Students who are interested in enrolling in Physics 105 should solve
and hand in these problems. They will be graded and will count towards
your 105 grade. This is in addition to the normal 103
assignments. This set is to be turned in at the first Physics 105
lecture, Friday Oct 5, or by 4:30 PM in Jadwin 208.
Reading: Phy103 assignment plus K&K 4.1-4.7.
Problem 1. Sports/power/work/food.
Note: to do this problem, you will have to look up some
conversion factors, and you will have to
estimate the typical height per floor of an office building.
Problem 2. A particle of mass m experiences a force that depends only on the particle's position. The force is given by
Calculate the work done by this force as the particle moves from the origin (0,0,0) to the point (x1,y1,0) via these two paths:
Problem 3. En route to Tycho Magnetic Anomaly 1. A space station consists of a hub connected to a ring by four spokes. The whole station turns as a unit with period T to provide ``artificial gravity'' to the occupants, who, of course, walk around on the OUTER wall of the ring. Note: there is no real gravity in this problem. The spokes contain elevators to bring people and equipment to and from the docking port at the center of the hub.
Assuming no friction and a massless elevator cable, how much work does the elevator motor do in bringing a load of mass M (including the elevator car), slowly and at constant speed, from the ring at radius R to the center of the hub? Without regard to your detailed calculations, is this work positive, or negative? Assume that the walls of the spoke keep the elevator car turning around the hub with period T and with negligible effect on the rotation of the station as a whole.
Warning: There is a strong temptation to use
W=delta K here. In this case, however, the walls of the
are doing the work that changes the speed of the car, not the elevator
Hint: a Taylor series will tell you the behavior of U(x) near x=x0.
Note how general this is: for small displacements from equilibrium, (almost) everything acts like a simple spring! Given your derivation, can you think of an exception?