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

`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`

Step-by-step explanation:

As we know that

`F_x = -(dU)/(dx) = 2xy + z^3`

`F_y = -(dU)/(dy) = x^2`

`F_z = -(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`