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Succeding in Learning Physics

These Guidelines are a product of the effort that I and my colleagues from Wellesley College, Yale University, MIT, and Olin College of Engineering have put together over the years.
Welcome to the Physics component of the cohort course, Physical Foundations in Engineering I! We hope that you find this course to be an engaging introduction to our science as well as a solid basis for your engineering courses. Introductory Physics is designed to initiate you into the ways in which physicists approach and analyze the physical world. The quantitative tools, logical structures, and information presented to you can make this course be demanding for many students, both in terms of time commitment and intellectual effort. We believe that the effort is well worth it! Here are some suggestions for studying the material, preparing for exams, and completing problem sets.

I. How to Study Physics

A primary goal of learning physics is to develop a flexible approach to analyzing novel or previously unfamiliar situations, based on the application of a small number of important concepts and principles. In this context, what will be taught in class, practiced on problem sets, and tested on exams is not the ability to be able to do problems that you've already done but ones that you haven't done. We will try to teach general principles and ways of analyzing and thinking that we'd like you to be able to extend and generalize to new situations. It is important to recognize at the outset of this course that memorizing solutions to a set of problems is not an effective short-term or long-term strategy for mastering the course material.

Students are often advised that a good way to study for exams is by doing lots of problems. A common follow-up complaint is "I did that and then the problems on the exam were different from the homework problems or the ones we did in class." Exactly! There is little point in presenting exam questions that require you to repeat solutions to known problems. Instead, we ask you to strive to learn how to make the leaps, the extensions, and the generalizations to new problems. It's HARD to do this; be patient and don't get discouraged. You will be a winner at the end and your skills will be applicable to any other field of science or engineering.

Read your text early and often. Your physics text needs to be read in a different manner from most other material. You need to be actively engaged as you read. This means, for example, making sure that you understand the logic used in each step as an important equation is derived, or being able to close the book and work through, on your own, a sample problem. Physics texts must be "read" with pencil and paper in hand! It is important to read the text several times (for example, once before the material is covered in class, again before attempting the problems, and a couple of times when studying for the exams).

You are responsible for all the material in the assigned readings, whether or not it is explicitly covered in class. Some important material is also fairly straightforward and we will leave it to you to learn it through reading the text and working homework problems. It is crucial that you keep pace with the assigned reading and problems.

Don't Do It Alone! Whether the physics component of the cohort course ends up being a frustrating experience or an invigorating one depends, in large part, on how you approach it. In order to minimize the frustration and maximize the invigoration, we encourage collaboration among students. This is potentially a very effective way to learn, however, there are some risks involved. It is the student's responsibility to collaborate in ways that facilitate his/her learning. Bouncing ideas and explanations off friends is a powerful way to learn, but it certainly doesn't help to let someone else do all the work and then just copy down the answer. Also, having others do the work is a strategy that will surely come back to haunt you on exams, during gates, in any of your future endeavors. At a minimum, answers to homework problems cannot simply be copied. The solutions you write up must the product of your own thinking after you have "digested" the solution with your peers.

Another very important resource available to you is your istructors' office hours. However, issues similar to the ones discussed above also apply here. We (the instructors) can provide valuable guidance but you must take advantage of this resource wisely. If you try to get us to do the problems for you, you won't learn much. These resources will be most helpful when you have read the relevant material, made honest attempts at the problems, and have formulated specific questions about what you don't understand.

The physics classroom is a crucially important component of this course. The classroom is a time to be active. This means not just listening, but listening with a critical ear; not just taking notes, but deciding what is important to remember and what isn't. And most of all, it means participating in the class. Never hesitate to ask what you may consider to be "simple" or "dumb" questions in class. In our experience, such questions do not exist. And never hesitate to answer questions or to engage the instructor and other students in reasoned argument!

II. How to Approach Homework Problems

It is expected that a typical Olin student who spends approximately 9 hours per week on this course material productively, both in and out of class, should comfortably achieve a grade of B. Homework will be assigned and graded in order to help you utilize your time effectively.

  1. Problems are usually posed in nonscientific prose; as a simple example: "An athlete swims the length of a 50 meter pool in 20 seconds. On average, how fast was she swimming?" Clearly, the question is full of extraneous information - it doesn't matter that it was an athlete or that she was swimming in a pool. Problems like this must be "translated" into the language of physics, and the inconsequential material ignored. A first step might be "An object moves 50 meters in 20 seconds." Now you are ready to apply the relevant physics.


  2. Symbolically represent both the given information and the information to be solved for:
    "d = 50 m, t = 20 s, vavg = ?"
    Simple sketches and diagrams (well labeled!) are very helpful at this stage. Try to work through the subsequent analysis symbolically. Never substitute numbers in until you have solved a problem symbolically. This will become easier and more natural as you gain experience.


