**Homework, reading guide and Solutions
**

On every homework assignment please do the following.

a) On the top right corner neatly print the following, making appropriate
substitutions as appropriate.

Sally Rogers

HW 2 DUE SEPT 6, 2000

TAM 203

Section 3 at 10:10

b) STAPLE your homework in the top left corner.

c) At the top clearly acknowledge all help you got from TAs, Faculty, students,
or ANY other source (but for lecture, text and section only). Examples could
be "Mary Jones pointed out to me that I needed to draw the second FBD in problem
2." or "Nadia Chow showed me how to do problem 3 from start to finish." or "I
basically copied this solution from a tau beta sigma frat file." etc. If your
TA thinks you are taking too much from other sources he/she will tell you. In
the mean time don't violate academic integrity rules and be unclear about what
of your presentation you worked out on your own.

d) Every use of force, moment, momentum, or angular momentum balance must be associated with a clear correct free body diagram.

e) Your vector notation must be clear and correct.

f) All computer output should have your name clearly visible, as printed by the computer (e.g., title plots with your name, put your name in a comment in the first line of any .m files, etc.)

g) Every line of every calculation must me dimensionally correct. (Carry your units.)

h) Your work should be laid out neatly enough to read. Part of your job as an engineer is not just to get the right answer, but to communicate its justification clearly. So that is part of your job on the homework as well.

**Homework 1, due Thursday Aug 31, 2000 in lecture:**

Reading guide:

The Pratap Matlab book:

You should know all the tutorials thoroughly.

You should know the ODE section.

You should skim the rest of the book so you know what is there, at least

glance at every page.

A problem from a 203 final exam a few years ago.

below which we assume are both in the same directory on your computer.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %These 4 lines are in a script file [t,z]=ODE23('iknowthis', [0 2*pi], [1 0]); plot(z(:,1), z(:,2)) axis('square') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function zdot=iknowthis(t,z) % These seven lines are in the file iknowthis.m z1 = z(1); z2 = z(2); z1dot= z2; z2dot= -z1; zdot=[z1dot, z2dot]'; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 1) Answer this question without using a computer (give yourself at least half an hour to work on puzzling it out): What happens when you run the first file above? Explain your prediction. 2) Type the files in, and run the first. Print the results and hand them in. Title the plot with your name. If what comes out is different than you expected, explain your error. 3) By changing the files above make a plot that shows an ODE solution that you think looks nice (visual aesthetics is the criterion). Title the plot with your name. Print out the files you used to generate the plot and explain them in a way that reflects the thought that went in to creating them.

**Homework 2, due Wed Sept 6 in lecture:**

**Reading guide:** (All in Part I, The red statics book)

First two tables inside the cover: Without studying them explicitly, you will
learn all that's in these tables as the semester progresses. Read through them
quickly at the start of the semester and check your progress occasionally as
the semester progresses.

Back four tables: By the end of the semester you should be able to navigate
around these tables and use them comfortably. You should know which formulas,
say for rate of change of angular momentum, apply to which situation. In the
process you will undoubtedly learn some of the formulas. But at the start of
the semester just look through them to get a sense of what is there.

The first 4 chapters are basically a review of statics, but you need to know
some of the material very well.

Preface: Read and absorb pages vii - xii.

Chapter 1: Read and understand pages 1-5, skim page 6.

Chapter 2: You need to know all of this vector material well. Skim the whole
chapter and read carefully any sections that you are insecure about.

Chapter 3: You also need to know the material here well. Skim the chapter and
carefully read sections you have doubts about.

Chapter 4: The ideas in the introduction and sections 4.1, 4.5 and 4.6 are essential
for dynamics. Skim the rest of the chapter so you know what's there and can
read it when you need it.

**Problems
**1) 4.20

2) 4.23 (parts d and e are challenges)

3) 4.31

**Homework 3, due Wednesday September 13: **

**Reading guide:** Sections 5.1-3 on pages 217 - 256 (note the box on 226-227).
Almost all of this is review of physics 112 or math 293.

**Problems**

1) 5.18

2) 31

3) 34

4) 37

5) 38

**Homework 4, due Wednesday September 20:
Reading guide:** Sections 5.4 & 5.5 (though you need not master all details).
Section 5.6. Section 5.7. Section 5.8.

