Physics 141, Fall 2009.

1.     (50%) WeBWorK set # 3.

 

2.     (15%) There is no general analytical solution for the motion of a 3-body gravitational system.  However, there exists an analytical solution for the very special case shown in the Figure below.  In this Figure, three stars are shown, each of mass m, which move with the same speed in the plane of the page along a circle of radius r.  The three stars move in a clock-wise direction.  Calculate how long it will take for this system to make one complete revolution.

 

 

3.     (15%) A hanging copper wire with a diameter of 2 mm has an initial length of 3 m and hangs vertically from the ceiling of your dorm room.  When a 5 kg mass is attached to its end, the wire stretches by 0.425 mm; when a 10 kg mass is attached to its end, the wire stretches by 0.85 mm.  The density of copper is 9 g/cm³ and one mole has a mass of 63 g.  Find the approximate value of the effective spring stiffness of the inter-atomic force.  Explain your analysis and any assumptions you may have made.

 

4.     (15%) In the software download area of the Physics 141 web site (located at http://teacher.pas.rochester.edu/phy141/Software/SoftwareIndex.htm) you will find two movies that shows someone tossing a ball in an elevator that is moving up (ElevatorMovie1.mov and ElevatorMovie2.mov).  Use Logger Pro to analyze the motion of the ball in both movies and answer the following questions:

a.     What is the acceleration of the ball in each toss?  In ElevatorMovie1.mov you will only be able to examine one toss, while in ElevatorMovie2.mov you will be able to examine multiple tosses.

b.     What can you say about the difference in the motion of the elevators in the two movies?

 

5.     (5%) The long-term season average of (total wins)/(total games played) of the Yankees is 0.60 with a standard deviation of 0.04.  The corresponding number of the Red Sox is 0.50, also with a standard deviation of 0.04.  What is the probability that the Red Sox end up with a season average of above 0.59 and the Yankees end up with a season average below 0.53?  You may want to refer to Section C.2 in the Error Analysis textbook (page 250).

Note: I do not claim these numbers are accurate.  They should be correct, but they are based on believes, not facts.

 

6.      (Optional; 25% extra credit) Download the VPython program threeBodyOrbit.py from the Physics 141 software area that simulates the 3-body star system discussed in Problem # 2.  The program assumes that the stars in this system have a mass equal to the mass of our sun, and the radius of the orbit is equal to the radius of the earth around the sun.

a.     Using this program, modify the initial conditions of one of the stars (e.g. its momentum or the direction of its momentum; the location where these initial conditions are defined is clearly indicated in the program) and find at least one set of initial conditions for which you observe a long-lasting orbit, much different from the circular orbit studied in problem 1.  Report, via email to professor Wolfs, the initial conditions and attach a screen shot of the trajectories of the stars.  Note: make sure that you check if the step size is appropriate for the initial conditions (e.g. if you make the step size smaller by a factor of 5, do you get the same results?)

b.     Find at least one set of initial conditions for which one of the objects wanders off without returning. Report, via email to professor Wolfs, the initial conditions and attach a screen shot of the trajectories of the stars.  Note: make sure that you check if the step size is appropriate for the initial conditions (e.g. if you make the step size smaller by a factor of 5, do you get the same results?)