F = -2px i - py j (p constant) on a particle.

Show F is conservative and that p(x^2 + (y^2/2)) is a potential energy function for F.

Find work done to move particle from (5,0) to (0,5)

Question

F = -2px i - py j  (p constant) on a particle.

Show F is conservative and that p(x^2 + (y^2/2)) is a potential energy function for F.

Find work done to move particle from (5,0) to (0,5)

anonymous · Answer

derivative of  -2p x wrt to y is 0

derivative 0f -py wrt to x is 0 


hey they are the same , hence conservative


$$-2p \int x dx $$

$$-p  x^2 + g(y)$$


$$-p \int y dy $$

$$-p \frac{y^2}{2}+ h(x)$$


$$p(x,y)=-p  x^2  -p \frac{y^2}{2}$$

anonymous · Answer

p(x,y) at (0,5)-p(x,y) at (5,0) = work done

anonymous · Answer

Yup, 25p/2

anonymous · Answer

Now, if they weren't conservative , it would be a pain trying to remember stoke