Path integral

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February 8th 2010, 12:37 PM
qwesl

Path integral

If $C$ is the curve given by $r(t)=(1+5sin{t}){i}+(1+2sin^2{t}){j}+(1+5sin^3{t}) {k}$ and $0\leq t\leq \frac{\pi}{2}$ and $F$ is the radial vector field $F(x,y,z)=x{i}+y{j}+z{k}$ , How do you compute the work done by $F$ on a particle moving along $C$
February 8th 2010, 01:34 PM
HallsofIvy

Quote:

Originally Posted by qwesl

If $C$ is the curve given by $r(t)=(1+5sin{t}){i}+(1+2sin^2{t}){j}+(1+5sin^3{t}) {k}$ and $0\leq t\leq \frac{\pi}{2}$ and $F$ is the radial vector field $F(x,y,z)=x{i}+y{j}+z{k}$ , How do you compute the work done by $F$ on a particle moving along $C$

$r(t)=(1+5sin{t}){i}+(1+2sin^2{t}){j}+(1+5sin^3{t}) {k}$ so
$dr= \frac{dr}{dt}dt= (5 sin(t)i+ 4sin(t)cos(t)j+ 15sin^2(t)k)dt$

Integrate the dot product of F and that from t= 0 to $\pi/2$ .

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