Force acting on particle is given by `vec(F) = 2xyz hat(i) + x^(2)x hat(j) + x^(2) y hat(k)`. Report the amount of work done in joule in displacing a particle of mass 2 kg from (0, 0, 0) to (1, 2, 3), acted upon by the given force.

Answer

6

Explanation

`d omega = vec(F) . vec(d)r`
`d omega = (2xyz hat(i) + x^(2) z hat(j) + x^(2) y hat(k))`
`(dx hat(i) + d y hat(j) + dz hat(k))`
`omega = int 2xyz dx + int x^(2) zdy + int x^(2) y dz`
force is conservative,
So, `omega = 2yz underset(0)overset(1)int x dx + x^(2)z underset(0)overset(2)int dy + x^(2)y underset(0)overset(3)int dz`
`overset(~)omega_(1) " " overset(~)omega_(2)" " overset(~)omega_(3)`
`omega_(1) = 2yz underset(0)overset(1)int x dx = 0`
`y = z = 0`
`omega_(2) = x^(2)z underset(0)overset(2)int dy = 0`
`x = 1, z = 0, y = 2`
`omega_(3) = x^(2)y [z]_(0)^(3)`
`omega_(3) = (1)^(2) xx (2) (3) = 6 J`
`omega = 6 J`