PHYSICS 321 - Classical Mechanics I
Spring 2010
Homework
Set #1 (due 1/20/10)
1. Thornton
and Marion, problem 2.9. Write the
retarding force as –kmv. The answer to
part (b) contains a log term. When you
have done part (b) you should expand the logarithm (see Appendix A) for small
values of air resistance and check that the first term of the expansion
corresponds to the answer to part (a).
The second term is the correction to lowest order in k.
2. Thornton
and Marion, problem 2.17.
3. Thornton
and Marion, problem 2.24.
4. Thornton
and Marion, problem 2.26. In the second
part, remember that the total distance in meters that the block slides across
the floor is (2 + x) where x is the amount that the spring is compressed.
5. Thornton
and Marion, problem 2.29. (An 8% grade
means that sin θ = 0.08.)
6. Thornton
and Marion, problem 2.41. It is
possible to do this problem in your head and just write down the answers. But then check your answers in the following
way. Assume that the woman exerts a
constant force F on the ball during a time Δt. Express F in
terms of m, v, and Δt
using Newton’s 2nd Law, and then calculate the work done by the
force F and check that it matches your answer to part (c). For part (d) note that the train exerts that
same force F on the woman while she is throwing the ball. You will need to calculate how far the woman
moves with respect to the ground while she is throwing the ball.
7. A race
track has a curve banked at an angle θ = 40 degrees with respect to
the horizontal. The radius of the curve (looking down from directly above) is R =
50 m.
(a)
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)
On a dry day, the coefficient of friction between the tires and the
track is μs = 0.5. What are the minimum and maximum speeds that the car could go
around the curve without sliding up or down the track?