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PH 1111, Principles of Physics - Mechanics

An introductory course in Newtonian mechanics that stresses invariance principles and the associated conservation laws. Topics include: kinematics of motion, vectors and their application to physical problems, dynamics of particles and rigid bodies, energy and momentum conservation, rotational motion. Mathematical level: concurrent study of MA 1023 (or higher) is assumed. Students with limited prior college-level calculus preparations are advised to take PH 1110.

The text is "Newtonian Mechanics" by A.P. French (W.W. Norton Co.), available in the bookstore. We meet in OH 223 at 15:00 on MTRF. Your labs are in OH 208 on Tuesdays and Thursdays at 16:00. Instructor: Professor NA Burnham, nab@wpi.edu, www.wpi.edu/~nab.

Course objectives

Final grade determination

Your final grade will be determined in the following way:

%
 Course component
10%
 The ten labs (required, penalty for late submission)
18%
 The eighteen homework assignments, no late work accepted
  6%
 The six groupwork assignments, credit only for attendance, penalty for late submission, no make-ups
  6%
 The group quiz, credit only for attendance, no make-ups
60%
 The three exams, 10% penalty for make-ups

For your final grade in the course, nominally A > 80%, B > 70%, and C > 60%. The borders between letter grades could lower, depending on the difficulty of the exams. After the second exam, I'll give you an indication of how you are doing. Because I do not curve, there is no harm in helping each other...if you all earn As, you will all get an A. Similarly, if you all earn fewer than half of the points in the course, you will all receive NRs.

Labs

Labs 1-10 are required in order to pass the course. Please read about them, in particular how to prepare your lab reports, here. Any questions about labs should be directed to the Lab Manager, who is Frederick L Hutson, flh@wpi.edu. If you have any extenuating circumstances, Mr Hutson prefers that you visit him in person, OH 217. 

Homework and reading summaries

There are eighteen homework sets; each problem or reading summary is worth five points. About half of the points are for your problem-solving methodology and clarity. See below for the assignments. Homework will not be accepted late, although I recommend that you do all problems even if you can't turn them in on time. If you can not or choose not to attend class, I expect to see your work in my mailbox (near the Physics Department office) at 14:50 the day that it is due. Solutions will appear at myWPI shortly after the due date.

Most homework assignments will include summaries of a few sections of our textbook. Below is an example of a summary of an intermediate mechanics book by Taylor. Note that there are neither equations nor symbols. It is not long; however, all important points are included. Reading summaries should be 300-600 words long, with a word count stated at the end. Reading summaries help prepare you for doing your homework.
Mechanics is the study of motion. Its history dates from Galileo and Newton and was developed further by Lagrange and Hamilton. About a hundred years ago, scientists started to develop relativistic mechanics and quantum mechanics, and to distinguish among them, the traditional form of mechanics has become known as "Classical Mechanics".

Newton's famed three laws of motion are based upon ideas that concern space, time, mass, and force. Space can be described by coordinate systems, the simplest one being the cartesian coordinate system, which has three orthogonal axes. The position of an object can be determined by a position vector, and the next few pages of the text reviews vector algebra. After further reminders of time, reference frames, mass, and force, Newton's laws are introduced.

The First Law says that a particle moves with a constant velocity unless acted upon by an external force. The Second Law states the relationship between mass, a scalar, and acceleration, a vector. Their product equals the vector sum of all the forces acting on a particle. Since acceleration is the second derivative of position with respect to time, the Second Law is a differential equation. Newton's Laws hold in what are called inertial reference frames. They do not always hold for relativistic or quantum systems. Nonetheless, they are valid over a wide range of scales in size and speed and are thus worthy of study.

