Solved: A skateboarder with his board can be modeled as aparticle of mass 76.0 kg

Chapter 11, Problem 48

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A skateboarder with his board can be modeled as aparticle of mass 76.0 kg, located at his center of mass,0.500 m above the ground. As shown in Figure P11.48,the skateboarder starts from rest in a crouching positionat one lip of a half-pipe (point A). The half-pipeforms one half of a cylinder of radius 6.80 m with itsaxis horizontal. On his descent, the skateboarder moveswithout friction and maintains his crouch so that hiscenter of mass moves through one quarter of a circle.(a) Find his speed at the bottom of the half-pipe (pointB). (b) Find his angular momentum about the centerof curvature at this point. (c) Immediately after passingpoint B, he stands up and raises his arms, lifting hiscenter of gravity to 0.950 m above the concrete (pointC). Explain why his angular momentum is constant inthis maneuver, whereas the kinetic energy of his bodyis not constant. (d) Find his speed immediately after hestands up. (e) How much chemical energy in the skateboarderslegs was converted into mechanical energy inthe skateboarderEarth system when he stood up?

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