work - calculus

kittycat · #1 $Old$ November 1st, 2007, 01:59 AM

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 · #2 $Old$ November 1st, 2007, 06:48 AM

Quote:

Originally Posted by kittycat $View Post$

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 · #3 $Old$ November 1st, 2007, 07:45 AM

Quote:

Originally Posted by kittycat $View Post$

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.

Quote:

Originally Posted by kalagota $View Post$

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 · #4 $Old$ November 1st, 2007, 08:45 AM

Quote:

Originally Posted by CaptainBlack $View Post$

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 · #5 $Old$ November 1st, 2007, 10:08 AM

Quote:

Originally Posted by kalagota $View Post$

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 · #6 $Old$ November 1st, 2007, 09:07 PM

Quote:

Originally Posted by CaptainBlack $View Post$

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 · #7 $Old$ November 1st, 2007, 10:26 PM

Quote:

Originally Posted by CaptainBlack $View Post$

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..