<p>A skateboarder with his board can be modeled as a particle of mass 80.0 kg, l

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<p>A skateboarder with his board can be modeled as a particle of mass 80.0 kg, located at his center of mass (which we will study in Chapter 9). As shown 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 7.00 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 6.50 m. <br /><br /><br />Figure P8.67<br /> (a) Find his speed at the bottom of the half-pipe (point B).<br />11.71 <br /> <br />Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m/s<br /> (b) Find his centripetal acceleration.<br /> m/s2<br /> (c) Find the normal force nB acting on the skateboarder at point B.<br /> N<br /> Immediately after passing point B, he stands up and raises his arms, lifting his center of mass from 0.500 m to 0.930 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 0.430 m. (You will be able to solve this problem with a more accurate model in Chapter 11.) <br /> (d) What is the work done on the skateboarder's body in this process?<br /> J<br /> Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 6.07 m. His body is horizontal when he passes point D, the far lip of the half-pipe. <br /> (e) Find his speed at this location.<br /> m/s<br /> (f) At last he goes ballistic, twisting around while his center of mass moves vertically. How high above point D does he rise?<br /> m<br /> (g) Over what time interval is he airborne before he touches down, 2.00 m below the level of point D?<br /> s<br /> (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.)</p>

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