A 30 kg child sitting 5.0 m from the center of a merry-go-round has a constant speed of 5.0 m/s. while she remains seated in the same spot and travels in a circle, the work the seat performs on her in one complete rotation is

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