PHI 203 Midterm: PHYS 203 Princeton MidFall2003
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Find the di erential equation for the shape of the track on which a cart released from point a (at height h) reaches point. Assume that gravity is the only force in the game, and that the cart starts at a with zero velocity. (this is the classic brachistochrone problem. The solution is a cycloid, but you do not need to solve the equation here. ) On april 1, 1977, four members of the oxford university"s dangerous sports club performed the rst ever bungee jump from the clifton suspension bridge. They had just taken the oxford version of death mechanics, and wanted to check their calculation of the tension in the rope as function of the angle . To explain the puzzle of the missing mass of the universe, physicists hypothesize the existence of dark matter , a cloud of unknown particles surrounding the center of galaxies.
