Mechanics & Wave Motion Problem Set 2

The rest of Y&F Chapter 2 (if you haven't read it already) and Y&F Chapter 3 through section 3.3.

Here's the hammer and feather experiment done on the moon, in case you're still skeptical that all objects experience the same acceleration due to gravity.  Of course, the acceleration of gravity is less on the moon, but the point is that the hammer and feather behave the same way. 

Due in class (9 AM) on Wednesday February 10.

1. Assignment 2 on our MasteringPhysics course site. 
2. A while ago I duct-taped one of the  lab accelerometers to the luggage rack on the top of my car and recorded data as I drove.  I went out to Stadium Drive by the UMass football stadium, stopped, and put the car in second gear.  From a dead stop, I floored the gas pedal from about t=3s to about t=14s, then slammed on the brakes and stopped in about 4 seconds.  Download the a_x  data here and import into your favorite math program (for instance, for older Excel use File > Import.  For newer Excel use File > Open, but you may need to ask Excel to accept non-.xls files). Then:
   
   1. Plot acceleration vs time.  Notice that the acceleration looks pretty constant but the braking does not, probably because my antilock brakes started pulsing. 
   2. Calculate velocity and distance as a function of time.  You may check your answer using the constant-acceleration formulas, but you should perform the integration numerically.  If you've never done numerical integration before, copy an example from the web or adapt this little Excel spreadsheet.  Do not turn in a long table of numbers, just print out a plot of a vs t, v vs t and x vs t.  Label your axes, including units.
   3. What was my peak speed (in miles per hour)?  Remembering that I was basically driving in a parking lot, your answer should explain why I gathered this data late at night with my lights off, after checking there were no police in the vicinity.
   4. How far did I travel?
3. Part 1 only of the following (click to enlarge to readable size).  Part 2 looks pretty hard: I don't think I can write down a closed-form solution myself.  If you really want to try it go ahead.  Part 3 is a search / optimization problem which is more appropriate for a computer science course.
   
4. Y&F end of chapter problems.
   1. 2.90.  Tricky.  This interview with the author of The Physics of Superheroes will explain why Superman can't simply fly downward (with acceleration greater than g) to catch the student, in case that's bothering you.
   2. 3.4
   3. 3.53
   4. 3.54
   5. 3.56.  Tricky.  The physics is the same in 11th and 12th editions, but the storyline changes from launching a burning match into a wastebasket to filling a bucket with a stream of water.  Perhaps the publisher was afraid of lawsuits.