Physics 321 -- Spring 2004

Homework #1, due Wednesday Jan. 21 at beginning of class

1.         [3pts] Marion & Thornton: Appendix A, problem A-3

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

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

4.         [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.

5.         [2pts] Marion & Thornton, problem 2-17.

6.         [3pts] Marion & Thornton, problem 2-25, parts (a)-(c) only.  You may find it easier to do part (c) before you do part (b).

7.         [4pts] Marion & Thornton, problem 2-32.

8.         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. What are the minimum and maximum speeds that a racecar could go around the curve so as not to slide up or down the track?

            Hints: Draw a picture of the car looking from directly in front of it or behind it.  (It will be tilted to one side.)  Then draw the forces on the car before writing any equations.  Do the whole problem algebraically before putting in any of the numbers.

9.         [5pts] Repeat Marion & Thornton problem 2-17, but this time include the effect of air resistance that is proportional to velocity. (Air resistance proportional to the square of the velocity would be more realistic, but would be much harder to solve.) Make a table of the required initial velocity as a function of the free-fall terminal velocity of the ball. (You will need to some electronic helper to do this problem: use Mathematica, Maple, C++, Fortran, or whatever your favorite similar tool is.)