374chw3 - v , acted on by a force that depends on the...

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HW#3 —Phys374—Spring 2008 Prof. Ted Jacobson Due before class, Friday, Feb. 22, 2007 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374c/ [email protected] 1. Equation of motion for a stretched string : In class we derived the equation of motion for a stretched string by applying Newton’s law to each bit of string. This is also called the one-dimensional wave equation. The derivation is written up and posted at the supplements link to the course web page. (I just posted a 2008 version, which modifies somewhat the 2007 version.) For this homework, do the four exercises, a , b , c and d that are included with that supplement. [4+3+3 +(3+3+4)=20 pts.] 2. Convergence of improper integrals (a) Show that R 1 dtt n is finite if and only if n < - 1. (b) Show that R 0 dt ( a + bt ) n , with a,b > 0, is finite if and only if n < - 1. Be careful to treat the n = - 1 cases properly. [5 pts.] 3. Consider a particle of mass m in one dimension with a positive velocity
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Unformatted text preview: v , acted on by a force that depends on the velocity as-bv n , where b is a positive constant and n is a positive dimensionless number. This force acts to slow the particle down. (a) Use dimensional analysis to find an expression for how (i) the time for the particle to come to rest, and (ii) the distance it travels before coming to rest, can depend on the initial velocity v , together with m , b , and n . [5 pts.] (b) By integrating Newton’s law, determine for which values of n the particle comes to rest in a finite time, and determine that time. Compare with part 3a. [5 pts.] (c) Determine for which values of n the particle travels a finite total distance before coming to rest (whether or not it actually stops in a finite time). Find an expression for that distance and compare with your result from part 3a. [5 pts.]...
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This note was uploaded on 12/29/2011 for the course PHYSICS 374 taught by Professor Jacobson during the Fall '10 term at Maryland.

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