8 In physics work done by a constant force F on an object th

(8) In physics, work done by a constant force F on an object that is displaced s is F · s. Find the work done by a constant force F = 8i 3j + 7k that moves an object from point (0, 4, 7) to the point (6, 15, 13) along a straight line. The distance is measured in meters and the force in newtons.

Solution

object moves from point A(0,4,7) to point B(6,15,13)

displacementS=AB=p.v. of B - p.v. of A

                            =(6i+15j+13k) - (0i+4j+7K)

                             =(6-0)i+(15-4)j+(13-7)k

                            =6i+11j+6k

so workdone by the constant forceW=F.S=(8i-3j+7k).(6i+11j+6k)

                                                             =[(8)(6)+(-3)(11)+(7)(6)]

                                                             =48-33+42

                                                             =57 newtons