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MIT16_07F09_hw06

# MIT16_07F09_hw06 - NAME Massachusetts Institute of...

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NAME : . . . . . . . . . . . . . . . . . . . . . Massachusetts Institute of Technology 16.07 Dynamics Problem Set 6 Out date: Oct 10, 2007 Due date: Oct 17, 2007 Time Spent [minutes] Problem 1 Problem 2 Problem 3 Problem 4 Study Time Turn in each problem on separate sheets so that grading can be done in parallel

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Problem 1 (10 points) The geometry of a ”half-pipe” as used in skateboard competition is a ﬂat horizontal surface separating two circular arcs of radius R 0 . Pumping is the process by which the skateboarder does work and gains kinetic energy to make the next spectacular move. (This really works!!!! But maybe I’ve been watching too much TV.) Consider a skateboarder of mass m in the half-pipe. Assume he starts from height h 0 with zero velocity. He is standing up so that his center of mass is R 1 from the center of curvature of the circular section of the pipe. As he goes through the ﬂat section, the height of his center of mass above the track is h = R 0 R 1 . (Represent the skateboarder as a point mass located at his center of mass. Assume for your convenience that R 2 R 1 << R 0 .) A-1 1. In case a, he traverses the pipe without change of stance. Ignoring wind resistance and friction, what height will be reach on the other side of the pipe? A-2 What normal force is felt on his feet as a function of position in the half pipe? In the round section? In the ﬂat section? Now consider case b). He starts with the same initial conditions. However, in this case, when he reaches the ﬂat section, he crouches so that his center of mass is now at
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