Question

The force F = 4 i + 2 j moves an object 3 ft along the x-axis in the positive direction. Find the work done if the unit of force is the pound.

Answer 1

Work is defined as:\[W=\vec{F}\cdot \vec{d}\]

Answer 2

Work done is scalar = Force . Displacement = | Force | * |Displacement| * cos theta
Theta = angle between force and displacement.

Or do it by the dot product method. [Which is much faster]

If
Force [F] = Fx + Fy + Fz
Displacement [S] = Sx + Sy + Sz

Then work done is their dot product which is
= Fx*Sx + Fy*Sy + Fz*Sz [That is multiply their magnitudes]

Got it? :D

Answer 3

Here you have F = 4i + 2j OR 4x + 2y
Displacement is along x axis so S = 3x or 3i

Now simply find the dot product by the latter method! :D

Answer 4

12 right for the dot method?

Answer 5

correct