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1 Physis Cousewae oden Physis Enegy and oentu Relatiisti oentu: p γ Kineti enegy: K. E. ( γ ) Auxiliay equation: E + 4 p whee is the est ass and E is total enegy. Poble.- What has oe ass at est: i) A sodiu 3 Na nuleus ii) potons and neutons Solution: The nuleus has less ass. The diffeene in ass ties is the binding enegy. Poble.- Calulate the total enegy of a uon (whose ass at est is 06eV/ ) that is oing at a speed of Solution: Enegy γ γ (0.97) So, Enegy γ 4.345(06eV/ ) 436 ev Poble 3.- If the kineti enegy of a patile of ass is equal to its est enegy, how uh is its oentu? (A) p (B) p (C) p 3 (D) p (E) p 0. 5 Solution: we use the anillay equation: ( + ) p + 4 p 4 E p p p 3 answe: C
2 Poble 3a.- What is the speed of a poton whose kineti enegy is thee ties its est enegy? Solution: Aoding to the poble K.E.3, so: K.E. ( γ ) 3 ( γ ) γ 4 But γ, so: / 4 / / 6 / / Poble 3b.- If the kineti enegy of a patile of ass is equal to fou ties its est enegy, then the agnitude of the patile s elatiisti oentu is: Solution: Aoding to the poble K.E. 4, so the total enegy is E 5 and using the anillay equation: E p + ( 5 ) p + 5 p + Soling fo p: 4 p 4 p 4 Poble 3.- If the kineti enegy of a patile of ass is equal to twie its est enegy, then the agnitude of the patile s elatiisti oentu is: Solution: Aoding to the poble K.E., so the total enegy is E 3 and using the anillay equation: E p + ( 3 ) p + 9 p + Soling fo p: 4 p 8 p 8 Poble 4.- How uh enegy do you need to gie an eleton to aeleate it fo est to 0.99? Gie you answe in eleton olts. (A) 3.eV (B) 4.eV (C) 5.eV (D) 6.eV (E) 7.eV
3 Solution: we alulate the kineti enegy: K.E. (γ ) eV ( ) ev answe: A Poble 5.- A lup of lay whose est ass is 4 gas is taeling at 3/5 the speed of light when it ollides head-on with an idential lup going the opposite dietion at the sae speed. If the two lups stik togethe and no enegy is adiated away, what is the ass of the oposite lup? (A) 4g (B) 6.4g (C) 8g (D) 0g (E) 3.3g Solution: we alulate the total enegy befoe and afte: 4g TEbefoe TEafte γ γ 0g ( 3/ 5) 0.6 answe: D Poble 6.- A patile leaing a yloton has a total elatiisti enegy of 0 and a elatiisti oentu of 8 /. What is the est ass of this patile? (A) 0.5 (D) 6 (B). (E) 6 (C) Solution: we use the anillay equation: E p + ( 0 ) (8/) answe: D Poble 6a.- A patile leaing a yloton has a total elatiisti enegy of.3 ev and a elatiisti oentu of. ev/. What is the est ass of this patile? Poble 6: Using the anillay equation: 4 4 E p + (.3eV ) (.ev / ) + Soling fo : eV.44eV + ev
4 Poble 7.- Deonstate that if the foe is paallel to the eloity of a patile you an wite Newton s seond law of otion as 3 F γ a dp Solution: Aoding to Newton s seond law: F whih is still alid in speial dt elatiity, but we need to use the elatiisti oentu, not p as in lassial physis. If the foe and eloity ae paallel we an dop the eto notation and teat the poble as a one diensional poble: dp dγγ d d d F dt dt dt / d / dt Notie that we used the hain ule of deiaties and also notie that d/dt is the aeleation a, so the foe beoes: / / d / / + / F a a a d 3/ / / ( / ) a 3 γ a 3/ ( / ) Note: Be aeful when using this foula that is the eloity of the patile, not the eloity of a fae of efeene. Reebe that this is only alid if the foe and eloity ae paallel. Poble 8.- A patile of ass deays fo est into two patiles. One patile has ass and the othe patile is assless. The oentu of the assless patile is: ( ( A) 4 ( ( B) ( ( C) ) ) ) ( ) ( D) 4( ( E) )
5 Solution: Conseation of enegy: 4 + p + p p + p p p answe (B) Poble 9.- What is the kineti enegy of an eleton whose speed is K. E. γ Solution: ( ) 79? 37 In joules: 4 K. E J, and in ev: K. E. 5keV
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