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homework4 - UNIVERSITY OF COLORADO AT BOULDER PHYS 2210...

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PHYS 2210 UNIVERSITY OF COLORADO AT BOULDER CLASSICAL MECHANICS AND MATH METHODS, SPRING, 2011 Homework 4 (Due Date: Start of class on Thurs. Feb 3 ) NOTE: Be sure to show your work and explain what you are doing. (Correct answers, for which we cannot follow the work, are worth no credit). 1. Consider a sports car which is braking hard. There are two significant resistive forces acting on it, a quadratic ( cv 2 ) air drag, and a constant ( μmg ) frictional force. When you write Newton’s law, if you are interested in finding v(x) (rather than v(t)), there is a nice trick, known as the “v dv/dx rule”, which uses the chain rule to rewrite ˙ v = dv dt = dv dx dx dt = v dv dx . (a) Write down the equation of motion for ˙ v = f ( v ) and use the “v dv/dx” rule to solve the equation of motion directly for v(x), and show that the distance the car needs for a full stop is: x max = A 2 2 μg ln A 2 + v 2 0 A 2 (1) here μ is the friction coe cient. What is the constant A in this case ( in terms of given parameters in the di ff erential equation?) (b) The SSC Ultimate Aero TT, one of the world’s fastest production cars (at a cool $600,000+), has a maximum speed of 412 Km per hour. The engine provides maximum forward force of 11260 N on the 1200 kg car. For this car, c =0.86 kg/m. On a race track, the car exits a turn with a speed of v 0 = 300 km/hr. As soon as the driver enters the straight track after the turn, she realizes there is another car blocking the track 2 km away. The driver slams on the brakes. Assuming a friction coe cient μ = 0 . 7, use your above result to compute the distance required for the Aero TT to stop. Compare
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