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The potential energy function of a particle in x-y plane is given by U=k(x+y) where k is a constant .The work done by the conservative force in moving a particle from (1,1)to (2,3) is..

The potential energy function of a particle in x-y plane is given by U=k(x+y) where k is a constant .The work done by the conservative force in moving a particle from (1,1)to (2,3) is..

Grade:11

1 Answers

Susmita
425 Points
5 years ago
Let the displacement vector be r.
\vec{r}=xi+yj
d\vec{r}=dxi+dyj
Also force 
\vec{F}=-\vec{grad}U=-(i\frac{\delta}{\delta x}+j\frac{\delta}{\delta y})U
                                 =-ki-kj
Work done
dW=F.dr=-kdx-kdy
Integrating dx from 1 to 2 and dy from 1 to 3
W=-3k
 
 
 

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