Question

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

Answer 1

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