Ch. 11 Energy I: Work and kinetic energy ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy Ch. 11 Energy I: Work and kinetic energy
11-1 Work and energy Example: If a person pulls an object uphill. After some time, he becomes tired and stops We can analyze the forces exerted in this problem based on Newtons Laws, but those laws can not explain: why the man's ability to exert a force to move forward becomes used up For this analysis, we must introduce the new concepts of Work and Energy ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy 11-1 Work and energy Example: If a person pulls an object uphill. After some time, he becomes tired and stops. We can analyze the forces exerted in this problem based on Newton’s Laws, but those laws can not explain: why the man’s ability to exert a force to move forward becomes used up. For this analysis, we must introduce the new concepts of “Work and Energy
Notes: 1)The "physics concept of workis different from the work in daily life of its 2)The" of a system is a measure its capacity to do work ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy Notes: 1) The “physics concept of work” is different from the “work in daily life”; 2) The “energy” of a system is a measure of its capacity to do work
11-2 Work done by a constant force 11-3 Power 1. Definition of work The work W done by a constant force f that moves a body through a displacement s in the directions of the force as the product of the magnitudes of the force and the displacement W=FS (Here S/F)(11-1) ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy 11-2 Work done by a constant force 1.Definition of ‘Work’ The work W done by a constant force that moves a body through a displacement in the directions of the force as the product of the magnitudes of the force and the displacement: (11-1) F s W = Fs (Here ) s//F 11-3 Power
EXample: In Fig 11-5, a block is sliding down a plane The normal force n does zero work; the friction force f does negative work, the gravitational force mg does positive work which g s mgs o= mgh Fig 11-5 or mgs cos =s(mg cos o) ch 11 Energy I: Work and kinetic energy
Ch.11 Energy I: Work and kinetic energy The normal force does zero work; the friction force does negative work, the gravitational force does positive work which is or → N → N mgscos = mgh mgscos = s(mg cos) → m g → m g → f s h v Fig 11-5 → f Example: In Fig11-5, a block is sliding down a plane
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 +