Introductory Physics I: Mechanics and Wave Motion Midterm I

Particular problems I observed in the first exam:

1. When I say "use units" I do not simply mean "append a unit to anything you've calculated or I'll take some points off".  Units are actually very useful – especially if you do your calculations with variables instead of with numbers.  A quick check of the units in your final formula will reveal most algebra errors.  You can then go back and check units at intermediate steps: a dropped factor of m, for instance, will show up as a missing unit of kg in all the intermediate steps from the point of the error onward. 
2. Force are vectors.  You cannot add the x component of one vector to the y component of another; in fact, (unless you're doing graphical vector addition) to add vectors you always need to find components and then add together x components and y components separately.
3. Newton's 2nd law (F_net = m a) has two sides.  Some people did a good job with the LHS (adding the force vectors) but didn't think hard enough about the RHS.  Typically, this involved incorrectly assuming that some acceleration was zero.  When an object is not moving, its acceleration is zero.  But an object undergoing circular motion, or being pushed on by an outside force, does not have a zero acceleration; there is often one particular component of its acceleration that is zero, but you must identify that component carefully.  If you set up your axes wrong, you will assign zero acceleration to a direction that is not, in fact, zero.
4. There are only 26 letters in the English alphabet.  Even throwing in Greek (and occasionally Hebrew), we do not have enough letters to give a unique letter to every object in physics.  Distinct and totally different concepts often end up with the same letter.  For instance, both tension in a rope and the period of revolution are labeled T.  You need to have in mind the meaning of every variable that you use so that you don't conflate the period T with the tension T.  If both appear in the same problem, the safest thing to do is relabel one of them (for instance, call the tension F instead of T).

Final tally of points on Midterm 1.  Broken out by question:

Question 1: 19 ± 6 points

Question 2: 17 ± 8 points

Question 3: 17 ± 6 points

Question 4: 12 ± 5 points

Exam total: 64 ± 16 points

You may bring two sides of paper crammed with as many handwritten notes as you can fit.  You must prepare these notes yourself, however, as part of the process of reviewing for the exam.  This means that I will not provide equations on the exam itself.

Bring a calculator.

My plan is for next week's lab sections to be converted into a short lesson on error propagation (mandatory - probably less than an hour long) followed by an optional free-form review for the exam.

We are about halfway through Chapter 5 of Y&F, so I consider you responsible for all the material through Chapter 4 and a few of the topics in Chapter 5.  Roughly speaking, I consider the following fair game:

1. Vectors
2. Uniform acceleration problems (free-fall or projectile or 'catch the bus' type)
3. Newton's laws, including all of chapter 4, such as
   
   1. free body diagrams
   2. Newton's 3rd law pairs
   3. friction and normal force questions, though not coefficient of friction questions (Chapter 5)
4. Some topics from Chapter 5, such as
   1. massless ropes, frictionless pulleys, frictionless planes, inclined planes
   2. simple static equilibrium problems
   3. uniform circular motion

This is a lot of problems.  I do not expect you to complete every one of these.  I do suggest that you attempt each one.  If you are confident you can do a problem, skip it.  Otherwise, rough out a solution by writing down a system of equations and thinking through how you would solve them.  Check against the posted solution to see if your thinking is correct, but you probably don't need to do all the algebra  unless your approach is different from the solution's and you're unsure whether they concur.

I will be available during office hours next week and during the review session (on your normal lab day) and may also have a Wednesday evening review session.

Questions	Answers
From Y&F (12th edition).  Classification is approximate, since there is lots of overlap between categories. Vectors: 1.68 Free fall: 2.66, 2.76, 2.97 (hard) Projectile motion: 3.54, 3.82, 3.86 (hard) Free body diagram: 4.37 Newton's 3rd law: 4.52, 5.4, 5.14 Compute a: 4.45, 4.49, 4.54 (hard), 4.57, 5.71 Circular motion: 5.55, 5.59, 5.114

Preface

1. I try to write difficult exams.  This is not because I want to discourage you, but because I need to see how much of the material the class understands.  Most of my questions have several parts, with the parts getting progressively trickier.   I expect that most of you will be able to answer some parts of all the questions, but that few will be able to answer all of all of the questions.  My grading will take this into account.
2. The questions in the practice exam are all rejects from the actual exam: they were either too hard or too easy, involved too much algebra, or were too similar to another question I liked more.  Please take this under advisement when deciding whether to panic.
3. The version of the practice exam solutions posted on 10/6 had calculator errors in the answers to 3 and 4b. 
   
   1. The correction has notes superimposed on the page: make sure you have the up-to-date version AND that the notes print out.
   2. I calculated an angle and a square root incorrectly the first time, but because I solved the problem algebraically and only plugged in numbers at the very end, I only had to correct a couple of places.  This is one of the big advantages of working in variables until the last moment.

QuestionsAnswers