**Homework policy, assignments, and
reading guide
TAM 203, Fall 2006**

**Homework policy: **To get credit, please do the
things listed below on every homework.

a) Homeworks are dueat the date named on the assignment. You need not bring your homework to the front of the class, hold on to it. It will be collected from the class at the start of class. Homework handed in after the start of class or later will be marked "late." For example, you should have the first homework assignment (due Aug 31) in hand at your seat, following the policies below, at the start of lecture on Thursday August 31.

b)On the top right cornerneatly print the following, making appropriate substitutions as appropriate:

Sally Rogers

HW probs 1-3, Due Aug 31, 2006

TAM 203

Section 1 at 12:20

TA: Manish Agarwal

b)STAPLEyour homework at the top left corner.

c)At the top clearlyacknowledge all helpyou got from TAs, faculty, students, or ANY other source (but for lecture, text and section). 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 the solution of Jane Lewenstein " 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:be clear about which parts of your presentation you did not do on your own.Every use of force, moment, momentum, or angular momentum balance must be associated with a clear correctViolations of this policy are violations of the Cornell Code of Academic Integrity.

d)free body diagram.Your

e)vector notationmust be clear and correct.Every line of every calculation should be

f)dimensionally correct(carry your units).Your work should be

g)laid out neatlyenough to read by someone who does not know how to do the problem. Part of your job as an engineer is not just to get the right answer, but convincingly so. That is your job on the homework as well.

h)Some problems may seem likemake-workbecause you already know how to do them.

If so, you can get full credit by writing in full "I can do this problem but don't feel

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

i)Computer work should be well commented. At the top the computer text file should include your name which you

later highlight or circle with colored pen. Part of any computer output should also include your name, printed by the computer. Also highlight this or circle it with colored pen.

j)At least one problem in each assigment should be "solutions quality". This should start on a fresh page, use single sides, and not have a new problem start on the same page. It should be self-contained, including, for example, enough of a problem restatment so that a reader need not see the original problem statement. It should be clear and convincing enough so that another TAM 203 student who has not done the problem and does not know how to do it, can read your solution, understand it, and judge that it is correct. The first word of this solution should be "SOLUTION".

**BONUS PROBLEMS: **Numbered I, II, etc. Each problem is worth
a full homework assignment, not just one homework problem, if you send a
solution before a solution is posted. This adds to your homework score. Solutions
must be clear, authoritative and complete (e.g., not speculative) in nature.
The document must be self-contained. That is, what you send in needs to be
clear to an intelligent reader who has not read, and is not going to look
at the book or any other sources. For example, the solution needs to include
a coherent description of the question that is being answered. A student
should learn from your solutions as should a professor. The reasoning should
be sufficiently clear that there is no argument about whether or not it is
correct. Please do not put your name on your solution. Send
pdf scan of a clear solution to ruina@cornell.edu and your TA. Send copies
of any correspondence you have about bonus questions to your TA. If your
solution is not good enough you will be given a chance to improve it. You
may discuss the problem, or improvements to your solution, at office hours.

**WRITE-AN-EXAM-QUESTION BONUS: ** Due Dec 1. Write from
1 to 5 candidate final exam questions. Write clear complete solutions. Hand
writing and clear hand-drawing are fine. These cannot be taken from any books
or from any old exams. Questions can be of any style that you think is appropriate
(even multiple choice or essay, if gradeable). If appropriate, they may be
the basis for actual final exam problems. Send pdf scan to ruina@cornell.edu
and your TA.

(e.g., Aug 29 assignment is not set in stone until Aug 30 at 3 AM)

Problems are from MK (Meriam and Kraige) unless otherwise specified (as BJ, Beer & Johnston STATICS, or RP, Ruina & Pratap DYNAMICS, or written out in text)

**Aug 24 Thurs:** Intro lecture , Readings: Review Matlab, don't
hand in anything

**Aug 29 Tues:** 1D mechanics and Matlab demo of simple ODEs.
Skim MK Chapter 1. 2.1-4, 3.1-4 (covers next 3 lectures)

Due Thursday Aug 31:

1) Reread the homework policy above. Write the following "I have read the course homework policy. If I ever find anything unclear about it I will ask Prof. Ruina for clarification."

2) A ball drops in honey. Find position vs time using numerical integration and using analytic formulas and compare the results. Use any values for parameters and initial conditions you like. Make sure to use a time interval that is appropriate to show the nature of the solution.

**Aug 31 Thurs: **Harmonic oscillator. 2.1-4, 3.1-4, 1D mechanics
parts of sections 8.1-3

Due Thursday Sept 7 (see below also):

1) a) Simulate mass hanging from spring with damping. You set all parameters (mass, gravity, spring constant, rest spring length, damping constant) and initial conditions. Learn to use Matlab's subplot command so you can make sensible stacked plots of x vs t, v vs t, and Tension vs t.

b) Plot v vs x (pick axes, time and parameters that show an interesting plot.)

