A particle in a certain conservative force field has a potential energy given by U= (20 xy)/(z). The force exerted on it is

A particle in a certain conservative force field has a potential energ

1.	A particle in a certain conservative force field has a potential energy given by U= (20 xy)/(z). The force exerted on it is
Answer» `((20 y)/(Z)) hati + ((20x)/(z))hatj + ((20 xy)/(z^2))hatk` `-((20 y)/(z)) hati - ((20x)/(z))hatj + ((20 xy)/(z^2))hatk` `-((20 y)/(z)) hati - ((20x)/(z))hatj - ((20 xy)/(z^2))hatk` `((20 y)/(z)) hati + ((20x)/(z))hatj - ((20 xy)/(z^2))hatk` SOLUTION :Given `U = (20 xy)/(z)` For a CONSERVATIVE field, `vecF = -vec(nabla)U` where , `vec(nabla) = hati (DEL)/(del x)+ hatj (del)/(del y) + hatk (del)/(del k)` `:. vecF = -[hati (del U)/(del x) + hatj (del U)/(del y) + hatk (del U)/(delz)]` `= - [hati (del)/(del x) ((20xy)/(z)) + hatj (del)/(del y)((20 xy)/(z)) + hatk (del)/(del z) ((20 xy)/(z))]` `= -((20y)/(z)) hati - ((20 x)/(z)) hatj + ((20 xy)/(z^2) hatk`.