3.1 Work Done by a Constant Force
In Physics, the word "work" takes on a different meaning from the one commonly used. Work is defined as a force applied through a distance. Work done on an object by a constant force is the product of the objects displacement and the force acting parallel to the displacement. In mathematical terms
The SI unit for work is the joule (J). One joule is the product of one Newton and one meter, or a joule is a one-Newton force applied through one meter, J = Nm. For example, if a girl pushes a box with a 5.0-Newton horizontal force, and the box travels 2.0 meters in the direction of her push, the amount of work done is (5.0 N)(2.0 m) = 10 joules.
While Equation 3.1 is valid for forces applied parallel to the direction of travel of an object, non-parallel forces present a problem. To calculate the work done by a force applied in a direction that is not parallel to an objects displacement, we must calculate the component of the force applied in the parallel direction. To do this, we can use Equation 3.2:
where q is the angle between the directions of the force and the net displacement.
Consider a man carrying a bag of groceries and walking with a constant velocity of 0.75 m/s. The bag moves only in the horizontal direction (it travels with the man at a constant 0.75 m/s). What is the net work done to the bag in a one-minute interval?
In one minute, the bag travels (0.75 m/s)(1.0 min.)(60 s/min.) = 45 m. Next, we calculate the force applied to the bag. From carrying groceries (or anything else) ourselves, we know that the man must be applying a force to the bag in both the horizontal and vertical directions. However, recall Equation 2.1, representing Newtons second law of motion. Force is the product of mass and acceleration. The bag of groceries is not accelerating. The net force applied to the bag is 0 N, thus the net work done to the bag is (0 N)(45 m) = 0 J.
The net work done on an object is the algebraic sum of the work done by each acting force.