Question

Find out the potential energy of given by F=-2xi cap -2yj cap

Answer 1

Answer:

dU = -F{DC

=-[-2x^2/2 -2y^2/2]

=x^2+ y^2

Answer 2

Answer:

U = x² + y² + C

Explanation:

To find:the potential energy of given by F=-2xi^  -2yj^

Solution:

When conservative force does positive work then PE decreases,

i.e dU  = -dW

where, U = potential energy and W = work done

then,

$\displaystyle \int dU = \int - \left(-2x\hat{i}-2y\hat{j}\right).\left(dx\hat{i}+dy\hat{j}\right)\\\\\int dU = \int 2xdx+\int2ydy\\\\\boxed{U=x^2+y^2+C}$