length contraction problems and solutions pdf

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4. "special relativity in the shadow of geometry" by George Mpantes. trailer <<7B07ECA154354F9E8487A2B2FEA62786>]>> startxref 0 %%EOF 88 0 obj <>stream Group Problems #5 Solutions Wednesday, August 31 Problem 1 Time dilation and Length Contraction A railcar travels to the right with speed v, as shown in the Figure. 0000055986 00000 n Accounting for time dilation and length contraction, how much time does a beam take to propagate from the center, to the end of either arm, and back again, as measured by an observer moving with speed V?

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Length Contraction and Rotation Problem 1.15, page 46 A rod of length L 0 moves with speed valong the horizontal direction. Note that time dilation and length contraction are just special cases: it is time-dilation if ¢x = 0 and length contraction if ¢t = 0. ?��G�`U�vI~��ko��M��)��.��^�W�F$�� A*`�->�fp_�; 0000050443 00000 n

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Students will correctly solve problems involving length contraction.

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0000048595 00000 n TIME DILATION AND LENGTH CONTRACTION SHOWN IN THREE-DIMENSIONAL SPACE-TIME FRAMES Tower Chen Division of Mathematical Sciences University of Guam e-mail:tchen@ugm.uog.edu Zeon Chen e-mail: zeon chen@yahoo.com (Received 9 December 2008; accepted 18 February 2009) Abstract In classical Newtonian physics, space and time are abso-lute quantities. This implies that distance, too, depends on the observer’s relative motion. 0000024895 00000 n 19.

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0000053283 00000 n Does time dilation mean that time actually passes more slowly in moving references frames or that it only seems to pass more slowly? 0000004710 00000 n æ�!Í¢ˆ©´L:C‚^L¦æÕy¹šåuØ¨t[Ãn—~ Æ«&VD¹]ñ“r±[º¿-ƒ*á¢A4Â—Åœ´Ğ¼¯…äp‹ô�¡_Æ4µŒ;×QÀóÒ‹4�z4Ë*(w»¡m¹¨¥ÒWåbW‘²ÉTK‘^uúŞÔUT,š¹"÷A>\"8PÑcZÇD¨®á[y+-^ 0000037326 00000 n 0000055951 00000 n See this slide. Assume that in the rest frame of the interferometer, the arms are the same length L 0. 0000037148 00000 n %PDF-1.4

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0000044698 00000 n 0000045761 00000 n Note that the time dilation and length contraction equations are sufficient to do this problem, é=&Q2¯ÍÓÊ1�šeJö^Røµt,Ón~ª5çÓ±.şF¡Ñõ¬Ø´Ah]�}ëqü’ÇA›2�At8ÎÊ&ò¦›yµs@Ä´)çÅœ×e]Wõ˜CX&ÍŞ#¿�Ù*$|¢zU¤¹Io—å,(»$éuâ]Ì¶ ùaeNv~ˆAv ğnv«¦h"ŞF[p‚;ZQáv*pÆ-8øDH: 0000002046 00000 n (The speed of light: 3.00 x 108 m/s) 2. 0000001236 00000 n 3 0 obj <<

P€µÙ;w[EÚ4iŠh}HòÀH´D@RŠë~}Ïr–)Ñ²´íe8÷93k�,�¼¾à÷üşxuñì•°‰äÌZi’«ëD8Á8—‰5�eÒ&Wóä}úº®v7“©â2ı½®>ŠuC»oı¾«V»mYmšÉÇ«_Á2K„fJ[XÃt–LbFE†MœL‹ù¦hæùDfé]Ø_‚Ö/v‹]³ k›*A¥ë3œ oj:!G��>��;#��g}�ę��P6u�!�x!�yQ4��y��b��N x�b```b``cd`c`�cfd@ A�� Determine the angle the rod makes with the xaxis. Focus: Answer questions on previous assignment. 0000003301 00000 n Even though clocks measure different elapsed times for the same process, they still agree that relative speed, which is distance divided by elapsed time, is the same.

PROBLEM 2 – 10 points Planet X is 60 lightyears away from Earth.

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mathematically , the length contraction is a result of … œef_î/G¢´�¢«Ï¦“U:éQİŸN@÷IH§HÅÕ¾ƒı|u ²ô:×²d¶¾ø|�¦¦2§Úëşº½ì¾ŠÏŞ¬Eò²ºøÿ�»dG: ¦=Ô>êz�H#˜Ê. %PDF-1.4 0000051346 00000 n 0000007801 00000 n §e3f�“LÓéş6FÚ%ó�+k ˆe^ó�c las. what is reality?

��X1��Q�e0�B�u~Ŗor�8~[��Ol4[��W1��VNp�Hᶞb�w�Γ��{��M! 0000006698 00000 n One thing all observers agree upon is relative speed. 0000047620 00000 n 0000008686 00000 n 0000005968 00000 n V?

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/Length 1759 0000001724 00000 n If two observers see different times, then they must also see different distances for relative speed to be the same to each of them. 0000030854 00000 n /Length 2761

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If you were on a spaceship travelling at 0.50c away from a star, what speed would the starlight pass you? Assume that there is no relative motion between Planet X and Earth (i.e., from the Earth, it appears that Planet X is at rest and vice versa). 0000052839 00000 n

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mÁR&S÷‚xFÍ&S#M¿SE¼`Ôœè¯Êu)†§ór•íi—oæ´x;ÁÅf±]Òş§j³ÃY>k©÷¦ (Since the observer moving with the event measures a different time than the observer not moving with the event, are the lengths different?)

Special Relativity Questions & Problems (Answers) 1.

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