P301:Homework Assignment # 1
Due 8 Sept. 2010 (50 Points total)
Please write out complete solutions (not just provide answers) to the following Problems from the T&R text (take note: these are from the “Problems” section, not the “Questions” section of each chapter). Each question will be graded out of 10 points.
- In his television series “The Ring of Truth”, MIT Physicist Phillip Morrison provided a remarkable, yet simple, demonstration of the size of molecules he attributed to Ben Franklin. He poured ~1 ml of olive oil onto the surface of a small pond, and he observed the size of the resulting “oil slick” by noting changes in the surface waves on the pond (this size was ~200 m2). Using just this information, and reasonable values for the macroscopic physical properties of olive oil, estimate the size and molecular weight of an “olive oil molecule”. Consider both spherical and cylindrical (with say a 10:1 aspect ratio) molecular models.
- A rod moves with velocity 3c/5 in a straight line relative to an inertial frame S. In its own rest frame, the rod makes an angle of 60 degrees with respect to the forward direction of its motion relative to the frame S. Show that in the frame S, the rod appears to make an angle of cot-1(4/5*31/2 ) (i.e. about 75 degrees) with the direction of motion.
- T&R chapter 2, Problem 21. Assume that the track length specified is the mean value of the tracks for all muons travelling with that velocity.
- Suppose that a second muon left a track of 95 cm. How fast was this second muon travelling?
- T&R chapter 2, Problem 32
- The GPS system works by measuring the time needed for light to propagate from each of four satellites to the receiver (this gives the distance to those four satellites and from this the position of the receiver may be determined anywhere on Earth). Assume that the satellites are in geostationary orbits (42164 km in radius; they are not in such orbits, but this is close enough for our purposes and will simplify the details), and that their clocks are “synchronized” each day at midnight (in Boulder Colorado say). If the system did not account for time dilation of the satellites’ clocks due to their motion, what absolute error in the measurement of the distance to a given satellite would result for a measurement taken at noon (in Boulder)? The system must in fact take this into account (as well as an even bigger effect of opposite sign due to general relativity) in order to function. Relativity is not just important in textbooks, science fiction novels, and high-energy physics experiments!