**Homework and Solutions
**

**Homework 1, due Tuesday February 1:**

For your own education, check that you can do a few problems from each section
in chapters 1-4.

Please follow the directions in the Syllabus and Course information sheets.

Hand in: 4.177,

4.180 (misprint: change m to g in parts (b) & (c),

you need not use the coordinate system shown in the figure,

think
of parts (d) and (e) as challenges.),

4.188

"Solutions" 1:Solution1 for printing, 4 pgs. Solution1 for screen viewing, 12 pgs. (400k .pdf files)

(In the first figure of the "solution" of problem 4.188 point J at the center of mass is mislabeled as H.)

Homework 2, due Tuesday February 8:

Check that you can do a few problems from each section.

Please follow the directions in the Syllabus and Course information sheets.

Hand in:

5.18 (If you don't want to know the height
as a function of time, you can treat this as a first order system.
Your choice. In either case you need to make a plot of v vs t of your computer
solution.)

31, 34, 37, 38

"Solutions" 2:Solution2 for printing, 2 pgs. Solution2 for screen viewing, 6 pgs. (260k .pdf files)

**Homework 3, due Tuesday February15: **

5.41 (straightforward),

5.52 (requires time and thought),

5.57 (easy and quick),

5.103 (straightforward),

5.109 (easy),

5.113 (Requires time and thought (advised) unless you thoughtlessly copy from
WWW (not advised). A time interval of 10 seconds makes a decent plot. One check
of your solution is to compare the steady state falling speed to the falling
speed at the end of the simulation. (Minor typo: g= 10 m/s^2 not 10 m/s.)

** "Solutions"3:**
Solution3 for
printing, 2 pgs. Solution3
for screen viewing, 6 pgs. (240k
.pdf files)

**Homework 4, due Tuesday February 22:
**None of these problems is difficult (like, say, the last part of the trampoline
question)

5.120 (takes some time and thought),

5.111 (takes some time, thought and coding. Although in last week's section, its in this week's homework.),

5.124 (takes some time, thought and coding).

** "Solutions"4:**
Solution4 for
printing, 2 pgs. Solution4
for screen viewing, 6 pgs. (200k
pdf)

**Homework 5, due Tuesday February 29:
**Solutions will be on the WWW by Monday 6PM. If you use the WWW solutions
in what you hand in you must cite them thoroughly and completely for every use
made in every problem used.

6.13b [Typo: should refer to 6.14 not 6.31] (easy, you should also make sure you can do a,c,d),

6.14b [Typo: should refer to 6.13 not 6.30] (easy, you should also make sure you can do a,c,d),

6.18b,c (basically straightforward),

6.27a (requires some care, but not time consuming or difficult),

6.51 (takes time and thought, not very hard, but not trivial.)

Fully credit these for every use you make of them in the homework you hand in.The solutions below have a mistake in problem 6.18b. There is a sign error in the first momentum balance equation. The final answers can be made correct by replacing the "-" in the denominator with a "+". The book answer key solution is also wrong, but more deeply so.

Solution5 for printing, 3pgs. Solution5 for screen viewing, 9 pgs. (360k pdf)

"Solutions"5:

***************

**Prelim 1, Feb 29, 2000, (unsolved), Prelim
1 solutions ** (2nd draft fixes Matlab error) (250k
pdf),

**Prelim 1 and 2 grade statistics**** **(All
the raw data too, calculate anything you want. Improved 4/10/00.)

Please come talk to us if you have questions about grading. We do make mistakes
and hopefully are big enough to admit them. Please look over the solutions
and
comments on grading before coming to talk to us.

********************

**Homework 6, due Tuesday March 7:
**The textbook WWW page has "answers" to the *'d problems.

6.74 (Takes some thought, but of a type you should be good at by now.)

7.16 (pretty easy to set up)

7.29 (easy),

7.43 (requires some time and thought for a beginner, easy afterwards),

7.44 (straightforward, a slightly suprising place to find exponential decay).

"Solutions"6:Solution6 for printing, 2pgs. Solution6 for screen viewing, 6 pgs. (260k pdf)

**
Homework 7, due Tuesday March 14 at the start of class:
**7.57 (pretty easy),

7.66 [typos: equal signs needed after r_B, lambda_A, and lambda_B.

part (c) should refer to r_C not lambda_C.]

(not wildly difficult, but will take some thought and time),

7.92 (basic, you have to know this, takes some thought the first time),

7.93 (quick, short, and easy),

7.98 (takes some time and thought to come up with a control function)

"Solutions"7:Solution7 for printing, 3 pgs. Solution7 for screen viewing, 7 pgs. (240k pdf)

**
Homework 8, due Tuesday March 28 at the start of class:
**7.106 (easy)

7.121 (easy )

7.128 (Takes some time. Not to hard. Can use calculator for plots if Matlab not available.)

7.148 (No tricks or special problems. Takes some time but nothing deep or too involved.)

