Question

A 22.0 kg child is riding a playground merry-go-round that is rotating at 40.0 rev/min. What centripetal force must she exert to stay on if she is 1.25 m from its center?

a) 361 N
b) 482 N
c) 603 N
d) 724 N

Answer 1

To calculate the centripetal force, convert rotational speed to linear velocity and use the formula F = mv^2/r. The calculated force is 582.7 N, which is closest to option c) 603 N.

Step-by-step explanation:

The question involves calculating the centripetal force a child must exert to stay on a rotating merry-go-round. To find the centripetal force, we use the formula F = mv2/r, where m is the mass of the child (22.0 kg), v is the linear velocity, and r is the radius of the circular path (1.25 m).

First, we need to convert the rotational speed from rev/min to m/s. The merry-go-round makes 40.0 revolutions per minute, which is 40.0 rev/min * 1 min/60 s = 0.6667 rev/s. The circumference of the circle is 2πr, so the linear velocity v = 0.6667 rev/s * 2π * 1.25 m/rev = 5.236 m/s.

Once we have the linear velocity, we can calculate the centripetal force: F = 22.0 kg * (5.236 m/s)2 / 1.25 m = 582.7 N. Therefore, the centripetal force she must exert to stay on is 582.7 N, which is closest to option c) 603 N when considering significant figures.