Classical mechanics is an extremely well tested model. Hundreds of years worth o
ID: 2077148 • Letter: C
Question
Classical mechanics is an extremely well tested model. Hundreds of years worth of experiments, as well as most feats of engineering, have verified its validity. If special relativity gave very different predictions than classical physics in everyday situations, it would be directly contradicted by this mountain of evidence. In this problem, you will see how some of the usual laws of classical mechanics can be obtained from special relativity by simply assuming that the speeds involved are small compared to the speed of light. Two of the most surprising results of special relativity are time dilation and length contraction, namely, that measured intervals in time and space are not absolute quantities but instead appear differently to different observers. The equations for time dilation and length contraction can be written t= t 0 and l= l 0 / , where = 1 1 u 2 c 2
Substituting your answer from Part E gives the equation
(E2E1)(2mc^2)=p2^2c^2p1^2c^2 .
Divide both sides by 2mc2 to find an expression for E2E1 .
Express your answer in terms of p1 , p2 , m , and c .
(PART E=E2+E1=2mc^2)
Explanation / Answer
E2E1)(2mc^2)=p2^2c^2p1^2c^2
dividing both sides by 2mc2
we get
E2E1)(2mc^2) / (2mc2)=(p2^2c^2p1^2c^2) / 2mc2
E2E1=(p2^2c^2p1^2c^2) / 2mc2