788 Work and Energy △W,=F△rcos AW2= F2Arcos 0, △W.=F△rcos日 +)AW=F△rcos W=∑AW=∑ F Ar cos e
7&8 Work and Energy 1 1 1 W = F r cos 2 2 2 W = F r cos i i i W = F r cos n n n +） W = F r cos i n i W = W =1 i i n i F r cos 1 = =
788 Work and Energy Letr→>0 Cost W=lim∑F;4 rcos 6 Fdrcos0=Fdr B B W=F·dF=| Fcos adr When a particle moves from A to B along a curve path, the total work done by the force equals the integral from a to B
7&8 Work and Energy Let r → 0 i i n i r W F r lim cos 1 0 = → = Fdr cos b a = = b a F dr = = B A B A W F dr F cosdr Fcos A r B dr r r o When a particle moves from A to B along a curve path, the total work done by the force equals the integral from A to B
788 Work and Energy 4 Special expression in scalar product(p154) F=Fi+Fj+Fk, and dr=dxi +dyj+dck W=F·cF=(Fax+F如+F) =F+["F4+[F W=∫fdx+∫Fdy+∫Fdz 历=W+W+
7&8 Work and Energy , and ˆ ˆ ˆ F F i F j F k = x + y + z . ˆ ˆ ˆ dr = dxi + dy j + dzk = + + = = + + f i f i f i z z z y y y x x x B A x y z B A F dx F dy F dz W F dr (F dx F dy F dz) 4 Special expression in scalar product(p154) W = F x + F y + F z x d y d z d W =W x +W y +W z
788 Work and Energy 5 Work is a scalar quantity, no direction dw=F cos ]dr=Fcos ads dW= f 0°<6<90°,dW>0 positive work B 90°<6<180°,dW<0 negative work drke.F 6=90°F⊥dFdW=0 zero work
7&8 Work and Energy 5 Work is a scalar quantity, no direction. 0 90 , dW 0 dW = F cos dr = F cosds 90 180 , dW 0 W F r d = d = 90 F ⊥ dr dW = 0 F r d Fi 1 dr i r d B * * i 1 A F1 positive work; negative work. zero work;
788 Work and Energy 6 Geometrical Representation of Work: The work done by a force Cost equals the area under the F versus r curve 变力曲线 与位移轴在极限x,x2之间所包围ord7B 的面积 Example 7-5 and 7-6
7&8 Work and Energy 6 Geometrical Representation of Work: The work done by a force equals the area under the F versus x curve —— 变力曲线 与位移轴在极限x1, x2 之间所包围 的面积. Fcos A r B dr r r o Example 7-5 and 7-6