Physics I (Calculus Treatment)
Physics I (Calculus Treatment) PHYSICS 209
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This 9 page Class Notes was uploaded by Susanna Hodkiewicz on Tuesday October 27, 2015. The Class Notes belongs to PHYSICS 209 at University of Wisconsin - Milwaukee taught by Staff in Fall. Since its upload, it has received 28 views. For similar materials see /class/230286/physics-209-university-of-wisconsin-milwaukee in Physics 2 at University of Wisconsin - Milwaukee.
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Date Created: 10/27/15
Special Relativitv with highschool algebra Inertial frames y 3 0v S x 39 Z Z If the velocity of some object is measured on S 1739 1 170 velocity as velocity as measured in 8 measured in S same in all inertial t a a Newton s laws are the 4 Av39 Av A145 a m 39 frames Einstein s Postulates l The form of the laws of mechanics is the same in all inertial frames 2 The speed of light has the same value c3X108 meterssecond 1 85 000 miles second in any inertial very countepimu ive frame independently of the state of motion of the light source or the observer Consequences ofthe second postulate A Time dilation Consider a ash of light in a moving train that re ects off the top of the train and compare the time it takes in the different frames given that the speed of light is the same in both frames gt y L Iquot d I x CAtZ CAI2 d A d At 2dc vAtZ vAtZ dCAW2 P tha oras cAt22 vAt22 d2 y g Will take these two equations and use them to relate and gt y V y39 w I l W I S x S 0 x A 2 CAI2 A 39 2d 7R d d d cAfZ vAtZ vAt 2 Pythagoras cAtZ2 vAtZ2 d 2 CAtZ2 VAtZ2 cAt3922 gt cAt2 VAt2 CAt392 gt CAt2 VAt2 cAt392 gt 62 12At2 CZAt39Z gt 1 v2 czAt2 At392 At39 11 12262 gtAt At39 1 At39 Vl vzcz y y ll vZc2 Since v gt 0 y gt 1 2 At gt At39 2 Moving clocks run slow At Motion is a time machine to the future This is a fact Measured experimentally True not just for clocks but other physical chemical and biological processes B Length contraction gt V L According to Houston trip to star takes a time At L v The time elapsed for the people in the ship is less 39 than that we ve just seen this At At y People in the spaceship see the star approaching them at a speed V and the arrive in a time At39 They calculate the distance to be L VAld Putting all this together distance as seen from spaceship L39 vAt39 v 2 2 vAtyLy L lL h V C distance as seen from Houston If an observer measures the length of anhjeet t0 heLthen an observer moving at speed measures the length of the object to be LashW yn But observer in S doesn thnnw she s moving To them the picture looks like this 7 n i39 x St Z Moving objects contract These effect is tiny at normal speeds that s Why noone noticed it before You have to be moving close to the speed of light for noticeable effects to occur For example A 100 meter long ship travels to Alpha Centauri at 99 of the speed of light It takes the ship 45 years according to Houston to get there a How long does it take for the astronauts in the ship b By how much does the ship contract for observers on earth 1 1 m 7 1 xl v202 l 0992 3 At Aty 45years71 75 months v0990 gty b L Lly 100m71 141m C Mass and energy 1 RelatiVistic mass m ymo y m0 rest mass 1 v2 c2 Energy E mocz mc2 Kinetic energy energy associated With motion 2 2 K E moc y lmOC In the nonrelativistic limit When speeds are small compared With c 2 If v ltlt 6 y 1 v2 cz12 3 l Binomial expansion 6 2 l l K z 1 1mOC2 Emovz Which is the AP Physics at UWM Physics 209 or 120 kinetic energy de nition
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