auThere exists :- Vβ = FFxax Follow your passion then money will comeEnergy:Universal quantityBut there is no exact definitionMechanical energyElectronic energyE=mcBig familyThermal energyAtomicenergy
There exists : F − = x U Fx = − Follow your passion then money will come. Universal quantity. But there is no exact definition. Energy: Big family Mechanical energy Electronic energy Thermal energy Atomic energy 2 E = mc
Feynman story about the conservation law of energy2-2 Law of conservation of mechanical energyParticle: dw, = J, ·dr, = d(_m,v.)Edw, =Ed(Ek,)System:Conservative force =0Work done by non-conservative force-0fin→ Dissipative force=0Definition:depend on the frameHeat individually Time inversion:invertible process
Feynman story about the conservation law of energy . 2-2 Law of conservation of mechanical energy Particle: ) 2 1 ( 2 i i i i i dw = f dr = d m v System: = i i ki dw d(E ) f in f ex Conservative force =0 Work done by non-conservative force=0 Dissipative force=0 Heat individually Definition:depend on the frame Time inversion:invertible process
E.+E=CConservative Systemgas Energy can neither be created or destroyed.only convert from one form to another
E p + E k = C Conservative System: Energy can neither be created or destroyed, only convert from one form to another. gas
$ 3.Potential Energy CarveConservative force F(x) U(x) potentialdU(x)F(x)=F=-VU(r)dxExample:U(r)=x+y+z=r一U()=1%(++2)+(++2)+%(+y+2)axOzov- 2(xi + yj + zk)= 2rCentral force: F = -2rMmMmU==-GGrV(x + y2 +22)
§3.Potential Energy Carve Conservative force F(x) U(x) potential dx dU x F x ( ) ( ) = − F = −U(r) Example: 2 2 2 2 U(r) = x + y + z = r xi yj zk r x y z z x y z k y x y z j x U r i 2( ) 2 ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 = + + = + + + + + + + + = F r Central force: = −2 ( ) 2 2 2 x y z Mm G + + = − r Mm U = −G
MmMm1-D: U(x) = -F(x)= -(工子xU(x)~x: U (X)d'U<0E.dx?EidF>0dx0XExampleSpring and blockOscillator (harmonic motion. point of stable equilibrum)
0 2 2 dx d U 0 dx dF Example: Spring and block Oscillator (harmonic motion. point of stable equilibrum) U(x)~x: 1-D: x Mm U(x) = −G 2 ( ) x Mm F x = −G U(X) o x 0 1 E E