A skateboarder with his board can be modeled as a particle of mass 76.0 kg, located at his center of mass (which we will study in Chapter 9). As in Figure P8.67, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point A). The half-pipe is a dry water channel, forming one half of a cylinder of radius 6.80 m with its axis horizontal. On his descent, the skateboarder moves without friction so that his center of mass moves through one quarter of a circle of radius 6.30 m. (a) Find his speed at the bottom of the half-pipe (point B). (b) Find his centripetal acceleration. (c) Find the normal force nB acting on the skateboarder at point B. Immediately after passing point B, he stands up and raises his arms, lifting his center of mass from 0.500 m to 0.950 m above the concrete (point C). To account for the conversion of chemical into mechanical energy, model his legs as doing work by pushing him vertically up, with a constant force equal to the normal force nB, over a distance of 0.450 m. (You will be able to solve this problem with a more accurate model in Chapter 11.) (d) What is the work done on the skateboarder€™s body in this process? Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.85 m. His body is horizontal when he passes point D, the far lip of the half-pipe. (e) Find his speed at this location. At last he goes ballistic, twisting around while his center of mass moves vertically. (f) How high above point D does he rise? (g) Over what time interval is he airborne before he touches down, 2.34 m below the level of point D? [Caution: Do not try this yourself without the required skill and protective equipment, or in a drainage channel to which you do not have legal access.]

Transcribed Image Text:

Figure P8.67