F-ZFForce can be described by vector' Experimental factm Newton's Laws (for system of particles)Fex(external forces)Total force: F Fin(internal)in一F-Fex+Fin-Efex+EfinmFin=01dFpaEmia, =(Ep)ex一dt一dt11
= = ( ) i i i i i p dt d m a Newton’s Laws (for system of particles) Force can be described by “vector” Experimental fact = i F Fi F in ex F F (external forces) (internal) Total force: = + = + i i in i i ex ex in F F F f f p dt d Fex = = 0 Fin
Law of conservation ofmomentummOne particle:F= O,p = constant.(First law)Fex = O,P1 + p2 = constant.Two particles:JFx =0pxi =0pi =0N-particles:Fy ±0i* This law is very important, especially in modern“Force”meaninglessPhysics.* The discovery of Neutrinospin 1/2no chargeMass lessweakinteraction
weak interaction no charge Law of conservation of momentum One particle: F = 0,p = constant.( First law) Two particles: F 0,p p constant. ex = 1 + 2 = N-particles: p 0 i i = F 0 F 0 y x = pxi = 0 This law is very important, especially in modern Physics. “Force” meaningless. The discovery of Neutrino spin 1/2 Mass less
A > B+eIf A is static , motionless, B and e muston a line. (Pauli 1930 predicted, 26y after observed in lab)Electromagnetic field also has momentumcloud chamber beer Symmetries and conservation law: Noethertheorem(German lady), Invariance of translation inspace.Application of the law: Rocket* velocity of the rocketu velocity of the dm
A→ B + e If A is static , motionless, B and e must Electromagnetic field also has momentum. on a line. (Pauli 1930 predicted, 26y after observed in lab) cloud chamber beer Symmetries and conservation law: theorem(German lady), Noether Invariance of translation in space. Application of the law: Rocket v velocity of the rocket u velocity of the dm
tt +dtmm+dmXV+dhmmi = (m + dm)( + d) +ü(-dm)v+d= m + mdh + rdm + dmdh -udmmd+(-u)dm=0c=u-dmmh-cdm=0一d=CumdmJ.dv=-cf"dmmo一v=cnmUmom
v dv + u v v dv + mv = (m + dm)(v + dv) + u(−dm) mv mdv vdm dmdv udm = + + + − t t + dt m m+ dm m m dm x mdv + (v − u)dm = 0 mdv −cdm = 0 c u v = − m dm dv c = − = − m m v m dm dv c 0 0 m m v c 0 = ln
m Impulse theorem of momentumF=dpF=F(t)→Fdt=dp→di=dpdtWe only concern the effect of accumulation, don't carethe process" F(t)dt = m(-)= IFIvector,"Flow of mass"Example:Finding pressureParticles: density n,speed v. O福(1),Vback = O → Perfect inelastic collision
Impulse theorem of momentum dt dp F = F F t = ( ) Fdt dp = We only concern the effect of accumulation, don’t care the process. di dI dp = F t dt m v v I t t = − = ( ) ( ) 0 0 I vector,”Flow of mass” t F 0 Example: Particles: density n,speed v. (1). = 0 Perfect inelastic collision. back v Finding pressure