PHYSICS 321 - Classical Mechanics I

Spring 2007

Homework Set #1 (due 1/17/07)

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 2^nd 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 μ_s = 0.5. What are the minimum and maximum speeds that the car could go around the curve without sliding up or down the track?