Calculating Centripetal Acceleration and Net Horizontal Force Exerted on a Child on a Merry-Go-Round
Question:
What is the centripetal acceleration of a child sitting 1.10m from the center of a merry-go-round moving with a speed of 1.25m/s? And what is the net horizontal force exerted on the child with a mass of 25.0 kg?Answer:
To calculate the centripetal acceleration of the child, we can use the formula a = v²/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.
Given that the child is sitting 1.10m from the center of the merry-go-round and moving with a speed of 1.25m/s, we can plug in the values:
a = (1.25 m/s)² / 1.10 m ≈ 1.43 m/s²
Therefore, the centripetal acceleration of the child is approximately 1.43 m/s².
To calculate the net horizontal force exerted on the child, we can use the formula F = ma, where F is the force, m is the mass of the child, and a is the centripetal acceleration.
Plugging in the values with a mass of 25.0 kg:
F = (25.0 kg) × (1.43 m/s²) ≈ 35.8 N
Therefore, the net horizontal force exerted on the child is approximately 35.8 N.