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Consider adiabatic flow of air in a constant-area pipe with friction. At one section of the pipe, , and . If the cross-sectional area is and the Mach number at the exit is , determine the duct length. Assume the duct is circular and made from commercial steel. Plot the variations of pressure and Mach number versus distance along the duct.
From a large distance away, a particle of mass 2.00 g and charge 15.0 C is fired at 21.0 m/s straight toward a second particle, originally stationary but free to move, with mass 5.00 g and charge 8.50 C. Both particles are constrained to move only along the x axis. Find the distance of closest approach.
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