(a) a 19.0-kg child is riding a playground merry-go-round that is rotating at 50.0 rpm. what centripetal force must she exert to stay on if she is 1.50 m from its center?

781 Newtons The formula for centripetal force is: F = mv^2/r where F = force m = mass v = velocity r = radius Now the velocity will be a function of speed of rotation and radius. So v = 2*pi*r*a where v = velocity pi = Constant pi r = radius a = angular velocity Let's calculate v now. v = 2*pi*r*a v = 2 * 3.14159 * 1.5 m * 50 / 60 s/min v = 7.853975 m/s And now let's solve for the force. F = mv^2/r F = 19.0 kg(7.853975 m/s)^2/1.5 m F = (19.0 kg *61.6849233 m^2/s^2) /1.5 m F = (1172.013543 kg*m^2/s^2) /1.5 m F = 781.3423618 kg*m/s^2 F = 781.3423618 N So the child needs to exert 781 Newtons to stay in place.