Princeton Problems in Physics with Solutions (Princeton Paperbacks) - Softcover

Newbury, Nathan

Softcover

ISBN 10: 0691024499 ISBN 13: 9780691024493

Verlag: Princeton University Press, 1991

Inhaltsangabe

Aimed at helping the physics student to develop a solid grasp of basic graduate-level material, this book presents worked solutions to a wide range of informative problems. These problems have been culled from the preliminary and general examinations created by the physics department at Princeton University for its graduate program. The authors, all students who have successfully completed the examinations, selected these problems on the basis of usefulness, interest, and originality, and have provided highly detailed solutions to each one. Their book will be a valuable resource not only to other students but to college physics teachers as well. The first four chapters pose problems in the areas of mechanics, electricity and magnetism, quantum mechanics, and thermodynamics and statistical mechanics, thereby serving as a review of material typically covered in undergraduate courses. Later chapters deal with material new to most first-year graduate students, challenging them on such topics as condensed matter, relativity and astrophysics, nuclear physics, elementary particles, and atomic and general physics.

Über diesen Titel

Über die Autorin bzw. den Autor

Nathan Newbury & M. Newman

Auszug. © Genehmigter Nachdruck. Alle Rechte vorbehalten.

Princeton Problems in Physics with Solutions

By Nathan Newbury, Michael Newman, John Ruhl, Suzanne Staggs, Stephen Thorsett

PRINCETON UNIVERSITY PRESS

Copyright © 1991 Princeton University Press
All rights reserved.

ISBN: 978-0-691-02449-3

Contents

Preface, xv, 
I Problems, 1, 
1 Mechanics, 3, 
2 Electricity & Magnetism, 9, 
3 Quantum Mechanics, 16, 
4 Thermodynamics & Statistical Mechanics, 22, 
5 Condensed Matter Physics, 28, 
6 Relativity &: Astrophysics, 39, 
7 Nuclear Physics, 46, 
8 Elementary Particle Physics, 56, 
9 Atomic & General Physics, 66, 
II Solutions, 75, 
10 Mechanics, 77, 
11 Electricity & Magnetism, 97, 
12 Quantum Mechanics, 120, 
13 Thermodynamics & Statistical Mechanics, 145, 
14 Condensed Matter Physics, 166, 
15 Relativity & Astrophysics, 196, 
16 Nuclear Physics, 225, 
17 Elementary Particle Physics, 256, 
18 Atomic & General Physics, 283, 
Bibliography, 311, 
Index, 313, 

CHAPTER 1

Mechanics

Problem 1.1. A Wham-O Super-Ball is a hard spherical ball of radius a. The bounces of a Super-Ball on a surface with friction are essentially elastic and non-slip at the point of contact. How should you throw a Super-Ball if you want it to bounce back and forth as shown in Figure 1.1? (Super-Ball is a registered trademark of Wham-O Corporation, San Gabriel, California.)

* * *

Problem 1.2. Suppose a spacecraft of mass mo and cross-sectional area A is coasting with velocity vo when it encounters a stationary dust cloud of density ρ. Solve for the subsequent motion of the spacecraft assuming that the dust sticks to its surface and that A is constant over time.

* * *

Problem 1.3. The science fiction writer R. A. Heinlein describes a "skyhook" satellite that consists of a long rope placed in orbit at the equator, aligned along a radius from the center of the earth, and moving so that the rope appears suspended in space above a fixed point on the equator (Figure 1.2). The bottom of the rope hangs free just above the surface of the earth (radius R). Assuming that the rope has uniform mass per unit length (and that the rope is strong enough to resist breaking!), find the length of the rope.

* * *

Problem 1.4. Three identical objects of mass m are connected by springs of spring constant k, as shown in Figure 1.3. The motion is confined to one dimension. At t = 0, the masses are at rest at their equilibrium positions. Mass A is then subjected to an external driving force,

F(t) = f cos ωt, for t > 0. (1.1)

Calculate the motion of mass C.

