A `4.00-kg` particle moves from the origin to position C, having coordinate `x=5.00m` and `y=5m`. One force on the particle is the gravitational force acting in the negative y direction. Using equation `W=FDeltarcostheta=vecF.Deltavecr`, calculate the work done by the gravitional force on the particle as it goes from O to C along (a) OAC, (b) OBC, and (c) OC. Your results should all be identical. Why?

Explanation

`F_g=mg=(4.00kg)(10.0ms^-2)=40.0N`
a. Work done along OAC=Work along OA+Work along AC
`=F_(g)(OA)cos 90.0^@+F_(g) (AC)cos 180^@`
`=(40.0N)(5.00m) cos 90^@+(40.0N)(5.00m)cos180^@=-200J`
b. Work done along OBC=W along OB+W along BC
`=(40.0)(5.00m)cos180^@+(40.0N)(5.00m)cos90.0^@=-200J`
c. Work done along `OC=F_(g)OCcos135^@`
`=(40.0N)(5.00xxsqrt2m)(-1/sqrt2)=-200J`
Work done is same in all cases because gravitational force is a conservative force.