Question

force acting on a particle in conservative force field is
1. F=(2i+3j)
2.F=(2x i+ 2y j)
3.F=(yi+xj)
find the potential energy function if it is zero at origin

Answer 1

\[E=-\int\limits_{0}^{x}F_xdx-\int\limits_{0}^{y}F_ydy\]

Answer 2

\[ E=-\int\limits_{0}^{r}Fdr=-\int\limits_{0}^{r}(2i+3j)dr\]

Answer 3

dr=dxi+dyj+dzk

Answer 4

But Fdr is a dot product, then it is Fx·dx+Fy·dy

Answer 5

yyaa ryt
then how are u able to solve it furthermore u cnnot put the value of i and j in integration
can u?

Answer 6

F=2x+3y

Answer 7

of course minus F

Answer 8

You have to integrate:

\[(F_x \hat i+F_y \hat j)·(\hat i dx+\hat j dy)=F_xdx+F_ydy\]

Answer 9

kkk.....

Answer 10

Case number 2
\[E=-\int\limits_{0}^{r}(2x \hat i+2y \hat j)(\hat i dx+\hat j dy)=-\int\limits_{0}^{x}2xdx-\int\limits_{0}^{y}2ydy=-(x^2+y^2)\]

Answer 11

what will be dr in 1st case

Answer 12

dr=dxi+dyj+dzk

Answer 13

dr is always ^idx + ^jdy what changes is the force Fxi^+Fyj^

Answer 14

In first case Fx=2 and Fy=3, the you have to integrate -2dx-3dy---->E=-(2x+3y)

Answer 15

how will we solve for third part

Answer 16

integrate -(Fxdx+Fydy)= integrate -ydx-xdy----->E=-(yx+xy)=-2yx

Answer 17

bt in answer it is given as only -xy

Answer 18

Then they have given the wrong answer

Answer 19

yaa u mst be right bcuz i m also getting the same answer aftr its integration