Question

Determine the work done by a force f=xyi+yzj+xzk in taking along a path defined by the equation. r(t)=ti+2t²j+t³k; 0_<t<_1from t=0 to t=2 . Is this force conservative?

Answer 1

Gives

$F=xyi+yzj+xzk\rightarrow(1)$

$r(t)=ti+2t^2j+t^3k\rightarrow(2)$

$w=\int F.dr\rightarrow(3)$

$dr=i+4tj+3t^2k$

at Point(0,2) $dr=i+8j+12k$

equation (3) put value

$w=\smallint(xyi+yzj+zxk).(i+8j+12k)$

$w=xy+8yz+12zx$ Jule

Work done by force