UNIVERSITY PHYSICS I CHAPTER 8 Work, Energy and The CWe Theorem §8.1 Work done by variable force 1. Why we introduce the concepts of work and energy? F total=ma CWE theorem CWE theorem Conservation of energy (More universal) 2. About the systems that we discuss Ignore the size, internal structure, internal motion, deformations, and thermal effects
1 1. Why we introduce the concepts of work and energy? F ma CWE theorem r r total = CWE theorem Conservation of energy (More universal) 2. About the systems that we discuss Ignore the size, internal structure, internal motion, deformations, and thermal effects. §8.1 Work done by variable force
88.1 Work done by variable force 3. The work done by a constant force W=F.Scos6=F·S 4. The work done by variable force differential work b dw s F dr F.dr. cos 0 Fcos ads F 88.1 Work done by variable force Define the differential work done by any force is dW= fdr The work done by a particular force eis w=dw=Fdr In Cartesian coordinate system W=(Fi+E,j+F) dr d b dxi+dvj+dzk) (F dr+ f dy+F,dz) F
2 W F S F S v v = ⋅ ⋅ cosθ = ⋅ θ F v s v F v 3. The work done by a constant force F s F r W F r cos d d cos d d θ θ = = ⋅ ⋅ = ⋅ v v v differential work a b o F v r v d ds r v r′ v θ F r 4. The work done by variable force §8.1 Work done by variable force §8.1 Work done by variable force Define the differential work done by any force is W F r r r d = ⋅d The work done by a particular force is F r ∫ ∫ = = ⋅ f i W F r r r W d d In Cartesian coordinate system: ( d d d ) )ˆ d ˆ d ˆ (d ) ˆ ˆ ˆ W ( F x F y F z xi yj zk F i F j F k y z r r x y z r r x f i f i = + + + + = + + ⋅ ∫ ∫ r r r r a b o F v r v d ds r v r′ v θ F r
88.1 Work done by variable force w=l(F dr+ F dy+ F, dz) Fd+∫F中+F Work done by a constant force: =x1++k x l+yr/+3 W=∫Fx+「F+Fdz F(x-x)+F,(r-yi)+F(z-i) W=F·=F(7-) 88.1 Work done by variable force The properties of the work Work is a scalar quantity; A<0,A=0,A>0 @the work done by a force depends on the path followed by the system w=f&dr=f2 AF=(fni).(si)=-frs H=「m7·d=7:,=()(-s)=s Welsdnath =w+w=-fis-fiS=-2fRS
3 ∫ ∫ ∫ ∫ = + + = + + f i f i f i f i z z z y y y x x x y z r r x F x F y F z F x F y F z d d d W ( d d d ) r r Work done by a constant force: r x i y j z k r x i y j z k f f f f i i i i ˆ ˆ ˆ ˆ ˆ ˆ = + + = + + r r ( ) ( ) ( ) W d d d x f i y f i z f i z z z y y y x x x F x x F y y F z z F x F y F z f i f i f i = − + − + − = + + ∫ ∫ ∫ ( ) f i W F r F r r r r r r r = ⋅∆ = ⋅ − §8.1 Work done by variable force The properties of the work: 1work is a scalar quantity; 2the work done by a force depends on the path followed by the system; §8.1 Work done by variable force W f r f r f i si f s k k k B A = k ⋅ = ⋅ = − ⋅ = − ∫ )ˆ ) ( ˆ d ( r r r r ∆ W f r f r f i si f s k k k A B = k ⋅ = ⋅ = ⋅ − = − ∫ )ˆ ) ( ˆ d ( r r r r ∆ A B s x y W W W f s f s f s k k k 2 clsd path = + ′ = − − = − A < 0, A = 0, A > 0
88.1 Work done by variable force @the work done by a force depends on the choice of the reference frame. Elevator: W=0, Earth:W≠0 @the work done by a pair of forces is not always zero. M N +形 N 0 W,+W<0 88.1 Work done by variable force 5. The work done by the total force The work done by the total force acting on the system is the algebraic, scalar sum of the work done by the individual forces total ∫m(丙++ F1·d+F2dr+ W,+W,+
4 3the work done by a force depends on the choice of the reference frame. Elevator:W=0, Earth: W≠0 y W g r v r + ′ = 0 W N W N N r ′ v c N r v m f c r ′ s s ′ M + ′ < 0 W f W f f r m §8.1 Work done by variable force 4the work done by a pair of forces is not always zero. 5. The work done by the total force The work done by the total force acting on the system is the algebraic, scalar sum of the work done by the individual forces. §8.1 Work done by variable force L L r r r r r L r r r r = + + = ⋅ + ⋅ + = ⋅ = + + ⋅ ∫ ∫ ∫ ∫ 1 2 1 2 total total 1 2 d d d ( ) d W W F r F r W F r F F r f i f i f i
88.1 Work done by variable force 6. The the geometric interpretation W=Fdx+”F+Fdz The work done on the system by the force component as the system moves from r tor is the area under the curves of the graph of that force components versus the corresponding coordinate. 88.1 Work done by variable force Positive or negative work(area) depends on both the sign of the force and the direction of Ar Initial position Final position Initial position Ar=(x-x)i Ar=(x-x)i Parallel to 1 Parallel to-i
5 §8.1 Work done by variable force 6. The the geometric interpretation ∫ ∫ ∫ = + + f i f i f i z z z y y y x x x W F dx F dy F dz The work done on the system by the force component as the system moves from to is the area under the curves of the graph of that force components versus the corresponding coordinate. ir r f r r Positive or negative work (area) depends on both the sign of the force and the direction of . r r ∆ §8.1 Work done by variable force