Some material on this page is written up as the class develops, often in hand (and then scanned). Please let me know if there is a problem with legibility, or clarity of explanation. Most important: Please note that these are meant to be only starting or additional resources, for your work: you will actually understand (and know) only what you learn through your own work and practice.
Information about past midterm has been moved down the page.
Homework #1: Ch2: 9,12,47,51,53. Due by Tue 06.29, in class.
(brief solutions)
Homework #2: Ch2: 50,77; Ch3: 27; Ch4: 12,13,42,44.
Due Wed 07.07, by 1pm.
Homework #3: Ch4: 45, 50, 52, 80, 81.
Due Wed 07.14, by 1pm.
(brief solutions)
Homework #4: Ch6: 1,3, 7, 21, 41, 47.
Due Wed 07.21, by 1pm.
Homework #5: Ch6: 42, 48, 52; Ch7: 23, 29, 31, 33.
Due Wed 07.28, by 1pm.
(solutions)
Homework #6: Ch7: 34, 35, 38, 39, 42.
Due Wed 08.04, by 1pm.
(solutions)
Homework #7: Ch9: 38, 42; Ch10: 34, 55, 70; Ch11: 44, 53, 56.
(short solutions)
Due Thu 08.12, last day of class, by 1pm.
Practice These are homework sets from previous terms.
There are solutions, and the typed-up ones are written up very carefully, and
are good reviews of the material too. But please note the following:
it is imperative that you
first do these problems on your own. I cannot emphasize this strongly
enough. Only once you have solved them, is it OK to look at solutions.
Otherwise, you'd be missing the most important part – your work.
( Summer 09 )
Ch2: 10, 13, 18, 45.
(HW1 solutions.)
Ch3: 44. Ch4: 46, 47, 49.
(HW2 solutions.)
Ch2: 64. Ch4: 80. Ch6: 6, 35, 37.
(HW3 solutions.)
Ch6: 44, 46, 52; Ch7: 29, 41.
(HW4 solutions.)
Problems, and
solutions.
Ch10: 17, 49; Ch11: 50, 55, 57, 73.
(HW6 solutions.)
Ch10: 42, 43, 51, 52, 71; Ch11: 74.
(HW7 solutions.)
( Spring 10 )
hw1 – Ch2: 1,4,13,14.
(hw1 solutions)
hw2 – Ch2: 49,64; Ch3: 28; Ch4: 12.
(hw2 solutions)
hw3 – Ch2: 48,66,71; Ch4: 51,53,80.
(hw3 solutions)
Also, “short hw1” – Ch4: 11,50,52.
(shw1 solutions)
hw4 – Ch2: 77; Ch4:45,81; Ch6: 31,37,38.
(hw4 solutions)
hw5 – Ch6: 42,43,45,51.
(hw5 solutions)
“short hw3” – Ch6: 40,52.
(shw3 solutions)
hw6 – Ch6: 47,48; Ch7: 19,28,30,39.
(hw6 and shw4 solutions)
“short hw4” – Ch6: 50; Ch7: 24.
hw7: problems.
hw8 – Ch9: 38, 47. Ch10: 49, 53. Ch11: 41, 43, 48
“short hw6” – Ch10: 10, 34.
hw9 – Ch10: 24,(35),39,(51),55,(72). Ch11: 29,(45),51,(55),74.
Ch9: 53.
“short hw7” – Ch10: 12, 16.
Parenthesized problems were optional (but you should disregard this comment).
Class 1 (slides), Mon 06.21.
Sketchy notes of the introduction to this class.
(A typo corrected.)
Class 2 (slides), Tue 06.22.
Notes of the derivation of the kinematics equations, with a
(barely stated) example.
Class 3 (slides), Wed 06.23.
Previous example; motivation and derivation of the
“third equation” of kinematics.
Examples for our classes 4 and 5 are in
these notes.
(Numeric answers are given below.)
Class 6: a free fall example,
related notes.
