Chapter 4 Kinetics of a Particleslope = lim: tangentdxAxdfdxdifferenti al = df = slope × △x :0 and f"<0Local maximum occurs, when0 and f"> 0Local minimum occurs, whendxmaxf(x)Afminx△xJumpto firstpage
Jump to first page Chapter 4 Kinetics of a Particle 0 and " 0 d d Local minimum occurs, when 0 and " 0 d d Local maximum occurs, when d d d differenti al d slope tangent d d slope lim = = = = = = = = f x f f x f x x f f x x f x f x f(x) x f max min
Integration: the reverse of differentiationTo calculate the area under the curve from xoto x :xNf(x)Z f(xi)Ax; = [ f(x)dxlimAx -→0i=1小。x+△xdj f(x)dxTf(x)dx- j f(x)dxXoXoxolimdxAxAr → 0xAxf(x)Axxof(x)x x+△x△xJumptofirstpage
Jump to first page Integration: the reverse of differentiation xo x+x x x f(x) x ( ) ( ) ( ) ( ) lim ( ) ( ) ( ) lim To calculate the area under the curve from : 0 1 0 f x x f x x x f x dx f x dx dx d f x dx x x f x dx i x i f x x t o x x x x x x x x o o o o x N i o x i = − = + → → =
Newton's 2nd lawF2ZF=maiFF =maF=maand F=ma1yyFwhere F.= F. +F2xLx1F, = Fi, + F2yF=F+ F,12zZ17Newton's 1st lawZF =O, ma=0, a=0, =constant7Jump to first page
Jump to first page F2 F1 FR z z z y y y x x x x x y y z y i F F F F F F F F F F ma F ma F ma F ma i 1 2 1 2 1 2 where , and = + = + = + = = = = Newton’s 2nd law F = 0, ma = 0, a = 0, v = constant i i Newton’s 1st law
POW!Newton's 3rd lawaction = reactionPOW!Jump to firstpage
Jump to first page Newton’s 3rd law action = reaction
Work donedU=F.dr = Fds cosα,= F,dx+ F,dy+ F,dzdrwhere ds = |driαTotal work done U = [ F .drFExample 1 What is the work done by aB个iforce on a articlegha)in circular motion?b)horizontal motion?FAc)from A to B?/////////Jump to first page
Jump to first page Work done dU =F dr = Fds cos, F x F y F z = x d + y d + z d ds dr where = U = F dr Total work done Example 1 What is the work done by a force on a article: a) in circular motion? b) horizontal motion? c) from A to B? F dr v F A B h g