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# Manfra6 - Course Business PHYS342 Lecture 6 Due Friday Jan...

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Course Business: PHYS342 Lecture 6 Due Friday Jan 28th in class Problem set 2 From Modern Physics chapter 2: Problems: 12 through 17 and 19 through 21 and problem 23

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Proper Length When both endpoints of an object (at rest in a given frame) are measured in that frame, the resulting length is called the Proper Length . We’ll find that the proper length is the largest length observed. Observers in motion will see a contracted object.
Length Contraction Proper length 0 2 2 2 2 ( ) v( ) 1 v / 1 v / r r r x x t t L L x x L c c γ - + - = - = = = - - l l l r t t = l x l r x where Mary’s and Melinda’s measured length is: r L x x = - l 2 2 0 0 / 1 v / L L L c = = - Moving objects appear thinner! L 0 Frank Sr. Frank Sr., at rest in system K, measures the length of his somewhat bulging waist: L 0 = xr - x Now, Mary and Melinda measure it, too, making simultaneous measurements ( ) of the left, , and the right endpoints, Frank Sr.’s measurement in terms of Mary’s and Melinda’s:

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So Mary and Melinda see Frank Sr. as thinner than he is in his own frame. But, since the Lorentz transformation is symmetrical, the effect is reciprocal: Frank Sr. sees Mary and Melinda as thinner by a factor of γ also. Length contraction is also known as Lorentz contraction . Also, Lorentz contraction does not occur for the transverse directions,
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Manfra6 - Course Business PHYS342 Lecture 6 Due Friday Jan...

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