Class 7: two dimensions, coordinates, vectors; kinematics.
Related notes.
Class 8: kinematics in 2D, horizontal projectile.
Notes (in these notes
there is a bit more on vectors, trig etc).
Fourth of July observed, no class on 07.05.
Class 9: kinematics in 2D, horizontal shot summary, and more general projectile.
Notes.
Class 10: kinematics in 2D, general projectile.
Notes.
Class 11: some more kinematics; first look at Newton's Laws.
(See next class notes.)
Class 12: Newton's Laws, an introduction.
Notes.
Class 13: Newton's Laws and model of forces: gravity; normal force.
Notes.
Class 14: Normal force; friction. First complete examples.
Notes.
Class 15 Notes:
Friction, examples.
(Related notes from spring:
notes_c15,
notes_c16.)
Class 16: review for the midterm.
Class 17: discussion on tests, some more friction.
Class 18: more on friction.
Related notes.
(Also use the above notes on friction.)
Class 19: Introduction to working with multiple objects: a complete example.
Class 20: Multiple objects, the next complete example.
Notes from Spring dealing with multiple objects:
notes_c18,
notes_c19,
notes_c21.
Class 21: Multiple objects, various examples. (Use the above notes.)
For the remaining classes, particularly on energy and work, go to
Notes from Spring 2010 (scroll down the page a little).
(Two slides per page: c1, c2, c3. These files are from Spring 2010, but are almost identical.)
HW #3. Problem Ch4.81. You set up kinematics equations, and apply them to the point where the arrow hits the ground. So you get two equations, for the coordinates of that point (xf, yf). As it is common, you don't know the time (to hit the ground) in these equations – but now you also don't know either of the horizontal or vertical coordinate of that point! Still, you can use the given angle and trigonometry to relate the two, and this will allow you to solve the system of equations (eliminate the time and find the needed distance). Also note: one of the (reasonable) coordinate systems that you could use requires more work than others: think about where to put your coordinate system!
HW #2. Problem Ch2.77. The bolt is a part of the rocket, and it reaches a certain height, and builds up speed, with the rocket, until it separates. After that, it is a free fall for the bolt, with (some) initial speed upward, from (some) initial height. The little problem is that you only have symbolic expressions for this initial height and speed. (But, they contain the needed acceleration, and this allows you to eventually solve for it.) Another thing: don't forget that in the first part, while the bolt is on the rocket, the gravity acts too.
Class 4, Thu 06.24.
This is a statement of the examples offered in class (with numeric answers).
In the previous class, we used the example of a car that starts braking, in
order to start getting accustomed to kinematics equations. In this class we
use this same setup (of a car braking) to construct a few specific problems.
Most of these are solved symbolically in the notes linked above. Think about
your results: do they make sense? How can you tell, and how reliable are these
assessments? Make sure to compare the results between similar questions.
(1)
First, the question that was discussed in our introductory invocation of this
example: what is the stopping distance? Here is the precise question. A car
is cruising at 10 m/s, when the driver
decides to brake. But by the time the brake is actually applied, the car
has travelled over the distance of 10 m.
(This is a way to account for the ‘reaction,’ the fact that the
car doesn't start slowing down right as we decide to brake. Often the
“reaction time” is given though.) Once the braking starts,
the car is slowing down at the (constant) rate of
1 m/s2.
What is the stopping distance (from where the decision was made)?
[Numeric answer: 60 m.]
(2)
Look again at a car cruising, but now at
60 mph. Let us now ask this question: what
minimal (constant) acceleration is needed in order to half this speed within
a distance of 50 m (from where the braking
starts) ?
[Numeric answer. It needs to brake with at least:
5.39 m/s2.]
(3)
Now look at the time involved when braking. We'll start with an example when
the acceleration is given. A car driving at
60 mph starts slowing down at the rate of
5 m/s2. What time does it take
to cross 50 m, from when it starts braking?