The Third Law states the relationship between "action" forces and "reaction" forces. They are equal in magnitude and opposite in direction, but act on two different bodies. From the Third Law, which considers only one particle, one can construct a theory for many particles. Internal forces in a multiparticle system have no influence on the total momentum. In other words, if the external forces are constant, then momentum is conserved. Taylor gives an example where, apparently, the Third Law is violated, but then explains that mechanical momentum is not the only form of momentum. It can, for example, be electromagnetic. However, Taylor assures us that for the rest of his text, we will consider situations only in which the Third Law holds.

353 words

Groupwork

Groupwork will be done in groups of three or four. The principal purposes of groupwork are to promote communication about physics and to enhance learning. (Educational research has shown improvement in performance when students work in groups.)  Each group member will have an assigned role, which rotates from day to day. Each group turns in one set of work, and all members of the group who attended that day receive the same grade. You must attend class to receive credit for groupwork.

The groupwork is also meant for you to meet people in the class and to prepare you to work in teams. You will be part of a team at many times during your life. At WPI, many IQPs and MQPs are done in teams, and in your later life, you will likely find yourself in a team at work. Most corporations look for previous team experience while hiring. We will pay attention to group dynamics during class, and you will be able to transfer your team experience to your academic and professional future.

The styles of problem that you will see as a group will range from conceptual questions, to symbolic and quantitative ones (like the homework), to "context-rich" problems. These last are problems that you might see in a real situation, not a situation from the textbook, and they demand more emphasis on the physics of a problem, i.e. the setup, rather than number crunching. Typically these problems are too hard for individuals to solve independently.

Exams

There are three two-hour cumulative exams. The exams are closed book, closed notes, but you may bring a one-page formula sheet. No calculators or other electronic devices may be used. During an exam, you may ask questions that clarify the problem statement, but you may not ask questions regarding approaches to the solutions.

Help

There is often a physics graduate student in the physics library, OH 118, who is paid to help you. He or she sits near the sign labeled "Physics Help". There should be a schedule posted on the library door and online. You are encouraged to collaborate on the homework problems; you can communicate with your classmates through the Communication link at myWPI. Collaboration is expected for the groupwork. I have office hours four hours a week;  please come see me if you need help. You may also visit the course Teaching Assistant, Mr Raj Basu, basu@wpi.edu, OH 004, (508) 831-5282.

Communication

My office is OH 219. I am sometimes in my lab, OH 009, or in the department office, OH 119. My mailbox is between the doors of OH 118 and 119. I answer my email about once a day. I'm typically available to chat for a few minutes after class. Email nab@wpi.edu, web www.wpi.edu/~nab, office phone with voice mail (508) 831-5365; fax (508) 831-5886; my schedule, with office hours, is posted here. The web address for this page is www.wpi.edu/~nab/PH1111.html.

Syllabus

The syllabus and assignments are embodied by this calendar. Bold-faced items indicate deadlines. The five underlines show the "double days", when more than one thing is due. The three different colors reflect the three different units of the course: motion and forces, momentum and energy, and rotation and gravitation.
 
Week of Monday Tuesday Wednesday Thursday Friday
6. January 2007 Activities
What's due		  
1. Introduction, Vectors, Lab1
--
 2. 1D Kinematics, Diagnostic Test
HW1
13. Januar 3. 2D Kinematics
HW2 (postponed one day due to snow) 		4. Equilibrium, Lab2
Lab1 		--
HW3 (postponed one day due to snow)
 5. 1D Dynamics, Lab3
Lab2
 GW1
HW4
20. January 6. 2D Dynamics
HW5
7. Examples, Lab4
Lab3, GW1 		--
HW6
 GW2
Lab4, HW7
 EXAM 1 on lectures 1-7
--
21. January 8. Momentum and impulse
--
 9. Particle streams, Lab5
GW2
 --
HW8
 10. Work-energy, Lab6
Lab5
 GW3
HW9
3. February 11. Energy
HW10
12. Examples, Lab7
Lab6, GW3 		--
HW11
 GW4
Lab7, HW12
 EXAM 2 on lectures 1-12
--
10. February 13. Angular momentum
--
 14. Moment of inertia, Lab8
GW4
 --
HW13
 Advising Day
Lab8
 		GW5
HW14
17. February 15. Rotational dynamics
--
 16. F and M, Lab9
GW5
 --
HW15
 17. The solar system, Lab10
Lab9
 GW6
HW16
24. February 18. The universe
HW17
 GROUP QUIZ on lectures 1-16
Lab10, GW6  		--
HW18
 EXAM 3 on lectures 1-18
--
  