* * *

Problem 1.5. A uniform density ball rolls without slipping and without rolling friction on a turntable rotating in the horizontal plane with angular velocity Ω (Figure 1.4). The ball moves in a circle of radius r centered on the pivot of the turntable. Find the angular velocity a; of motion of the ball around the pivot.

* * *

Problem 1.6. A blob of putty of mass m falls from height h onto a massless platform which is supported by a spring of constant k. A dashpot provides damping. The relaxation time of the putty is short compared to that of putty-plus-platform: the putty instantaneously hits and sticks.

a) Sketch the displacement of the platform as a function of time, under the given initial conditions, when the platform with putty attached is critically damped.

b) Determine the amount of damping such that, under the given initial conditions, the platform settles to its final position the most rapidly without overshoot.

* * *

Problem 1.7. A mass m slides on a horizontal frictionless track. It is connected to a spring fastened to a wall. Initially, the amplitude of the oscillations is A1 and the spring constant is k1. The spring constant then decreases adiabatically at a constant rate until the value k2 is reached. (For example, suppose the spring is being dissolved by nitric acid.) What is the new amplitude?

* * *

Problem 1.8. A soap film is stretched between two coaxial circular rings of equal radius R. The distance between the rings is d. You may ignore gravity. Find the shape of the soap film.

* * *

Problem 1.9. A bead of mass m slides without friction on a circular loop of radius a. The loop lies in a vertical plane and rotates about a vertical diameter with constant angular velocity ω (Figure 1.5).

a) For angular velocity ω greater than some critical angular velocity ωc, the bead can undergo small oscillations about some stable equilibrium point θo. Find ωc and θo(ω).

b) Obtain the equations of motion for the small oscillations about θo as a function of ω and find the period of the oscillations.

* * *

Problem 1.10. If the solar system were immersed in a uniformly dense spherical cloud of weakly-interacting massive particles (WIMPs), then objects in the solar system would experience gravitational forces from both the sun and the cloud of WIMPs such that

Fr = - k/r2 - br. (1.2)

Assume that the extra force due to the WIMPs is very small (i.e., b<< k/r3).

a) Find the frequency of radial oscillations for a nearly circular orbit and the rate of precession of the perihelion of this orbit.

b) Describe the shapes of the orbits when r is large enough so that Fr ≈ -br.

CHAPTER 2

Electricity & Magnetism

Problem 2.1. A conductor at potential V = 0 has the shape of an infinite plane except for a hemispherical bulge of radius a (Figure 2.1). A charge q is placed above the center of the bulge, a distance p from the plane (or p - a from the top of the bulge). What is the force on the charge?

* * *

Problem 2.2. A "tenuous plasma" consists of free electric charges of mass m and charge e. There are n charges per unit volume. Assume that the density is uniform and that interactions between the charges may be neglected. Electromagnetic plane waves (frequency ω, wave number k) are incident on the plasma.

a) Find the conductivity σ as a function of ω.

b) Find the dispersion relation — i.e., find the relation between k and ω.

c) Find the index of refraction as a function of ω. The plasma frequency is defined by ω2p [equivalent to] 4πne2/m, if e is expressed in esu. What happens if ω < ωp?

d) Now suppose there is an external magnetic field B0. Consider plane waves traveling parallel to B0. Show that the index of refraction is different for right- and left-circularly polarized waves. (Assume that the magnetic field of the traveling wave is negligible compared to B0.)

* * *

Problem 2.3. A cylindrical resistor (Figure 2.2) has radius b, length L, and conductivity σ1. At the center of the resistor is a defect consisting of a small sphere of radius a inside which the conductivity is σ2. The input and output currents are distributed uniformly across the flat ends of the resistor.

a) What is the resistance of the resistor if σ1 = σ2?

b) Estimate the relative change in the resistance to first order in σ1 - σ2 if σ1 ≠ σ2. (Make any...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 1991
• Sprache: Englisch
• ISBN 10: 0691024499
• ISBN 13: 9780691024493
• Einband: Taschenbuch
• Anzahl der Seiten: 336
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar