南开大学：《力学》课程教学资源（PPT课件，英文讲稿）Chapter 2 Dynamics

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