**Sept 5 Tu: **1D particle motion. 2.1-4, 3.1-4.

Due Thursday Sept 7:

2) 3.5, 3) 3.6, 4) 3.21

** Sept 7 Th: **Pulley mechanics. ** ** 2.1-4, 3.1-4.

Due Tuesday Sept 12

1) Ruina and Pratap (RP) 6.12 (on pdf page 44)

2) 3.26b

3) 3.27

4) RP 6.22 (The answer for part C is genuinely subtle.)

**Sept 12 Tu: **2D motion 3.5 and ballistics from Chapter 2

Due Thursday Sept 14 (nothing hard, nor time consuming nor tricky here).

1) Given g, launch speed = v0, launch angle =theta and mass = m, find how far a projectile goes when launched from

ground level to a landing on level ground. No friction. Find an analytic solution. Best to do this without quoting any

formulas from any book.

2) Pick numbers, integrate the equations in Matlab and find the distance traveled.

(use z = [x vx y vy] or z = [x y vx vy], your choice, both work.)

3) Find the difference between the numerically calculated range and the analytically calculated range

(do this as well as you can using the Matlab skills available to you and without too much effort).

** Sept 14 Th: **Polar coordinates, a nut slides on a rotating
rod. 3.5 in text. Not on homework yet.

Homework due Tuesday Sept 19 (about ballistics)

0) a) Download matlab samples canonballbig and canonballminimal.

b) Run them in Matlab.

Print them out.

Compare them.

Change this and that in them until you understand how they work, well enough to rewrite them without

looking at them (but ok to use Matlab help).

1) Consider the motion of a .22 caliber bullet launched from level ground. Use mass = 2.5 grams, v0=400 m/s.

This is an approximate formula for the drag on a bullet, its not exact, especially near the speed of sound where

the coefficient changes :

Drag Force = C_d A rho v^2/2

where A = cross sectional area (use diameter = 0.22 inches, sorry about the mixed units)

rho = density of air (use 1 kg/m^3) (NOT per meter squared, as it was mis-typed until Sept 18, 2006 at 2:45 PM)

v = velocity of bullet.

C_d = coefficient of drag = about 0.3 for bullets (use 0.3)

Derive equations of motion (as per lecture and section) and implement in Matlab.

2) Calculate the terminal velocity of a falling .22 bullet (a pencil and paper and calculator thing)

3) From how high do you have to drop a bullet to get to 99% of the terminal velocity? (pencil and paper or computer)

4) What is the range of a 22 bullet, launched at 45 degrees, if you neglect air friction? (pencil and paper or computer)

5) What is the range if you include air friction? (computer)

6) Including air friction, what angle should you shoot to maximize range, and how far does it go? (extensive computer question).

** Sept 19 Tu:** S3.5, mechanics problems with polar coordinates

Homework due Thursday Sept 21

1) 3.81

**Sept 21 Th: **Pendulum using polar coords. Pendulum in Cartesian
coordinates with added-in constraint equations.

HW due Tuesday Sept 26

1) 3.99

2 ) 3.100

3 ) 3.101

4) Consider a point-mass pendulum with mass 1 kg, L=3 m, g=10 m/s^2 and with initial condition of the mass stationary and the string horizontal.

a) What is the period of oscillation (a computer calculation)?

b) What is the period of small oscillation (a pencil and paper and calculator calculation)?

c) Compare a and b above.

d) What is the tension in the string when the mass passes through vertical (do both with pencil and paper and using the numerical integration, compare results)

e) speed at the bottom (do both ways and compare, as for d).

** ***Sept 26 Tu: PRELIM 1, Hollister 110 7:30-9:00+ ***** (includes
material through HW due on the prelim day)

**Sept 26 Tu: **Q&A. S3.6, Work and Energy.

Due Thursday Sept 28

1) a) Use the Cartesian added-in-constraint method of lecture on 9/21

to solve HW problem number (4a) due 9/26. Note that this makes use of the backslash command "\" to solve simultaneous equations inside your right-hand-side ODE function.

Quantitatively compare the results with 4a).

b) Plot x vs y for 1000 or more oscillations. What gives?

** Sept 28 Th: **S3.6-7, Work and Energy

Due Tuesday Oct 3

1) 3.119

2) 3.131

3) 3.146

4) 3.169

5) 3.177

** Oct 3 Tu: **S3.8-9, S3.11-12, Impulse and momentum and collisions

Due Thursday Oct 5

1) 3.187

** Oct 5 Th: **More about collisions, with computer demo.

Due Thursday Oct 12

0) On a separate piece of paper write at the top TAM 203 feedback, Oct 12, 2006

Then write things you like about the course and things you wish were different.

Best if its typed to keep it anonymous.

1) Write: "I wrote up a feedback sheet."

2) 3.208

3) 3.225

4) 3.259

5) 3.271

** Oct 12 Th: **3.10, 3.13, Angular momentum, central force
motion

Due Tuesday Oct 17

1) 3.237

2) 3.246 (Hint, use polar coordinates for position, velocity and acceleration).

3) 3.248

4) 3.301

a) Use conservation of energy and conservatin of angular momentum

b) Solve the equations of motion on the computer using the initial conditions at B.

