PHY 711 Classical Mechanics

MWF 11-11:50 AM OPL 107 http://www.wfu.edu/~natalie/f05phy711/

Instructor: Natalie Holzwarth Phone:758-5510Office:300 OPL e-mail:natalie@wfu.edu

Homework Assignments

PHY 711 -- Assignment #1

August 24, 2005

Read Chapter 1 in Fetter & Walecka and make note of useful appendices.

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PHY 711 -- Assignment #2

August 26, 2005

Continue reading Chapter 1 in Fetter & Walecka.

  1. Work problem #1.15

PHY 711 -- Assignment #3

August 26, 2005

Finish reading Chapters 1 & 2 in Fetter & Walecka.

  1. Work problem #1.16

PHY 711 -- Assignment #4

August 31, 2005

Continue reading Chapter 3 in Fetter & Walecka and also section 33 in Chapter 6.

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PHY 711 -- Assignment #5

September 2, 2005

Continue reading Chapter 3 in Fetter & Walecka.

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PHY 711 -- Assignment #6

September 5, 2005

Continue reading Chapter 3 in Fetter & Walecka.

  1. Work problem #3.10

PHY 711 -- Assignment #7

September 7, 2005

Continue reading Chapter 3 in Fetter & Walecka.

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PHY 711 -- Assignment #8

September 9, 2005

Finish reading Chapter 3 in Fetter & Walecka.

Read Sections I-III of the paper by Hans C. Andersen on Molecular Dyanmics Simulations. Work through the equations to find the equations of motion 3.14, correcting any typos along the way.

PHY 711 -- Assignment #9

September 12, 2005

Start reading Chapter 4 in Fetter & Walecka.

Work problem 4.2, parts a-c (d-e for extra credit) in Fetter & Walecka.

PHY 711 -- Assignment #10

September 16, 2005

Finish reading Chapter 4 in Fetter & Walecka.

Work problem 4.9 OR problem 4.12 (extra credit for working both) in Fetter & Walecka.

PHY 711 -- Assignment #11

September 19, 2005

Start reading Chapter 5 in Fetter & Walecka

Consider the rectangular solid shown in the diagram. Assume that it has a uniform mass distribution and that the lengths a, b, c are not equal.

  1. Find the moment of inertia tensor centered at the center of mass.
  2. Find the moment of inertia tensor centered at a corner.

PHY 711 -- Assignment #12

September 21, 2005

Continue reading Chapter 5 in Fetter & Walecka.

  • Write down the matrix transformation that takes the vector (x,y,z) --> (y,z,x). Find the corresponding Euler angles α, β, and γ.

PHY 711 -- Assignment #13

September 23, 2005

Continue reading Chapter 5 in Fetter & Walecka.

  • Work Problem 5.9 in Fetter & Walecka .

PHY 711 -- Assignment #14

September 26, 2005

Start reading Chapter 6 in Fetter & Walecka.

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PHY 711 -- Assignment #15

October 7, 2005

Continue reading Chapter 7 in Fetter & Walecka.

  • Work problem 7.9(a). Assume -a ≤ x ≤ a.

PHY 711 -- Assignment #16

October 12, 2005

Continue reading Chapter 8 in Fetter & Walecka.

  • Consider a square membrane of length 2a on each side with a square hole in the center of length a on each side. Assume each edge of the membrane is clamped in place. Find a general expression for the normal modes of this membrane. Find the first few frequencies and compare them with the frequencies of a membrane without a hole.

PHY 711 -- Assignment #17

October 17, 2005

Start reading Chapter 9 in Fetter & Walecka.

  • Consider Eq. 48.14 in Fetter & Walecka and "prove" it to your satisfaction.

PHY 711 -- Assignment #18

October 19, 2005

Continue reading Chapter 9 in Fetter & Walecka.

  • The above photo shows a syringe with a liquid (density ρ=1000 kg/m3 ) inside the barrel (cross sectional area 8 x 10-5 m2). Suppose a force of F = 1 N is applied to the barrel. What is the velocity of the liquid coming out of the needle (cross sectional area 8 x 10-7 m2)?

PHY 711 -- Assignment #19

October 21, 2005

Continue reading Chapter 9 in Fetter & Walecka.

  • Work Problem 9.3 in Fetter & Walecka.

PHY 711 -- Assignment #20

October 26, 2005

Continue reading Chapter 9 in Fetter & Walecka.

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PHY 711 -- Assignment #21

October 28, 2005

Continue reading Chapter 9 in Fetter & Walecka.

Consider the example shown in Fig. 51.1 which results in the power distribution given in Fig. 51.19. Estimate reasonable values for the parameters and plot the distribution as a function of angle. Find the angles of zero power.

PHY 711 -- Assignment #22

October 31, 2005

Continue reading Chapter 9 in Fetter & Walecka.

Consider an ideal monoatomic ideal gas moving as a non-linear traveling wave as discussed in Section 52 of your text. For this value of γ and your choice of waveform, determine the time for the onset of "shock" formation.

PHY 711 -- Assignment #23

November 4, 2005

Finish reading Chapter 9 in Fetter & Walecka.

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PHY 711 -- Assignment #24

November 9, 2005

Continue reading Chapter 10 in Fetter & Walecka.

Work problem 10.3 in Fetter & Walecka.

PHY 711 -- Assignment #25

November 11, 2005

Finish reading Chapter 10 in Fetter & Walecka.

Using the Soliton lecturenotes, find one or two of the terms eliminated from the equation and estimate their magnitudes relative to the terms kept in Eq. (24), in terms of the soliton solution.

PHY 711 -- Assignment #26

November 14, 2005

Start reading Chapter 11 in Fetter & Walecka.

Work problem 11.1 in Fetter & Walecka.

PHY 711 -- Assignment #27

November 16, 2005

Continue reading Chapter 11 in Fetter & Walecka.

Use Laplace transforms to find the trajectory Y(t) given an initial position Y(0) and initial velocity V(0) and constant acceleration Ÿ(t)=-g.

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