Question

Show that F= 2xy+z3+x2j+3xz2 is a conservative force field ,Find potential energy,Find work done in moving object from (1,_2,1) to ( 3,1,4)

Answer 1

Answer:

$U = - x^2y - xz^3$

since the work done in closed path for above function is independent of the path so this is a conservative field

$W = -204 J$

Explanation:

As we know that

$F_x = -\frac{dU}{dx} = 2xy + z^3$

$F_y = -\frac{dU}{dy} = x^2$

$F_z = -\frac{dU}{dz} = 3xz^2$

now from above 3 equations we have

$U = - x^2y - xz^3$

since the work done in closed path for above function is independent of the path

so this is a conservative field

Now work done in moving the object is given as

$W = U_f - U_i$

$W = (- 3^2(1) - 3(4^3) ) - (- (1^2)(-2) - 1(1^3))$

$W = -201 - 3$

$W = -204 J$