work - calculus

**kittycat** · October 31st 2007, 11:59 PM

given the force vector field F = <y,a> .
Find the work in moving an object through the vector field along the closed curve C formed by the arc of the ellipse x=acost , y=bsint, lying in the first quadrant, the x-axis, and the y-axis.

Please help me. thank you very much.

**kalagota** · November 1st 2007, 04:48 AM

Originally Posted by kittycat

given the force vector field F = <y,a> .
Find the work in moving an object through the vector field along the closed curve C formed by the arc of the ellipse x=acost , y=bsint, lying in the first quadrant, the x-axis, and the y-axis.

Please help me. thank you very much.

have you checked the previous post about work?
so,
$r(t) = x(t)i + y(t)j = (a \cos t)i + (b \sin t)j$
where t is from 0 to $\, \frac{\pi}{2}$
and
$F(x,y) = yi + aj$

note that
$W = \int_C F \cdot dr = \int_C <y,a> \cdot <dx,dy>$
$\, = \int_0^{\frac{\pi}{2}} y(t)dx(t) + a dy(t)$

can you continue?

**CaptainBlack** · November 1st 2007, 05:45 AM

Originally Posted by kittycat

given the force vector field F = <y,a> .
Find the work in moving an object through the vector field along the closed curve C formed by the arc of the ellipse x=acost , y=bsint, lying in the first quadrant, the x-axis, and the y-axis.

Please help me. thank you very much.

Originally Posted by kalagota

have you checked the previous post about work?
so,
$r(t) = x(t)i + y(t)j = (a \cos t)i + (b \sin t)j$
where t is from 0 to $\, \frac{\pi}{2}$
and
$F(x,y) = yi + aj$

Assuming kalagota is right and $F(x,y) = yi + aj$ is what is meant by F = <y,a> what field of study did you get this notation from. I'm sure that I'm not the only person at least partialy mystified by this notation

RonL

**kalagota** · November 1st 2007, 06:45 AM

Originally Posted by CaptainBlack

Assuming kalagota is right and $F(x,y) = yi + aj$ is what is meant by F = <y,a> what field of study did you get this notation from. I'm sure that I'm not the only person at least partialy mystified by this notation

RonL

we also that notation for vector fields, i.e. if we have a Field vector
$F(x,y)$
then it is equivalent to saying that
$F(x,y) = <x,y>$

**CaptainBlack** · November 1st 2007, 08:08 AM

Originally Posted by kalagota

we also that notation for vector fields, i.e. if we have a Field vector
$F(x,y)$
then it is equivalent to saying that
$F(x,y) = <x,y>$

Yes, but in this context who is the "we" you refer to?

That is what area of study uses this notation (I ask because it is not used
in any thing I have studies in this way).

RonL

**Jhevon** · November 1st 2007, 07:07 PM

Originally Posted by CaptainBlack

Yes, but in this context who is the "we" you refer to?

That is what area of study uses this notation (I ask because it is not used
in any thing I have studies in this way).

RonL

i've seen that notation before. it is from vector calculus, and you see it even in calc 3. in general we can use $\left< x_1, x_2, ..., x_n \right>$ to represent a vector with $n$ components. if the components are functions, as opposed to just numbers, we obtain a vector field, that is, a function that assigns an nth dimensional vector to each point

**kalagota** · November 1st 2007, 08:26 PM

Originally Posted by CaptainBlack

Yes, but in this context who is the "we" you refer to?

That is what area of study uses this notation (I ask because it is not used
in any thing I have studies in this way).

RonL

"we" as in all students of math/physics in our university..
we used it in our calc 3 also..

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