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homework9 - 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 9 (Due Date: Start of class on Thurs. March 10 ) 1. You are stranded on the surface of the asteroid Vesta. If the mass of the asteroid is M and its radius is R , how fast would you have to jump o ff its surface to be able to escape from its gravitational field? (Your estimate should be based on parameters that characterize the asteroid, not parameters that describe your jumping ability.) Given your formula, look up the approximate mass and radius of the asteroid Vesta 3 and determine a numerical value of the escape velocity. Could you escape in this way? (Briefly, explain) If so, roughly how big in radius is the maximum the asteroid could be, for you to still escape this way? If not, estimate how much smaller an asteroid you would need, to escape from it in this way? Figure 1: 2. Consider two identical uniform rods of length L and mass m lying along the same line and having their closest points separated by a distance d as shown in the figure (a) Calculate the mutual force between these rods, both its direction and magnitude. (b) Now do several checks. First, make sure the units worked out (!) The, find the magnitude of the force in the limit L 0. What do you expect? Briefly, discuss. Lastly, find the magnitude of the force in the limit d → ∞ ? Again, is it what you expect? Briefly, discuss. Figure 2: 3. Practicing with complex numbers. (1 pt each) (a) If z 1 = 3 + i , draw z 1 in the complex plane. Compute its real and imaginary parts and magnitude. Write z 1 as Ae i θ and determine A and θ . (b) If z 2 = 1 / (1 + i ), draw z in the complex plane. Compute its real and imaginary parts and magnitude.
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