[Numeric answer: 2.40 s.]
This was the example misstated in class (and somewhat corrected).
I posed it with the condition that the speed gets reduced to a half in
the process. (I mixed two examples that I had in mind. Sorry.) For one thing,
it doesn't: from 60mph, when braking with 5m/s2, in 50m the speed
does not drop to exactly a half. Compute what the speed is actually
[14.8 m/s = 33.1 mph].
(Also, in the previous example you calculated what acceleration is actually
needed to reduce the speed in half.)
(4)
This was meant to be the next problem. A car slows down, reducing its initial
60 mph to a half, in
50 m. What time did it take? Again, dismiss
issues of reaction, consider the distance and time to be measured from when the
braking starts. [Hint. Find the acceleration as in
one of the previous problems. Then there are two ways to find the time –
using either of kinematics equations. One of them is way easier.
Numeric answer: 2.49 s.]
(*)
Do some of the previous problems including the reaction time (of say
0.5 s).
A comment: note how much we built out of a single example! Take a car that starts braking, and you can construct a number of little problems out of that! (And some aren't so little or easy.) This is one of the most effective ways to study and practice: once you have some idea of a certain example/setup/concept, then play with it – come up on your own with all kinds of questions (or problems) that can be posed. I cannot overstate just how useful this is, in many ways. (Of course, in order for this to make sense, you do need to have some understanding first, or you may end up spending a lot of time trying to solve really hard or ill-posed problems.)
Reference mi/hr → m/s conversion: 1 mph = 0.447 m/s (or: 1 m/s = 2.237 mph). Midterm formula sheet.
Systems of equations Here is a note on solving systems of equations; a few hand-written pages, scanned in a pdf file. (The problem numbers mentioned refer to a different book, but this is not critical, everything that matters for following the examples is stated.) This is elementary, except that: it explains how to manipulate whole equations: add or divide them, to achieve elimination of variables more directly.
Main practice and study resources will be/are: class material contains a lot of ideas and setups to work with; homework, and “Practice Homework” (from previous terms, linked below) cover a lot of ground – beside simply somehow solving those specific problems; and ‘suggested problems’ (on Classes page) contain yet more. I think that this is plenty, if not let me know. Also: please your book, of course. It is our main text, and it has a lot of useful material.
Spring 2010 (past term): web pages.
The coming midterm covers kinematics and Newton's Laws, with some friction.
It is strictly on the material that has been actually covered. (The best
guide for practice is: what has been done in class/notes, for homework, and
assigned for practice.) The exam will consist of 3 or 4 problems to solve,
each with multiple parts.
(There are no multiple choice questions.) Some of these will involve brief
explanations, but the emphasis is fully on being able to work out solutions
to specific questions. This
formula sheet will
be supplied. Now here is a little more specific statement on what is up for
the test.
Kinematics is clear: one and two dimensions, along the lines of what we talked
about in the class, and what has been done for homework and/or suggested for
practice. In short, pretty much all of kinematics. (Note that some of the
homework problems were meant to be challenging, and I consider them
inappropriate for this exam. This refers only to a very few of the homework
problems, as explained in class.)
A little more of an explanation is probably in order regarding Newton's Laws
(beyond “what we covered”). Use of Newton's Laws in one and two
dimensions without friction is all up for the exam (as covered). When it
comes to friction, even though it is ‘just’ another force, there
are issues and subtleties, and we have not yet dealt with them. So you only
need to be able to work with friction in a basic sense, within confines of a
few examples covered in class. In problems with friction there may be other
forces as well. You will not need to deal with static friction at all. Also,
there will be no need to work with friction in a motion on an inclined plane.
(Even as this is ‘only’ a specific setup, it comes with some very
specific (little) challenges, and since we didn't do even a single such example,
it is not up for this test.) In short: Newton's Laws without friction, and only
a basic use of friction. The next homework (due next Wednesday), to be posted
shortly, will summarize this.