What is the maximum height a child reaches on a swing based on speed?

[tony873004]

6. At a local playground, a child on a swing has a speed of 3.4 m/s when the swing is at its lowest point.

a.) To what maximum vertical height (above the bottom of the swing) does the child rise, assuming he sits still and "coasts"?
m

b.) Reanswer part a, with the initial speed of the child being half as much.
m

c.) During this process, how much work is done by the tension in the rope?
J

I got part A and B using $$\Delta K = - \Delta U$$

But for part C, $$W = \Delta K = \frac{1}{2}mv^2$$ and $$W = Fd$$ or $$W=mad$$
But the mass of the child is not given? How can I compute the work? Unless this is a trick question and the rope is doing no work. But the rope is what is responsible for the child rising, otherwise the child would continue on a straight path parallel to the ground. So the rope is doing work, right?

 

[Galileo]

Since you have used conservation of mechanical energy in parts a) and b), you already implicitly used the fact that the rope doesn't do work.
Consider the direction in which the force from the rope acts.

 

[tony873004]

Is that a real Einstein quote in your signature? That's funny

I guess you're right. The rope pulls towards the center of the circle but the child never gets closer to the center. D = 0, so regardless of mass, W must be 0.

Thanks.