The gravitational potential in a region is given by `V=20Nkg^-1(x+y)`. A. Show that the equation is dimensionally correct B. Find the gravitational field at the point `(x,y)` Leave your answer in terms of the unit vector `veci,vecj,veck`. C. Calculate the magnitude of the gravitational force on a particle of mass 500 g placed at the origin.

Explanation

(a) `V=20(x+y)`
`E_(x)=(delV)/(delx)=-20`
`E_(y)=-(delV)/(dely)=-20`
`vecE=E_(x)hati+E_(y)hatj`
`=-20hati-20hatj`
(b) `|vecE|=E=20sqrt(2)N//kg`
`F=mE=0.5xx20sqrt(2)=10sqrt(2)N`