WORK. The work is done by a force acting on a body while it undergoes a displacement.

Transcription

1 ORK The work is one by a force acting on a boy while it unergoes a isplacement.

2 S S

3 S S cos S S cos S S S ork is one by a component of Ԧ, parallel to the isplacement. S

4 The work value epns on: force Ԧ value isplacement ԦS value angle α between Ԧ an ԦS

5 ork one in horizontal shifting 1 cos() 0 S cos 0 0 The is no work in horizontal shiftng!!! Carrying weights we o not work!!!

6 ork one in lifting an object S Q mg 1 cos() cos 1 S hen lifting, we perform positive work!!!

7 ork one in lowering an object 90 1 cos() S 180 cos 1 S hen lowering, we perform negative work!!!

8 w 1 0 S S Lifting an lowering mgs Q mgs S S 1 0 hen lifting an lowering, the total work is zero!!!

9 Lifting an lowering with varying mass w 0 Q S S mgs 1 S m 1 gs 1 S m m 1 gs 0 fter mass ecrease at the top, the total work is positive hen rinking, we perform positive work!!!

10 Pressing S 0 cos 1 S Pressing the remote control button we perform positive work!!!

11 S

12 Q S S Q Q Q Q Q S S S S S S

13 ORK The work is an integral of force an isplacement scalar prouct. S ork is energy transferre to or from an object by means of a force acting on the object. Energy transferre to the object is positive work. Energy transferre from the object is negative work.

14 The Scalar Prouct (ot prouct) R 1 cos() Example: work: = Ԧ ԦS, z N z 0 S T Q -1 Q N T 0 0 0

15 Q mgs 1 1 S 3 Q3 0 Q S 1 S 41 S 34 Q mgs 34 Q41 0 Q S 1 S 34 S S cos QS 1 cos 180 QS1

16 Q Q Q The net work one by a weight on a particle moving aroun any close path is zero.

17 Q The work one by a weight on a particle mooving between any two points oes not epen on the path taken by the particle. S 1 1 0

18 force, which net work on any close path is zero (is inepenent on the path), is sai to be a conservative force.

19 Conservative force: - gravitational force - spring force - Coulomb force Nonconservative force : - friction force - rag force Tk < 0 D < 0 ൡ both forces are issipative

20 or conservative force it is possible to efine the change of the potential energy c c r c 0 c c c r c

21 POTENTIL ENERGY The change in the potential energy is efine to equal to the negative of the work one by a conservative force uring the shift from an initial to a final state. c c r

22 Conservative force Potential energy Gravitation mg mgh Grawitaion G m m 1 r r r m1m r G Spring force Coulomb 1 4 kx 0 q r q 1 r r 1 kx q 1 q r

23 mgh m m G 1 r

24 1 kx x 0 x

25 1 q1q r 40 oy aim to achieve a state of minimum potential energy

26 Integral = ntierivative y f x y x f x x x The integral is the inverse operation to the erivative the antierivative. c r c gra c x (in one-imensional motion) (in 3D-imensional motion)

27 x x x ( x )( ) min x 0 c x ( x ) ( ) max x 0 c x ) ( x) const 0 c x ( x 0 0 0

28 x ( ) min max const x EQILIRIM 0 0 c the boy remains at rest the boy remains at equilibrium - stable - unstable ( x ) ( x ) min max - neutral const ( x )

29 The boy is at equilibrium when: - net force is zero 0 w - remains at the extremum of the potential energy x an (ynamic equilibrium conition) (energetic equilibrium conition) 0 0 M w

30 w r t V m t mv t w p t V r t r V t V t V m V V m t r V t mv t w p t w p KINETIC ENERGY

31 m V V 1 mv 1 mv K 1 mv K K K w w r

32 KINETIC ENERGY The change K in the kinetic energy is efine to equal to the work one by a conservative force uring the shift from an initial to a final state. K K K w w r

33 hen acting forces are conservative: w c w r c r w c K

34 K K K K E E E K E const

35 PRINCIPLE O CONSERVTION O MECHNICL ENERGY If only a conservative forsec within the system oes work, then the total mechanical energy E of the system, the total sum of its kinetic K an its potential energies, cannot change w c E K const

36 V 0 K mgh K E 0 mv K E E E mv mgh g V H H

37 V C 0 K mgh K E 0 C C C C C mv K E C E E mgh mv C V C gh g V g V C V C V

38 K int E K ex c w r r r r ex c w ex E K int ex c w hen on a boy, except conservative foces Ԧ c, acts issipative forces Ԧ an external forces Ԧ ex : Q ex ex E K int

39 PRINCIPLE O TOTL ENERGY CONSERVTION E tot K E int ex The change in the total energy of the system is equal to the work one by an external force.

40 PRINCIPLE O TOTL ENERGY CONSERVTION ex 0 E tot K Eint 0 In an isolate system, (system without external foces) energy may be transferre from one type to another, but the total energy E tot of the system always remains constant.

41 INTERNL ENERGY E int 1. The change of the internal energy is equal to the negative of the issipative force work.. ork one by torque or rag foce Ԧ always increase the internal energy of the system E int > Internal energy coul be observe as: boy an environment heating, eformation, soun, light...

42 Discuss energy transfers occurring in each of the following 1 situations: a) not taking into account the occurrence of frictional force b) taking into account the occurrence of friction force V V V V V Ԧ V Ԧ V Ԧ V Ԧ V Ԧ V Ԧ V Ԧ V Ԧ 1) hich of the presente cases can not occur in reality?? ) In which of the presente cases the spee coul be constant? Discuss energy transfers in such a case.

43 1 1 t p t p t p t p t p 0 1 t p p const p p 1 COLLISIONS

44 PRINCIPLE O MOMENTM CONSERVTION If there is no external foce or net external force is zero, the net linear momentum of the system 0 wz cannot change. p c p i const 11z 1z z 31 1 z 3z z 3 z 3z 3

45 If in collisions acting forces are conservative then the mechanical energy is constant. 1 1 kx The collisions is then sai to be elastic. p1 p p1 p mv mv 1 1 mv mv MC MEC 0

46 p p p p 1 1 int 1 1 E mv mv mv V m MC TEC If in collisions acting forces are nonconservative The collisions is then sai to be inelastic. then the total energy is constant.

47 V C V C V C In elastic collisions: total mechanical energy is constant In inelastic collisions: total mechanical energy ecreases an follows: heating, eformation, soun generation, ligt generation.