Question

Find the work done by the force field F that is not conservative. The distance is between two points. How would you approach this problem since the Fundamental Rules of Calculus do no apply.

Answer 1

integrate along the path F.dr

Answer 2

Don't you need to Integrate?

Answer 3

ya

Answer 4

vector integral

Answer 5

vector is <z,x,y> how would you do it when the path is a straight line?

Answer 6

give us the question..well see

Answer 7

between point (3,0,0) to point (0,pi/2,3)

Answer 8

when the path between those two points is a straight line

Answer 9

I'm having trouble knowing what to do when it's path dependent.

Answer 10

whats the force?

Answer 11

F(x,y,z)= z i + x j + y k

Answer 12

gotcha

Answer 13

so dr is the distance between the two points?

Answer 14

first write the eqn of a line in cartesian form like
x=3+3k
y=k(pi)/2
z=3k

Answer 15

parametric representation of the line segment right?

Answer 16

the work done is F.dr
which is <zdx, xdy, ydz>
right

Answer 17

sorry write y=-k(pi)/2 and z = -3k

Answer 18

got it till here??

Answer 19

Kinda it's just hard to remember how to find the parametric equations of a line

Answer 20

no bt ive written em down fr u nw

Answer 21

kk so use dot product of the vector with dr right?

Answer 22

so you just replace x y z with the parametric equations right?

Answer 23

so here goes
dot prod gives zdx + xdy + ydz

for zdx
write (-3k)(dx)
(-3k)(3dk)

Answer 24

now integrate this
-9k^2 dk from k =0 to k=-1

Answer 25

coz k=-1 gives u ur final point

Answer 26

got it?

Answer 27

yup

Answer 28

now similarly compute it for xdy and ydz and then add all three/

Answer 29

got it?

Answer 30

Yes so my area of integration is going to change because I reperamatize right?

Answer 31

yes integrate all three frm 0 to -1

Answer 32

bcoz remmbr on ur line k=0 gives the initial pt and k=-1 givs d final pt...so as our integrating variable is k, we use the lim its fr k

Answer 33

that should do it i spose

Answer 34

yup my book shows it but in two dimensions....

Answer 35

js get the answer and tally it..its complicated enough...ur book mightve represented it in 2d..fr me dis is d way i thot dis cld be done

Answer 36

wt hapnd??

Answer 37

nothing I got the answer