Question

Find the work done by the force field F= (y2/2, Z, x) in moving a particle along the curve C, where C is the intersection curve of the plane x +z = 1 and the ellipsoid x2 + 2y2 + x2 = 1 oriented counterclockwise when viewed from positive z— axis.

Answer 1

Solution web Given that, The force field is ² =< y2, 2, x) in moving a particle along the cutive C, . where c is the intensection Clerve of the plane at z 2 and x+2y + 2 =1 The ellipsoid Now, 1. x²+2y + z = ii. X+ Z=1 X + 2 → .22"+2y-2x = 0 → 68 - 5)*+5° = ?

The parametric equation of the cusive c is r(t) = [ { cost+te, se sentes l_ cost- : 812) = (cost + ši sint, ý costą] Now we have to find the work done FF da FF (x (t)): 8'de - cost, } cost +į). - - Eu sint , { cast, . stat) at • - ?fstast + Cost-cos't+ sint cost + sint) dt 4.

The work done = { [-) :: (-114 [lo + 11) & 1 ] - {** 1950, f**; D4--]3 [plaasot), -) {heimso --033.84 1P (3,9-788) Sort 7p (_0+7 959 – 7603+0) 51 - 7P (otot750) - 7500 to 1