Homework assignments:

Topic Assignment number Summarize
 Solve problems
Motion and forces HW1 pp. 48-59
 2.1, 2.6, 2.7

HW2 pp. 66-72, 85-95
 2.10, 3.4, 3.6

HW3 pp. 95-108
 3.9, 3.10, 3.17

HW4 pp. 115-132
 4.2, 4.6, 4.10

HW5 pp. 187-194, 198-202
 7.3, 7.4, 7.7

HW6 pp. 161-173
 7.14, 7.19, 7.21

HW7 --
 2.8, 3.1, 4.13, 6.10
Momentum and energy
 HW8
 pp. 307-320
 9.1, 9.4, 9.5

HW9
 pp. 321-335
 9.10, 9.11, 9.14

HW10
 pp. 367-381
 10.1, 10.4, 10.6

HW11
 pp. 381-392
 10.15, 10.16, 10.21

HW12
 --
 9.13, 9.16, 10.7, 10.25
Rotation and gravitation HW13
 pp. 627-642
 14.3, 14.4, 14.6a,b

HW14
 pp. 643-654
 14.8, 14.9, 14.12

HW15
 pp. 226-231, 393-395, 659-663
 14.17, 14.18, 14.20

HW16
 pp. 654-659, 664-671
 14.15a-c, 14.16, 14.28

HW17
 pp. 252-256, 286-300
 8.16, 8.17, 8.19

HW18
 --
 14.5, 14.14, 14.19, 8.15

Homework and groupwork grading

I will give my homework grader the following guidance. Exam and group problems will be graded in a similiar fashion by me. You'll notice a big emphasis on effective communication. This is another aspect of your education that corporations examine during the hiring process. As often as practical, you should find a dimensionally correct symbolic solution first, before substituting in numbers, even if the problem does not specifically ask for a symbolic solution.
 
Points For each problem (out of five possible points):
-5 No symbolic solutions
-5
 Symbolic solution has wrong dimensions
-1 to -5  Write-up hard to read or understand
-1
 No commentary
-1 Vectors confused with scalars or vice versa
-1
 Missing or incorrect units on numerical answers
-1 No boxes around symbolic and numerical answers
  In general, for any given problem:
 5 =  Very good -- write-up clear and correct
 4 = Good -- write-up clear and mostly correct, or understandable and correct
 3 = Acceptable -- write-up understandable and mostly correct, or poor write-up and correct, or clear write-up and incorrect

For the summaries (out of five possible points):
-5
 Equations in summary
-5
Handwritten
-1 to -5
 Symbols in summary
-1 to -5 Not enough detail
-1
 Shorter or longer than specified length, in increments of 50 words
-1
 No word count
  And for an entire assignment:
-5 Electronic submission
-1 No name
-1 Ragged edges
-1 No staple

Laboratories:

 Lab #
Topic
1 Treatment of Experimental Data, with a string and nuts.
2 One-Dimensional Kinematics, with a cart and a track.
3  Static Equilibrium, with a ring, a stick, and a force table.
4 One-Dimensional Dynamics, with a cart and a track.
5 Impulse, with sand bags, balls, and a force plate.
6 Work-Energy Theorem, with a cart and a track.
7
 Conservation of Energy, with a spring and a mass.
8  Angular Momentum, with a pulley and masses.
9
 Dynamics of Rotation, with a rigid pendulum.
10
 Combined Rotation and Translation, with cylinders and a track.

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January 2008