Physics 321 -- Spring 2006

Homework #1, due Wednesday
Jan. 18 at beginning of class

1. [2pts] Marion & Thornton: Appendix A, problem A-2.
(Expand to order (x - pi/4)^5.)

2. [2pts] Marion & Thornton: Appendix A, problem A-3.
(Expand the integrand in power series, keeping enough terms to achieve the
necessary accuracy.)

3. [2pts] Marion & Thornton: problem 1-9.

4. [3pts] Marion & Thornton: problem 1-10.

5. [3pts] Marion & Thornton, problem 2-9. Write the retarding force as –kmv.

After you have finished this problem, check
that your answer to part (b) becomes the same as the answer to part (a) in the
limit when the air resistance is small.
Then go one step further:
Your answer to part (b) has a term that looks like ln(1+“stuff”). Expand the logarithm in a Taylor series to
second order in “stuff”. (See Appendix
A.) The first term in your answer
should be the same as the answer to part (a), and the second term is the
correction to lowest order in k.

6. [2pts] Marion & Thornton, problem 2-17.

7. [4pts] Marion & Thornton, problem 2-25, parts (a)-(c)
only.

8. [4pts] Marion & Thornton, problem 2-32.

9. A race track has a curve banked at an angle
theta = 34 degrees with respect to the
horizontal. The radius of the curve
(looking down from directly above) is R=54 m.

(a) [1pt] If the race track is icy, so that
the tires slide without friction, at what speed must the car go
around the curve so as not to slide up or down the track?

(b) [3pts] On a dry day, the coefficient of friction between
the tires and the track is mu_{s} = 0.35 (pretty bad tires!).
What are the minimum and maximum speeds that a racecar could go around the curve
without sliding up or down the track?

10. [4pts] Marion & Thornton, problem 2-55.
(This problem is not in Edition 4.)