Question

(3) (10 pts): The work-energy theorem relates the change in kinetic energy of a particle to the work done on it by an external force: AK = W = | Fdx. a) Writing Newton's second law as F=dp/dt, show that W = S v dp and integrate by parts using the relativistic momentum to obtain E = mc²y b) Use the expression for the relativistic energy and relativistic momentum of a particle of mass m to demonstrate the important relation E2 = (pc)2 + (mc2)

Answer 1

0 + м п bg wa Sich was dog xin - Job (1) TW z Tuto] [wa Juup/ db z mou. TT-VVEL ba mu - Ji-vir u 1-292) ou & B-V7 (2) 32 do zmill-va+vY/62) de (-1/2) Jp z mre (i-V762)32. Incede W z S T VY62%

let 1-4 = I auro de 2-mc 2 Suede - <me2 tox Udo z-chde ne z mca -V2702 W z E = my ore - To= Ymc2) 5) E = mc and - E22 (mo42 T-NYC 1-062 2 (0042 Yn be p² my rear m² r2 I 1-V2KL 1- Viz m2r2. 1. b 2 from and G

(MC212 = E2a E²-bel? from from equation (1) EZ E2 E2-61² = (mch? le= (pics? +(M (212) TEL (c)2+(MC42)