A child on a merry-go-round is moving with a speed of 1.40 m/s when 1.18 m from the center of the merry-go-round.
(a) Calculate the centripetal acceleration of the child. (and I got 1.08)
(b) Calculate the net horizontal force exerted on the child (mass = 25.0 kg).
(and I got 27.2)
Isnt acceleration= v^2/r ?
That does not give what you got.
To calculate the centripetal acceleration of the child, you 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 distance from the center of the merry-go-round.
(a) Given that the child's velocity (v) is 1.40 m/s and the distance from the center (r) is 1.18 m, you can substitute these values into the formula:
a = (1.40 m/s)^2 / 1.18 m
a = 1.96 m^2/s^2 / 1.18 m
a = 1.661 m/s^2
Therefore, the centripetal acceleration of the child is approximately 1.66 m/s^2.
To calculate the net horizontal force exerted on the child, you can use Newton's second law of motion:
F = m * a
Where:
F is the net horizontal force,
m is the mass of the child, and
a is the centripetal acceleration.
(b) Given that the mass of the child (m) is 25.0 kg and the centripetal acceleration (a) is 1.66 m/s^2, you can substitute these values into the formula:
F = 25.0 kg * 1.66 m/s^2
F = 41.5 N
Therefore, the net horizontal force exerted on the child is approximately 41.5 N.