h 2. Work as a dot product The work done by a force F can be written as W=F s (1)If Fls, the work done by the F is zero (2 )Unlike mass and volume, work is not an intrinsic property of a body. It is related to the external force (3 Unit of work: Newton-meter ( Joule) (4)The value of the work depends on the inertia/ reference frame of the observer ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy 2. Work as a dot product The work done by a force can be written as (11-2) (1) If , the work done by the is zero. (2) Unlike mass and volume, work is not an intrinsic property of a body. It is related to the external force. (3) Unit of work: Newton-meter (Joule) (4) The value of the work depends on the inertial reference frame of the observer. → F W F s → → = → → F ⊥ s → F → m g s h v
3. Definition of power: The rate at which work is done t if a certain force performs work Awon a body in a time At, the average power due to the force is △Ⅳ + The instantaneous power P is dw P (11-8) If the power is constant in time, then p=p ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy If a certain force performs work on a body in a time , the average power due to the force is (11-7) The instantaneous power P is (11-8) If the power is constant in time, then . av W P t = dW P dt = P = Pav 3. Definition of power: The rate at which work is done. W t
If the body moves a displacement d s in a time dt, F 110 Unit of power: joule/second ( Watt) See动画库/力学夹/2-03变力的 功A.exe1 ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy (11-10) Unit of power: joule/second (Watt) dW F d s d s P F F v dt dt dt → → → → → → = = = = If the body moves a displacement in a time dt, → d s See 动画库/力学夹/2-03变力的 功A.exe 1
11-4 Work done by a variable force 11-5 1.One-dimensiona Fig11-12 situation The smooth curve in Fig 11-12 shows an F F2(x) arbitrary force F(x) that acts on a body that moves from x to x X X X △ ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy Work done by a variable force 1.One-dimensional situation The smooth curve in Fig 11-12 shows an arbitrary force F(x) that acts on a body that moves from to . Fig 11-12 i x i x f x f x x x F F1 F2 F (x) x 11-5 11-4
We divide the total displacement into a number N of small intervals of equal width Ax. This interval so small that the F(x)is approximately constant. Then in the interval x, to x,+dx, the work AW=FAx and similar△W,=F2△x The total work is W≈△+△W,+.=E1△x+F,△x+ or W≈>F△x (11-1 n=」 ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy We divide the total displacement into a number N of small intervals of equal width . This interval so small that the F(x) is approximately constant. Then in the interval to +dx , the work and similar ……The total work is or (11-12) = W F x 1 1 x = W F x 2 21 x 1 x = N n n W F x 1 ... ... W W1 +W2 + = F1 x + F2 x +