Answer to Question #53428 in Mechanics | Relativity for Hassan
The ﬁgure illustrates a Lorentz transformation using the conventions described on p. 43. For simplicity, the transformation chosen is one that lengthens one diagonal by a factor of 2. Since Lorentz transformations preserve area, the other diagonal is shortened by a factor of 2. Let the original frame of reference, depicted with the square, be A, and the new one B. (a) By measuring with a ruler on the ﬁgure, show that the velocity of frame B relative to frame A is 0.6c. (b) Print out a copy of the page. With a ruler, draw a third parallelogram that represents a second successive Lorentz transformation, one that lengthens the long diagonal by another factor of 2. Call this third frame C. Use measurements with a ruler to determine frame C’s velocity relative to frame A. Does it equal double the velocity found in part a? Explain why it should be expected to turn out the way it does.