Work is the Dot Product of Force and Displacement
Work done by a constant external force is equal to the dot product of external force and displacement. In other words, work is equal to the magnitude of an object's displacement while an external force is applied to the object multiplied by the magnitude of the component of the external force which is along the displacement. Note: The dot product of two vector quantities gives a scalar result. Thus, work is a scalar quantity.
The work done by a constant external force on a system is equal to:
In physical science class, we will work mostly with the first two orientations of force and displacement listed above. In addition, it should be noted that work can be done on a system ONLY by forces external to the system.
The work done by a constant external force on a system is equal to:
- + (the magnitude of external force) x (the magnitude of displacement of the system), for force and displacement in the same direction,
- - (the magnitude of external force) x (the magnitude of displacement of the system), for force and displacement in opposite directions, and
- (the magnitude of external force) x (the magnitude of displacement of the system) x cosine (theta), for force and displacement arranged in any orientation, and for theta equal to the angle between force and displacement.
In physical science class, we will work mostly with the first two orientations of force and displacement listed above. In addition, it should be noted that work can be done on a system ONLY by forces external to the system.