A 36.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 23.00 m. When she is partway down the slide, at a height h2 of 13.00 m, she is moving at a speed of 9.40 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.).
http://newcapa2.cc.huji.ac.il/res/ms...ob15_slide.gif

Under free fall the kinetic energy an object gains is equal to mgh. If her velocity after falling height h is given as v, her actual kineitic energy at that point is 1/2 mv^2. So the difference must be the loss of energy due to friction.