Question

Let the C be the unit square in the ey-plane on the first quadrant with one vertex on the origin going from (0,0) (1,0) to (1,1) to (0,1) to (0,0). 7) Graph an estimate of F at (0,0), (1,0), (1, 1), (0,1), and (0,0) for each non-conservative F above; can yo tell why F is non conservative based on these plots? Explain in words. 8) Calculate SF. dr for F = (x, y) where is the top half-circle from (-4,0) to (4,0); hint: plot F along Ca at least three different points. C

Answer 1

solution- (7) (a) o F=(x, y) ənc y = LP, Q >. sy - Os) is conformation b) = (y,x) = <P,Q> ; = f is conervative. (C) F = Key, b> - <PQ> C. fis non conser op & Do mare vative F=<xy, a Foko,0> F=Lo17 (0, 1) - - - - - > (11) ito, 1)=40;o) Fe;いこく ) a Coo) Cio). 7 . As we nome from coo) to (10) to (1, 1) to cold to (0,0). The lit integral oda is so der to Sf.dr-o ; le der=positive quotity=1. I dr = -1 Sider=o. cy - Sodrto - F G non-conservative.

с (8) F=(x, y) = F G a conservative force - Line Integral of F y path Independent. Srider = ff.dr. coo) (4,0) (-40) (40) coo) c cuo) Coo) (40) = <x, f>. Ldx, o>+ say> <dx, o> (-40) F. doit c.dr. (10) 30,y> <dar Cool = 16+16-0