You are designing a sliding board for an amusement park.  You envision one of those tall slides with several of those large, subdued bumps and then a long, flat slide to a stop along a rough  surface at the finish.  In particular, each person would climb to the top of the slide and sit on a cloth sack to reduce friction.  Starting from rest at point A, the person  would slide down past point B to point C at ground level, where the person would encounter a long, horizontal rough surface having a coefficient of friction 0.86 .  Let’s consider a person of average mass 55 kg.

Data:      h_A = 8.6 m         h_B = 4.3 m       m = 0.86

(a) How fast is the person moving at point B assuming that the curved slide is frictionless? (b) How fast is the person moving at point Cassuming that the slide is frictionless? (c) Upon reaching the rough, horizontal section at the bottom of the slide, a person is actually found to slide a distance of d = 4.3 m before coming to a stop at point D.  What total amount of energy is actually lost due to friction along the curved slide?

Answers: (a) 9.2 m/s      (b) 13 m/s       (c) 2,660 J