Work 
Introduction
It is impossible to fully understand the physical concept of Work without an understanding of the concept of Energy. Unfortunately, energy is defined as the ability to do work.
You probably have a general idea about what energy is. You know it comes in many forms - light, heat, motion, for example. It turns out that work is just another form of energy. Light and heat can do work and work can create light and heat.
Mathematical definition of Work
Work is a transfer of energy caused by a force. When a force causes a mass to be displaced in the direction of the force, work is done by the force on the mass, transferring energy to the mass.
Officially the definition is, Work: the product of the magnitude of the displacement times the component of the force parallel to the displacement.
In equation form, we can write:
W = F d cosθ
Consider the case below where some dude is dragging a box with a rope through a distance d by a force F.
This dude is doing work on the box. He is transferring some of the energy stored in his muscles into the box. But only part of his energy becomes the force that does work. Because he does not pull in the direction of the dispacement, only the component of the force (Fcosθ) that points in the direction of d does work. The rest of the force is trying unsuccessfully to raise the box and thus does no work.
Work is a scalar (it has no direction) but it can be positive or negative. (More on what negative work is later).
The units for work, the Joule, can be derived from its formula:
force × distance = Newtons (N) × meters(m) = Joule(J)
It feels like work!
Using energy does not necessarily mean that work is being done.
Work is only done if:
- a force causes a displacement
- the force (or a component of the force) points in a direction parallel to the displacement
Here are some examples where a force is applied, where energy is expended, but where no work is done:
- pushing the classroom wall
- walking a bag of groceries across the room at a constant speed
- spinning a rock on a string in a horizontal circle at constant speed
Sign Convention
When energy is transferred into a system by a force, we say that positive work is done on the system. In the example with the dude pulling the box, the dude does work on the system, so this work is positive. The box should have more energy that it did before it was pulled.
But you know that when you stop dragging a box, the box does not keep moving. It doesn't seem to have any more energy. Where did the energy inputed by the work go?
There is another force acting on the box as it is dragged across the floor - friction.
The friction does negative work on the box. All the energy put into the box by the dude is taken out again by the friction force. Mathematically, the friction force is exerted at an angle of 180° to the displacement and the cosine of 180° is −1.
If you reduce the friction force, by putting the box on wheels for example, then when the dude stops pulling the box keeps moving - it has energy of motion (kinetic energy).
Example - Dude pulls a box
A) the work done by the dude.
B) the work done by friction if the box stops immediately after the dude stops pullling.
C) the value of the coefficient of kinetic friction.