  3. As problems become more complicated and interesting than the one above, it is very important to place the problem in context before attempting a solution. In other words, first determine the broad subject to which it pertains (e.g., does the problem refer to conservation of energy or to Newton's laws of motion?). Then, try to progressively narrow down the context - identify the specific issues within the broader context that are addressed by the problem. Almost without fail, the wrong approach to problem solving is to search for a formula in the text that seems to relate to the problem, and then to try to "fit" the problem to the formula. Many formulas in the text refer to very specific circumstances and are not appropriate for more general situations. It is much better to start with the general principle (e.g., conservation of energy) and then work your way toward an appropriate specific formula.


  4. Unless otherwise required, work all problems in metric units. Convert the given numerical information into appropriate units before substituting into equations. Carry the units for each term through the whole calculation as a double check that you haven't messed up the algebra: an answer of "5 km/s" for how far the chicken travels suggests that something is amiss; an answer of "5" tells you a good deal less and is incomplete. Always include units with your numerical answers; always check the units of symbolic answers.

  5. Watch out for the number of significant figures. If you travel 10.2 m (three significant figures) in 2.1 s (two significant figures), your average speed is 4.9 m/s (two significant figures), not 4.8571429 m/s (as your unthinking calculator might imply). When appropriate, express your answers in scientific notation.


  6. CHECK your answers!!! Arriving at an answer does not mark the completion of a problem. There are at least three checks that should be carried out:
    • Check for appropriate units as described in #4.
    • If the answer is numerical, think about its size. Often an error will produce a result that is unrealistically large or small. If you think the problem through so that you can anticipate the size, direction, sign, and so on, most computational errors will be spotted. A tennis ball falling from the roof a one-story building is not going to land on the ground with a speed of 5000 m/s.
    • If your answer is symbolic, check the sensibility of that answer for any special cases where you can predict with certainty the correct result.

III. How to Write Problem Sets

  1. EXPLAIN WHAT YOU ARE DOING, USING BOTH WORDS AND PICTURES. Just writing down a bunch of equations is not sufficient. It is your job to convince the grader, be it your instructor or a third party, and yourself that you know what you are doing.

  2. SHOW YOUR WORK. It's not necessary to include excruciating detail, but if a problem solution is nothing more than an "answer", the graders have no way of evaluating your understanding and nothing for which to give partial credit. Give each problem the best effort that you can. Please turn in a final version of your work, with clear statements explaining what you are doing. If your answer is clearly wrong and you don't know why, simply say so and explain why you think your result is wrong. Please indicate when you are done with a problem, even if you have not obtained an answer. If you do have a final answer, please put a BOX or CIRCLE around it.

  3. IT IS EXTREMELY IMPORTANT TO BE NEAT. It is unlikely that you turn in history or philosophy papers that are scribbled on, illegible, or have "road map" directions saying "For the conclusion of this paragraph, please see the left-hand margin of page 12." The same guidelines for your papers should be applied to physics problem sets. Consider each problem set as a "physics paper". The following suggestions for submitting your problem sets should be used as guidelines.
    • Your handwriting should be legible.
    • Homework with multiple pages should be stapled in the upper left-hand corner.
    • In the upper right-hand corner you should write (in this order).
      • Your Name
      • The Name(s) of Student(s) You Have Been Working With
      • Your Instructor's Name
      • Your Cohort Number
      • The Homework Set Number
      • The Due Date of the Homework
      • Each Page Should Be Numbered and Include Your Name.
    • Problems should be clearly labeled and numbered on the left side of the page.
    • There should also be a visible separation between problems.
    • You should leave the top left margin and the entire left margin blank so that graders may use this space for scoring and comments.
    • To ensure that each problem is graded, problems should be written in the order they are assigned.
    • It is good practice to first work out the solutions to homework problems on scratch paper, and to then neatly write up your solutions. This will help you to turn in a clean finished product.


  4. Your problem set should represent the results of your work - not a documentation of your first attempts at the problems.

  5. If you must use a pen, please use BLUE or BLACK ink.

  6. Please STAPLE pages together before handing them in.

  7. Please leave plenty of space for the graders' comments and suggestions.

  8. Generally, the following guidelines will be used in grading your assignments.
    • A correct understanding of the physics involved in a problem is worth 60-80% of the grade; this includes:
      • correct use of physical reasoning;
      • correct use of equations;
      • correct unit analysis;
      • correct use of diagrams;
      • use of figures.
      For example, incorrect units might result in a deduction of of a point or more per problem depending on the severity of the error.
    • Correct application of mathematics is worth 20-40% of the grade. For example, incorrect solution of an integral might result in a deduction of 1-2 points depending on the severity of the error.


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