Physics 321 -- Spring 2003

Homework #1, due Wednesday Jan. 15

1. (3) Marion & Thornton: Appendix A, problem A-3

2. (3) Marion & Thornton: problem 1-9.

3. (3) Marion & Thornton: problem 1-10.

4. (3) Marion & Thornton, problem 2-9. Write the retarding force as –kmv.

When you are done with this problem, you should 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. Let’s do that and go a 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. (2) Marion & Thornton, problem 2-17.

6. (3) Marion & Thornton, problem 2-25, parts (a)-(c) only. I suggest you do part (c) before you do part (b).

7. (4) Marion & Thornton, problem 2-32.

8. (4) A racetrack has a curve banked at an angle q=34° with respect to the horizontal. The radius of the curve (looking down from directly above) is R=54 m.

(a) (1) If the racetrack is so icy and slippery that the racecar tires slide without friction, at what speed must a racecar go around the curve so as not to slide up or down the track?

(b) (3) On a dry day, the coefficient of friction between the racecar tires and the track is m_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. Also, do the whole problem algebraically before putting in any of the numbers.