**Homework and reading guide
TAM 203, Spring 2002**

**Homework guidelines: **Homeworks are due at the
start of tuesday lecture. You need not bring it to the front of the class, it
will be collected from the class. On every homework assignment please do the
things listed below. After a few weeks of getting used to these you will have
to follow all of them to get any credit on homework.

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

Sally Rogers

HW 2 Due Feb 5, 2002

TAM 203

Section 3 at 10:10

TA: John Smith

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

d)Your vector notation must be clear and correct.

e)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.)

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

g)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.

h)

i)Some problems which are assigned may seem like make-work to you because you already know well how to do them.

If that is the case, you can answer a question and get full credit for it by writing "I can do this problem but don't feel

I will gain from writing out the solution". You can keep doing this unless your grader/TA challenges your judgement

about what you can do.

**Homework 1, due Tuesday Jan 29 at the start of lecture: **Solutions

**Reading
guide:**(note, text homework problems are only available on WWW from text
page)

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.

Dynamics text part I:*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. *Preface: Read and absorb the "guide to student" and pseudo-code pages. *Chapter 1: Read and understand. *Chapter 2: You need to know all of this vector material well.

**To hand in: **Consider
the two Matlab files below which we assume are both in the same directory on
your computer.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %These 4 lines are in a script file function zdot=iknowthis(t,z) [t,z]=ODE23('iknowthis', [0 2*pi], [1 0]); % These five lines are in the file iknowthis.m plot(z(:,1), z(:,2)) z1 = z(1); z2 = z(2); axis('square') z1dot= z2; z2dot= -z1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% zdot=[z1dot, z2dot]';

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Reading guide:

Reading guide:

Reading guide:

Problems: 1)

If you use the solutions in your homework, note that, like all other help, clearly on the homework you hand in.

Reading guide:

Problems:

**BONUS: **Add up to an extra 5 points to your course score (Equiv of about
2 HW assignments). Estimated total time to complete is 2 hours (me) to 20 hours
(someone who has to learn all as they go).

**Due:** May 19 midnight EST 100% strict. email submissions only. Credit
only for complete good jobs: code runs and correct results are obtained. One
hand in per person, but working together is allowed if fully acknowledged as
per the homework directions at the top of this page.

**Directions for handing in **(a,b,c below are strict requirements, make
sure you can handle them before the last minute, not following them will lead
to lost files on my computer and no grade for you**): **

a) email a single file with the name * first_last*_203extra.zip
(or .tar or .sit) where *first_last* is your name.

b) that file, when decompressed should contain only one folder named * first_last*_203extra

c) that folder should have any number of matlab files inside, one of which drives
all the others, and a file called *readme* that explains what you have done
(word or pdf with appropriate figures, 72 dpi scan of hand work is ok as a single
.pdf).

**Assignment: **(this, or make up a clear one on your own.)** **Make a
matlab cartoon of a car, drawn as a rectangle looking down, as it skids to a
stop with rear-wheel braking. One frame every fraction of a sec (you pick a
time interval that looks nice) until the car stops. On this cartoon draw a curve
of the path of the center of mass. Wheel base is 3m long, 2m wide. Center of
mass in the middle of the car at ground level. Car is on level ground. Initial
velocity is in the plus x direction at a speed of 30 m/sec. Initial angular
velocity is zero. Initial angle is 1 degree counter clockwise. Assume a coefficient
of friction of 1 on the skidding rear wheels (not me=zero as in lecture). Front
wheels roll with no side slip.** **g = 10 m/s^2.**
Hints:** The basic problem setup is as in lecture of April 29. But you need
to include the friction force on both of the skidding wheels. Also you need
to use linear momentum balance to see how the speed changes. Finally you need
to use kinematic relations to see how x and y components evolve, as well as
theta. To see how to make movies see the Pratap text or the Fourier series example
on the Matlab samples page. Your integrator might have trouble when the car
comes to a stop after about 6 seconds, so you will have to take this into account
somehow (two solutions: use "event detection" which is tricky the
first time, or make your ODEfile give zero accelerations if all velocities are
low enough).

**Bonus project solutions: **Here is a pretty good solutionfor the bonus
project, by student Mike. One technical flaw is that Mike assumes that the effect
of friction on the two skidding rear wheels is equivalent to a force on a single
skid midway between the wheels. This is not right, but is probably a good approximation
for most purposes.

PC version Mac
version