Exam 2 - volume contained by S More speci±cally Gauss²s...

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HPHY 253.02 Exam 02 (take-home) Spring Semester 2009 Dr. A. E. Bak Name Instructions. For each question, show all work leading to an answer and simplify as much as possible. 25 : 7 . A block having mass m and charge + Q is connected to an insulating spring having force constant k . The block lies on a frictionless, insulating horizontal track, and the system is immersed in a uniform electric ±eld of magnitude E directed as shown in Figure P 25 : 7 . The block is released from rest at a moment when the spring is unstretched (that is, when x = 0 ). (a) By what maximum amount does the spring expand? (b) What is the equilibrium position of the block? 2. Consider a closed surface S in a region of gravitational ±eld g . Gauss²s law for gravitation tells us that the gravitational ³ux through surface S is linearly proportional to the total mass m in occupying the
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Unformatted text preview: volume contained by S . More speci±cally, Gauss²s law states that I S g & da = ± 4 &Gm in : Note that g here is the total electric ±eld, due to mass sources both inside and outside S . The value of G , the gravitational constant, is about 6 : 673 ² 10 & 11 N & m 2 =kg 2 . (a) Earth²s volume mass density, at any distance r from its center, is given approximately by the function ± = A ± Br=R , where A = 1 : 42 ² 10 4 kg=m 3 , B = 1 : 16 ² 10 4 kg=m 3 , and Earth²s radius R = 6 : 370 ² 10 6 m . Calculate the numerical value of Earth²s mass M . Hint: The volume of a spherical shell, lying between radii r and r + dr , is dv = 4 &r 2 dr . (b) Determine the gravitational ±eld inside Earth. (c) Using the result of part b , determine the gravitational-±eld magnitude at Earth²s surface. 1...
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