General Phyiscs I, Fall '10

Homework 9 (covering Chapters 5 and 6 and the Wednesday in-class lab)

1. Show a graph of your data from part (a) of the lab (force vs. displacement). It should look pretty linear. Find the value of "k" (the "spring constant") that makes the formula "F = k * dX" a good fit. (Note that "k" should have units.)

2. In part (b) of the lab, you should have measured the oscillation period "T" for a couple/few different masses "M". And the "k" for your spring is also now known from the first part. Check the accuracy of the "magic formula" relating these that I wrote on the board in class: T = 2 * pi * sqrt(M/k). We'll talk in class on Friday about where this formula comes from and how it relates to the stuff we did in the first couple of weeks of the course with pendulums.

3. This problem is about safe driving on South Road in the winter. Suppose the coefficient of friction between road and tires is about 1.0 in nice weather, but is reduced to 0.05 in icy conditions. What is the maximum safe driving speed around "freshman curve" in nice weather? In icy weather? (You might have to field trip to freshman curve to estimate some relevant quantities.)

Extra credit: Suppose now you are going just under the maximum safe speed when you enter the curve, but you get scared and hit the brakes to slow down. What will happen and why? What's the lesson for driving?

More extra credit: What's the next most dangerous place for driving in the winter on south road, and why?