** Oct 17 Tu: **3.14, 3.15, Relative motion, review

Due Thursday Oct 19

1) 3.333

** Oct 19 Th: **S4.1-5, Systems of particles (general laws of
mechanics)

Due Tuesday Oct 24

1) 3.222

2) Starting from rest a person (mass = m_p) walks from the stern of a boat (mass = m_b) to the bow, a distance L, and stops.

a) assuming no friction, how far does the boat move?

b) Assuming that there is a drag force on the boat proportional to the boat speed (F = c*v_b),

how far has the boat moved when it eventually comes to rest (long long after the person stops walking in the boat)

i) Solve this numerically, and make relevant plots, using this form this function to describe the position

of the person relative to the boat (differentiate twice to get relative acceleration):

x_p/b (t) = 0 for t<0

L* (1 - cos (pi *t /T))/ 2 for 0<t<T (TYPO CORRECTED: 2 CHANGED TO 1)

L for T<t

and using L = 5 m, m_p = m_b = 100 kg, T = 4 s, c = 5 N/(m/s).

Test your code using c=0 to make sure you recover your answer to part (a).

ii) Use c = 5 N/(m/s) and note your suprising answer.

iii) Use pencil and paper to confirm your answer. (This takes careful reasoning and a small amount of calculation).

iv) If c is very small why doesn't the answer to (b) almost agree with the answer of (a)? (This is subtle.)

3) 4.3 (easy)

** ***Oct 24 Tu: PRELIM 3, Hollister 110, 7:30-9:00+ ***** (comprehensive,
includes material through HW due prelim day)

**Oct 24 Tu: **S5.1, 5.2, kinematics of 2D rigid-object rotation,
Q&A

Due Thursday Oct 26

1) 5.1

** Oct 26 Th: **S 5.1-4, 5.6, kinematics of rigid objects (cont'd)

Due Tuesday Oct 31

1) 5.81

2) 5.88

3) 5.91

4) 5.134

** Oct 31 Tu:** Rolling kinematics

Due Thursday Nov 2

1) 5.138

** Nov 2 Th:**

Due Tuesday Nov 7 (clarified Sat afternoon Nov 4 at 4:10 PM)

1) Learn the command "hold on" in Matlab. All on one plot plot these things. The trajectory (a cycloid) of a point P on the edge of a wheel which rolls on level ground. The wheel (a circle) at one typical instant in time. The line segment from the wheel center to P (the intersection of the circle and the cycloid). This drawing is much like the one on the blackboard from lecture on Thursday Nov 2.

2) 5.141

3) 5.205

4) 5.178

5) 5.185

** Nov 7 Tu: **

Due Thurs Nov 9

1) 5.203

** Nov 9 Th:** Its Chapter 6, 2D rigid-object Dynamics, from
Tuesday Nov 7 until the end of the semester (but for in the lab, where there
is a 3D experiment). Your goal is to be able to do every Chapter 6 book problem.

Due Tues Nov 14

1) 6.15 (just like Tuesday's lecture)

2) 6.25 (like the first example in Thursday's lecture)

3) 6.47 (start's like the second example in Thursday's lecture, then some optimization)

4) 6.38 ("Radius of gyration" is defined as r_gyr = sqrt (I/m), where I is the moment of inertia about the COM. For a ring of radius R the radius of gyration is R; for a point mass the radius of gyration is zero. Radius of gyration is a kind of average distance of the mass from the COM (in detail, the square root of the average of the square of the distance.)

5) 6.30 (like 6.15, but more involved)

** Nov 14 Tu:**

Due Thurs Nov 16

1) 6.76

** Nov 16 Th:**

HW due Tuesday Nov 21

This homework was not posted until Friday Nov 17 at 10:50 PM, a day late. If you had planned to work on it Friday Nov 17

you can get an extension. Write on your homework when you hand it in late: "I couldn't do this homework on time because I was going to work on it on

Friday Nov 17 and it had not yet been assigned."

1) 6.79 (Assume no slip and calculate friction force. If too big, assume slip and redo problem.)

2) 6.88

3) 6.94

4) 6.103

5) 6.101

** ***PRELIM 3 CANCELLED.***
Nov 21 Tu: PRELIM 3, Hollister 110, 7:30-9:00+ **(comprehensive,
includes
material through HW due prelim day)

**Nov 21 Tu: **Derivations involving COM, Energy of a rigid object.

Due Tuesday Nov 28

1) Derive text equation 6/9 on page 471. Start with the fact that the total kinetic energy is the sum, over all the bits

of mass, of mv^2/2. Derivation is much like the one's in class today.

2) 6.115

3) 6.125 (Note that wheel massmdrops out.).

** Nov 28 Tu:**

Due Thursday Nov 30

1) 6.168

** Nov 30 Th:**

Due by final exam (no more handed in homework):

1) Be able to do all problems in chapter 6.

2) Study in Thurston 102 to find other students to work with.

**Dec. 12 Tuesday Optional homework exam (see exams page):** By
request only. 12-4 PM

(Note, the date was changed from Dec 4 by popular request at class
on Nov 30.)

** Dec 14 Thu, 2:00 - 4:30 pm: FINAL EXAM** (comprehensive),
Ohlin 165.