spring2010exam-solutions

# spring2010exam-solutions - Physics Qualifying Examination...

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Physics Qualifying Examination Problems 1–6 Thursday, January 7, 2010 1–5 pm Problems 7-12 Friday, January 8, 2010 1-5 pm 1. Solve each problem. 2. Start each problem solution on a fresh page. You may use multiple pages per problem. 3. At the top of each solution page put the problem number (1–12) and your Social Security number, but not your name or any other information.

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Problem 1

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Problem 2
Solution

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Problem 3
Solution

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Problem 4
Solution

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Problem 5 Suppose the Moon were to have the same mass as the Earth, and you are trying to throw one of your textbooks from the Earth to the Moon. With what minimum velocity must the book leave the surface of the Earth? Neglect the relative motion of the Earth and Moon and the Earth’s rotation. The mass of the Earth is 24 610 E M kg =⋅ , the radius of the Earth is , and the distance from the center of the Earth to the center of the Moon is . Compare your answer to the escape velocity from Earth alone. The gravitational constant is 6 6.4 10 m 8 3.8 10 EM R m k g 11 2 2 6.67 10 / GN m
Solution Conservation of energy given by the sum of potential energy due to gravity and kinetic energy can be used to determine escape velocity. In the case of the Earth alone the potential is given by () E M m Vr G r =− where m is the mass of the book. The book will escape whenever the total energy at E rR = is greater than or equal to the maximum potential energy, which is zero when r is at infinity: 2 1 0 2 E E Mm mv G R which gives 2 11.2 / E E E GM vk R = ± m s In the case of the Earth and Moon acting together the potential is EM EM M mM m G G r where M M = M E . In this case the book will escape whenever the total energy at E = is greater then the maximum potential energy, which occurs at the point , and which is /2 EM = 4 2 EM E EM R VG R ⎛⎞ ⎜⎟ ⎝⎠ so we must have 2 1 4 2 EE M E E E M M m M mv G G G RR R R −− m which gives 2 2 2 1 57.4 59.4 58.4 10.9 / EM E EM E EM EM E R R vv v km s = ± ±

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Problem 6
Solution

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Physics Qualifying Examination Problems 1–6 Thursday, January 7, 2010 1–5 pm Problems 7-12 Friday, January 8, 2010 1-5 pm 1. Solve each problem. 2. Start each problem solution on a fresh page. You may use multiple pages per problem. 3. At the top of each solution page put the problem number (1–12) and your Social Security number, but not your name or any other information.
Problem 7

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Solution
Problem 8 A parallel plate capacitor with capacitance C is charged to a potential difference V and is then disconnected from the charging source. The capacitor has an area A and a plate separation z . Neglect fringe effects at the edges of the plates. (a) What is the force acting on the upper capacitor plate as a function of plate separation z ?

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## This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.

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spring2010exam-solutions - Physics Qualifying Examination...

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