Final answer:
To calculate the centripetal force needed to stay on a merry-go-round, convert angular velocity to rad/s, calculate the tangential velocity, and then use the centripetal force formula. The comparison with the person's weight involves calculating the gravitational force and comparing the two forces.
Step-by-step explanation:
The student's question pertains to the centripetal force that a person would require to stay on a merry-go-round that rotates at a given rate. We can solve part (b) of this problem using the formula for centripetal force, which states:
Fc = m × v2 / r
where Fc is the centripetal force, m is the mass of the person, v is the tangential velocity (which can be found from the angular velocity and radius of the merry-go-round), and r is the radius of the circle in which the person is moving.
Firstly, we convert the angular velocity from revolutions per minute to radians per second. The formula we use here is:
ω (rad/s) = (rev/min) × (2π rad/rev) × (1 min/60 s)
Knowing that v = ω × r, we can then calculate the tangential velocity. Subsequently, we can find the centripetal force with our values for m, v, and r.
The comparison with the person's weight can be determined by calculating the gravitational force:
Fg = m × g
where g is the acceleration due to gravity (9.81 m/s2). Lastly, we compare Fc with Fg to understand how the centripetal force compares with the person's weight.