Chapter 2Dynamics
Chapter 2 Dynamics
$1.Mass.momentum,forceand impulse1-1 Newton's Laws Newton's first LawIt is always possible to find a coordinate system withrespect to which isolated bodies move uniformlyNewton's first Law of motion is the assertion thatinertial systems exist. SO* One part of 1st Law is definitionDefinition of an inertial system* Another part of 1st Law is experiment factsuch inertial systems exists
§1.Mass,momentum,force and impulse 1-1 Newton’s Laws Newton’s first Law Newton’s first Law of motion is the assertion that inertial systems exist. SO One part of 1st Law is definition Definition of an inertial system. It is always possible to find a coordinate system with respect to which isolated bodies move uniformly. such inertial systems exists. Another part of 1st Law is experiment fact
It raises a number of questionisolated body =?"" “ inertial & non-inertial system"are absolute?* In our text book: Free particles always keep moving1uniformlyunique particles in the worldDon't useForce"but“interaction”福M Newton's Second LawdvF=dpmMomentummamp=midtdt
unique particles in the world Don’t use “Force” but “interaction” It raises a number of question: “isolated body =?” “ inertial & non-inertial system” are absolute? In our text book: Free particles always keep moving uniformly. Newton’s Second Law Momentum: p mv = ma dt dv m dt dp F = = =
* Key:See text book about the history of momentumOFαa Definition of “Inertial Mass"”“Gravitational MassRemarks:O F and a is relation of instantaneous effect. F = ma vector eq. (apply in coordinate system)Available for “particle"3m is constantOnly valid for lower speed
F a Key: Definition of “Inertial Mass”. “Gravitational Mass” Remarks: F and is relation of instantaneous effect. a F ma = vector eq. (apply in coordinate system) Available for “particle”. m is constant. Only valid for lower speed. See text book about the history of momentum
Newton's Third Law: Bird lawF, =-FInteractionbetweentwoparticlesjiRemarks:① Simultaneity(invalid for electro magnetic interaction) Be valid in inertial or non-inertial frame2③ In modern physics, replaced by conservation law ofmomentum.1-2 System of particles1.Superposition principle of forces
Newton’s Third Law: Bird law Fij Fji = − Interaction between two particles. Remarks: Simultaneity(invalid for electro magnetic interaction) Be valid in inertial or non-inertial frame In modern physics, replaced by conservation law of momentum. 1-2 System of particles 1.Superposition principle of forces. Fi
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