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Lecture 1

PHYS 242 Lecture 1: PHYS242_Lecture_16-17

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PHYS 242
Wolfgang Rau

48 ENPHPHYS 242 Fall 2014 L 16 1.3.7 Relativistic Dynamics The basic equation for classical dynamics is Newtons second law: In special relativity we use the same relation between force and momentum: We can calculate the derivative of explicitly a . With the definition of the acceleration we get: (45) We can now e.g. ask the question: how does the velocity of an object change with time if a constant force is applied? In classical mechanics this is very simple since is constant for a constant force: we find . In special relativity this is more complicated due to equation (45): In the last step we invert the derivative of from above to solve the integral on the left side. We can solve this equation for and find: 1 1 For small the second term ( ) dominates and we find the classical relation . For large the second term becomes negligible and we find (however, for an exact calculation of course we will always have ). Since goes to infinity when approaches we realize that (not surprisingy) 1es to 0. This means that for a constant force the acceleration decreases (in contrast to Newtonian dynamics). Even more: for any finite force the acceleration will go to zero if approaches (yet another facet of being the absolute speed limit). W. Rau
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