**Problems**

5.41 (straightforward),

5.52 (requires time and thought),

5.57 (easy and quick),

5.103 (straightforward),

5.109 (easy),

5.113 (Requires time and thought. A time interval of 10 seconds makes a decent
plot. One check of your solution is to compare the steady state falling speed
to the falling speed at the end of the simulation. (Typo: g= 10 m/s^2 not 10
m/s.)

**Homework 5, due Thursday September 28 in lecture: **

**Reading guide:** Sections 5.8, 5.9, 5.10

**Problems
**None of these problems is difficult (like, say, the last part of the trampoline
question)

5.120 (takes some time and thought),

5.111 (takes some time, thought and coding.),

5.124 (takes some time, thought and coding).

**Homework 6, due Wednesday Oct 4 in section: **

**Reading guide:** 6.1, 6.2

**Problems
**When reasonable

6.13b [Typo: should refer to 6.14 not 6.31] (easy, you should also make sure you can do a,c,d),

6.14b (easy, you should also make sure you can do a,c,d),

6.18b,c (basically straightforward),

6.27a (requires some care, but not time consuming or difficult),

6.51 (takes time and thought, not very hard, but not trivial.)

Solution6 (corrected 10/11/00)

**Homework 7, due Thursday Oct 12 in lecture: **

**Reading guide:** 7.1, 7.2

**Problems
**6.74 (Takes some thought, but of a type you should be good at by now.)

7.16 (pretty easy to set up)

7.29 (easy),

7.43 (requires some time and thought for a beginner, easy afterwards),

7.44 (straightforward, a slightly suprising place to find exponential decay).

**Homework 8, due Thursday Oct 19 in lecture: **

**Reading guide:** 7.3, 7.4

**
**7.57 (pretty easy),

7.66 [typos: equal signs needed after r_B, lambda_A, and lambda_B.

part (b) should refer to r_C not lambda_C.]

(not wildly difficult, but will take some thought and time),

7.92 (basic, you have to know this, takes some thought the first time),

7.93 (quick, short, and easy),

7.98 (takes some time and thought to come up with a control function)

**Homework 9, due Thursday Oct 26 in lecture: **

**Reading guide:** 7.5, 7.6

**
**7.106 (easy)

7.121 (easy )

7.128 (Takes some time. Not too hard.)

7.148 (No tricks or special problems. Takes some time but nothing deep or too involved.)

**Reading guide:** 8.1, 8.2

8.17 (easy)

8.22 (easy)

8.43 (not trivial, but not long and difficult)

8.25 (a serious problem)

Update (10/25/00). The following two problems are *not* due Thursday Nov
2:

**Reading guide:** 8.3-5

**Homework 11, due Thursday Nov 9 at the start of class: **

8.48 (not especially difficult)

5) (Challenge.) A uniform curved rod with mass of 3 kg is along the curve
x = sin(t), y = e^ t, z = t^2 for 0< t < 2, where the numerical values
in the formulas are the distances in meters. What is the moment of inertia matrix
for this rod. Assume the rod is one dimensional (has no width). You will probably
want to use numerical integration.**
**8.53 (somewhat tedius, but easy if you know what you are doing)

8.55 (easy)

8.63 (not hard but not trivial to calculate, neglect gravity)

8.81a (not very hard, but not trivial)

8.92 (requires thought and understanding, easy and quick if you get the ideas)

**Homework 12, due Thursday Nov 16 at the start of class
**9.6 (easy warmup, straight from section)

9.5 (same ideas as above, the trick is to think about the velocity of the point on the ladder that touches the step. What do you know about its velocity?)

9.7 (Not hard, but it should make you think about what rolling is all about. It will take some time.)

9.22 (not hard, but you have to know your basics)

9.28 (not hard)

**Homework 13, due Tuesday Nov 23 at the start of class: **

9.25** **(just like lecture)**
**9.37 (not too hard, kind of a fun answer. Note, for part c, that the ring
slides before it ends up rolling.)

9.47 (again not hard, but for the end, something you should use to add to your permanent intuition)

9.58 (just like section)

9.59 (an easier problem than above)

**Homework 14, due Thursday Nov 30 at the start of class: **

9.73** **(like section but disk also translates)**
**9.74 (sort of complicated but not too hard)

9.106 (like lecture but the launcher is bent)

9.113 (like lecture but with a spring attached to the mass)

9.119 (not hard)

**Homework 15, not collected:**

9.122 (not hard - sticks are massless)

9.127 (like lecture and section but the geometry is a bit more complicated)

9.130 (see problem 9.86 for the problem statement - use no slip)

9.140 (this one is lengthy)

9.146 (like section)

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