Mechanics & Wave Motion Midterm 1

You may bring two sides of paper crammed with as many 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.

We have finished Chapter 4 of Y&F, so I consider you responsible for all the material up to and including Chapter 4.  Since Chapter 5 is a more in depth version of Chapter 4, I'm suggesting some practice problems from the initial section of 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. Uniform circular motion
4. Newton's laws, including such topics as
   
   1. free body diagrams
   2. Newton's 3rd law
   3. ideal (massless, stretchless) ropes, the normal force and inclined planes.
   4. simple static equilibrium problems

If I ask about friction, it will not require coefficients of friction.  If I use a pulley, it will be a simple (fixed) pulley problem.

Note that in past years the first midterm has included more topics; as you look at past exams, ignore questions that are beyond this year's scope.

Particular problems I have observed in the past:

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 (or when it is moving with constant velocity), its acceleration is zero.  But an object undergoing circular motion, or being pushed on by an outside force, does not have 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).