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(d) Imagine that Alice constructs an array of sticks (at rest) which are uniformly distributed around a circle, one every twenty degrees, as shown. Bob is moving relative to Alice in such a way that he sees the array moving to the right at a speed of v = c. Draw an accurate diagram showing how the array appears to Bob. Feel free to work in Cartesian or Polar coordinates, and be sure to take advantage of any symmetry. One way to do this would be to create a ListPolarPlot[] (or just a ListPlot[]) in Mathematica, or you could make a polar plot in Kaleidagraph under Plot → PlotO could also choose to download the circular graph paper from the course Glow page Sets folder.

(d) Imagine that Alice constructs an array of sticks (at rest) which are uniformly distributed around a circle, one every twenty degrees, as shown. Bob is moving relative to Alice in such a way that he sees the array moving to the right at a speed of v = c. Draw an accurate diagram showing how the array appears to Bob. Feel free to work in Cartesian or Polar coordinates, and be sure to take advantage of any symmetry. One way to do this would be to create a ListPolarPlot[] (or just a ListPlot[]) in Mathematica, or you could make a polar plot in Kaleidagraph under Plot → PlotO could also choose to download the circular graph paper from the course Glow page Sets folder.

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Alice rides along in a high-speed wagon, carrying a fishing pole with a rest length lo along with her. She is holds the pole an angle 0o (as she measures it) to the horizontal. (a) Bob observes Alice from a position at rest on the side of the road, observing Alice to be moving at a speed v (forward). (i) What is the length of the fishing pole as measured by Bob? (ii) Show that according to Bob the fishing pole makes an angle 0 with the horizontal where 0 is given by (wagon frame) 0 = tan (y tan Oo). [Hint: this is a fairly straightforward application of length contraction.] (b) As a specific example, suppose that 00 = 45° and v = c. What is 0? (c) Rework the same problem using (inverse) Lorentz transformations. Here's a start: The stick is at rest in the primed (Alice) frame with one end at x (t') = 0,y, (t') = 0 and the other at x,(t') = xo, y,(t') = Yo, where xo and yo are constants. Use this information to find the coordinates in the unprimed (Bob) frame. In the end the results for the horizontal and vertical lengths (i.e. x2(t) – x1(t) and y2(t) – yı(t)) should reproduce the results you found in part (a).
Transcribed Image Text:Alice rides along in a high-speed wagon, carrying a fishing pole with a rest length lo along with her. She is holds the pole an angle 0o (as she measures it) to the horizontal. (a) Bob observes Alice from a position at rest on the side of the road, observing Alice to be moving at a speed v (forward). (i) What is the length of the fishing pole as measured by Bob? (ii) Show that according to Bob the fishing pole makes an angle 0 with the horizontal where 0 is given by (wagon frame) 0 = tan (y tan Oo). [Hint: this is a fairly straightforward application of length contraction.] (b) As a specific example, suppose that 00 = 45° and v = c. What is 0? (c) Rework the same problem using (inverse) Lorentz transformations. Here's a start: The stick is at rest in the primed (Alice) frame with one end at x (t') = 0,y, (t') = 0 and the other at x,(t') = xo, y,(t') = Yo, where xo and yo are constants. Use this information to find the coordinates in the unprimed (Bob) frame. In the end the results for the horizontal and vertical lengths (i.e. x2(t) – x1(t) and y2(t) – yı(t)) should reproduce the results you found in part (a).
(d) Imagine that Alice constructs an array of sticks (at rest) which are uniformly distributed around a circle, one every twenty degrees, as shown. Bob is moving relative to Alice in such a way that he sees the array moving to the right at a speed of v = c. Draw an accurate diagram showing how the array appears to Bob. Feel free to work in Cartesian or Polar coordinates, and be sure to take advantage of any symmetry. One way to do this would be to create a ListPolarPlot[] (or just a ListPlot[]) in Mathematica, or you could make a polar plot in Kaleidagraph under Plot → PlotOptions, but could also choose to download the circular graph paper from the course Glow page in the Problem Sets folder. you
Transcribed Image Text:(d) Imagine that Alice constructs an array of sticks (at rest) which are uniformly distributed around a circle, one every twenty degrees, as shown. Bob is moving relative to Alice in such a way that he sees the array moving to the right at a speed of v = c. Draw an accurate diagram showing how the array appears to Bob. Feel free to work in Cartesian or Polar coordinates, and be sure to take advantage of any symmetry. One way to do this would be to create a ListPolarPlot[] (or just a ListPlot[]) in Mathematica, or you could make a polar plot in Kaleidagraph under Plot → PlotOptions, but could also choose to download the circular graph paper from the course Glow page in the Problem Sets folder. you
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