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.
