A child of mass 54.7 kg sits on the edge of a merry-go-round with radius 2.3 m and moment of inertia 222.81 kgm2. The merrygo-round rotates with an angular velocity of 1.6 rad/s. What radial force does the child have to exert to stay on the merry-go-round? Answer in units of N.
taco
To find the radial force that the child must exert to stay on the merry-go-round, we can use the following equation:
Radial force = (mass of the child) × (centripetal acceleration)
First, let's calculate the centripetal acceleration. The formula for centripetal acceleration is:
Centripetal acceleration = (angular velocity)² × (radius)
Plugging in the given values, we have:
Centripetal acceleration = (1.6 rad/s)² × (2.3 m) = 5.12 m/s²
Next, we calculate the mass of the child:
Mass = 54.7 kg
Finally, we can calculate the radial force:
Radial force = (54.7 kg) × (5.12 m/s²) = 280.064 N
Therefore, the child must exert a radial force of approximately 280.064 N to stay on the merry-go-round.