Question

Find the work done by the vector field F(x, y) = {xy i + áraj (the vector field from Question 1) on a particle that moves from (0,0) to (0, 1) (moving in a straight line up and along the y axis) and then from (0, 1) to (3, 2) along the curvey= Vx+1. Thus the path is given by along the curve y=x+1 (0,0) up the y-axis + (0,1) (3,2) 1 F. dr 2 F. dr = 0 18 8.- 18.dr 10.- 9 = 2 1 2

Answer 1

Given vector field Elxsy) = 1 nyårt 2] $(0,1) up the y-ani's (0,0) along the curve Y=rati (3,2) E = 1 / nył + 24 25 š= xi ty dr = idx+j dy F. dr = 6 xy itt x j) (idxtjdy) dx + t x dy a) Hence along (0,0) –> (01) x=0,=dx =0, Ēdr £ ay dat tady y zo Žay y =o to I Sot 16,10 100) (0,0) = 0 b) (0,1) (3,2) (21,91) (22,92) 4-1 = 2-1) (2-0) (3-0) y 1 = 1/2 34-3=x 34= at 3 = "=1/3 (x+3) dy = 1/3 dy = /2 dx ; x=3 x=0 y=1 y=2 CS Scanned with CamScanner

Ź (34-3).Y. 3 dy + + (34-3}. dy 4 oyst y=1 = 4 9 2 (yysdy +9 +91 (571-2y) dy s 18 (4²9) + 91422y +1) dy = 65,7279?-364+9) dy = 4 27.4 - 36 2 day] = 4y - Rymd (72-72+18 - 9+1849) ť 3 t = 9 2 old 0 +2 = =0+9 old 2 Thus the work done by vector field is 9 option SF. dr = 9 cs Scanned with CamScanner