Let us say that v is the
tangential velocity of the object, a to be the centripetal (which acts towards
the center of the circle) acceleration and F as the centripetal force, r to be
the radius of the circle and m is mass of the child.
a = v^2 / r
F = ma = mv^2/r
Applying the given values to the equation:
F=30*(5^2/5) => 30*(25/5) => 30*5 => 150 Newtons
Now work is Force times distance, the distance is simply the circumference of the circle.
d = C = 2 * pi * r = 2 * pi * 5 = 10π m
W = F * d = 150 N * 10π m
W = 1500π J = 4712.39 J
