A child pushes a merry-go-round with a force of 55.0 N at an angle tangent to the circle (that is, perpendicular to a radius). If the child pushes it through exactly one full circle, and the merry-go-round has a radius of 1.15 m, how much work does she do?

The answer is not 518.4 J... this is what I put as my first answer and got it wrong.

W=M•φ =F•R•φ =55•1.15•2•π =397.4 J (!!!!)