Work has the potential to change us in profound ways. It can bring discipline, wisdom, skill, and a deeper sense of purpose to our lives. It can help us find meaning in our days and build relationships with people who matter to us. It can also rob us of time, energy and passions, leaving us feeling empty and cynical. And of course it can also give us money and jobs that let us live a good life.
But what do we mean when we talk about work? The scientific definition of work is the amount of energy transferred when a force causes an object to move. This energy can take the form of kinetic, mechanical, or thermal. The SI unit for work is the joule (J).
To do work, a force must be applied over a distance to cause an object to move. The magnitude of the force and the direction in which the displacement occurs determines whether the work done is positive, negative, or zero.
In order for work to be done, an object must have a net positive change in its kinetic energy. The amount of this change is equal to the product of the force times the displacement divided by the time over which the work was done.
However, this is only true in a limited number of cases. For example, a person can hold a car stationary and not do any work on the wheels even though the tires are moving at a constant velocity. The reason is that the force acting on the wheel can be perpendicular to the displacement vector, which gives a result of zero for work.
Usually, the directional component of the force must be in the same direction as the displacement vector for an object to do work. However, this is not always the case, as the green figure below shows.
This is because the forces in this example are not pointing in the same direction as the motion of the ball. As a result, no work is being done on the ball by either force.
The same is true if the force is parallel to the displacement vector, such as the blue figure below. The fact that the force is parallel to the displacement does not affect the total amount of work done, but it does change the amount of energy transferred.
As you can see, there are many cases in which a force will exert a large amount of energy on an object and yet do no work at all. This is why it is important to consider the direction in which the displacement and force are being applied. Moreover, it is also important to understand that work can be done even when the direction of the displacement and the force are not the same. This is because of the scalar product (also known as the dot product) between two vectors. This is discussed in more detail in the section below on vector algebra.
