s^2)
Calculate the net horizontal force exerted on the child (mass = 22.5 kg).
(in N)
To calculate the centripetal acceleration of the child, we can use the formula:
a = v^2 / r
where
a is the centripetal acceleration,
v is the velocity of the child, and
r is the radius of the merry-go-round.
Given:
v = 1.21 m/s
r = 1.39 m
Substituting these values into the formula, we have:
a = (1.21)^2 / 1.39
= 1.4641 / 1.39
= 1.0527 m/s^2
Therefore, the centripetal acceleration of the child is approximately 1.0527 m/s^2.
To calculate the net horizontal force exerted on the child, we can use Newton's second law of motion:
F = m * a
where
F is the net force,
m is the mass of the child, and
a is the centripetal acceleration.
Given:
m = 22.5 kg
a = 1.0527 m/s^2
Substituting these values into the formula, we have:
F = 22.5 * 1.0527
= 23.690175 N
Therefore, the net horizontal force exerted on the child is approximately 23.690175 N.
To calculate the centripetal acceleration of the child, we can use the formula:
Centripetal Acceleration (a) = (v^2) / r
where:
- v is the speed of the child (1.21 m/s)
- r is the distance from the center of the merry-go-round to the child (1.39 m)
Substituting the given values into the formula, we get:
a = (1.21 m/s)^2 / 1.39 m
a ≈ 1.049 m/s^2
Therefore, the centripetal acceleration of the child is approximately 1.049 m/s^2.
To calculate the net horizontal force exerted on the child, we can use the formula:
Force (F) = mass (m) * acceleration (a)
where:
- m is the mass of the child (22.5 kg)
- a is the centripetal acceleration calculated earlier (1.049 m/s^2)
Substituting the given values into the formula, we get:
F = 22.5 kg * 1.049 m/s^2
F ≈ 23.605 N
Therefore, the net horizontal force exerted on the child is approximately 23.605 N.