8.17, was 8.167 (easy)

(The problem numbers in chapter 8 changed on April 6 with the rehanding out of chapter 8 problems.)

"Solutions"8:Solution8 for printing, 3 pgs. Solution8 for screen viewing, 8 pgs. (480k pdf)

****************

**Prelim 2, March 28, 2000, (unsolved), Prelim
2 solutions ** (350k pdf), ** Comments
on grading** (130k pdf).

**Prelim 1 and 2 grade statistics**** **(All
the raw data too, calculate anything you want. Improved 4/10/00.)

Please talk to us if you have questions about grading. But please look over
the solutions and comments on grading first.

********************

**
Homework 9, due Tuesday April 4 at the start of class:
**Note: on April 6 the chapter 8 problems were renumbered. The first numbers
below are the new numbers.

8.43 was 8.44 (not trivial, not long and difficult)

8.25 was 8.26 (a serious problem)

8.48 was 8.49 (not especially difficult)

5) A uniform curved rod with mass of 3 kg is along the curve x = sin(t), y = e^ t, z = t^2 for 0< t < 2, where the numerical values in the formulas are the distances in meters. What is the moment of inertia matrix for this rod. Assume the rod is one dimensional (has no width). You will probably want to use numerical integration. (Challenge.)

"Solutions"9:Solution9 for printing, 3 pgs. Solution9 for screen viewing, 8 pgs. (370k pdf)

**Homework 10, due Thursday April 13 at the start of class:
**8.53 (somewhat tedius, but easy if you know what you are doing)

8.55 (easy)

8.63 (not hard but not trivial to calculate, neglect gravity, think of an air motor or something for inspiration)

8.81a (not very hard, but not trivial)

8.92 (requires thought and understanding, easy and quick if you get the ideas)

"Solutions"10:Solution10 for printing, 2 pgs. Solution10 for screen viewing, 5 pgs. (190k pdf)

**Homework 11, due Tuesday April 18 at the start of class:
**9.6 (easy warmup, straight from section)

9.5 (same ideas as above, the trick is to think about the velocity of the point on the ladder that touches the step. What do you know about its velocity?)

9.7 (Not hard, but it should make you think about what rolling is all about. It will take some time.)

9.22 (not hard, but you have to know your basics)

9.28 (not hard)

"Solutions"11:Solution11 for printing, 3 pgs. Solution11 for screen viewing, 7 pgs. (270k pdf)

**Homework 12, due Tuesday April 25 at the start of class: **

9.25** **(just like lecture)**
**9.37 (not too hard, kind of a fun answer. Note, for part c, that the ring
slides before it ends up rolling.)

9.47 (again not hard, but for the end, something you should use to add to your permanent intuition)

9.58 (just like section)

9.59 (an easier problem than above)

9.61 (more of a challenge, but nothing especially tricky in setting this up. The expression for v_hit involves the solution of a quadratic that is a big mess unless you pick numerical values for the various quantities. It would be very hard to do this problem without computer explorations of one kind or another.)

"Solutions"12:Solution12 for printing, 4 pgs. Solution12 for screen viewing, 12 pgs. (470k pdf)In problem 9.61 the free body diagrams of the bat are wrong. They should show the reaction forces that keep the bat rotating about the hands. The only mechanics equations used for the bat were angular momentum about the hands, so this error does not propagate. (details)

****************

**Prelim
3 solutions ** (516k pdf)

** Comments
on grading** (136k pdf).

**Prelim 1, 2, and 3 grade statistics**** **(All
the raw data too, calculate anything you want. Improved 5/3/00.)

Please talk to us if you have questions about grading. But please look over
the solutions and comments on grading first (will be posted soon).

********************

**Homework 13, due Tuesday May 2 at the start of class: **

9.73** **(like section but disk also translates)**
**9.74 (sort of complicated but not too hard)

9.106 (like lecture but the launcher is bent)

9.113 (like lecture but with a spring attached to the mass)

9.119 (not hard)

"Solutions"13:Solution13 for printing, 2 pgs. Solution13 for screen viewing, 5 pgs. (204k pdf)

**Homework 14, not collected:**

9.122 (not hard - sticks are massless)

9.127 (like lecture and section but the geometry is a bit more complicated)

9.130 (see problem 9.86 for the problem statement - use no slip)

9.140 (this one is lengthy)

9.146 (like section)

"Solutions"14:Solution14 for printing, 5 pgs. Solution14 for screen viewing, 14 pgs. (640k pdf)

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Here are some practice problems for the final exam.

Here are some solutions to those problems.

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****************

**Final exam solutions ** (280k pdf)

In the solution to problem 1, the "m"s should be replaced by "2m"s.

In the solution to problem 2, part f is also true if there is purely radial motion, i.e. if d is true.

In the solution to problem 4, there should be the applied force P in the FBD of the upper link. The associated term should be included in the LMB equation for that link.

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