Whenever an object is displaced, work occurs. Some examples of this include a bat hitting a ball, a coolie lowering a bag to the ground, or a cyclist paddling a cycle.
There is an uncanny symmetry between the way work is done and the energy it requires. The magnitude of force is equal to the magnitude of distance travelled. The cosine function is the key to handling the direction of displacement. A block sitting on a horizontal surface is subject to a constant force F. However, a ball rolling on a slippery surface is not affected by the horizontal force.
The SI unit of work is the joule. It is also known as the energy unit. The unit is named after 19th-century English physicist James Prescott Joule. It is a measure of the energy required to push or pull a mass of one meter through a given distance.
It is also the scalar product of the magnitude of the force and the distance travelled. The formula is a little more complicated than that. For example, a force of five newtons over a distance of three meters would move an object two meters. A car travelling at a constant speed of five meters per second will reach its destination in two minutes.
The best way to understand the concept of work is to look at the context. To define work in the context of the office, a worker may not be thinking of the same concept that applies to a laboratory. For example, a coolie pushing a heavy load of luggage to the ground is not doing the same sort of work that a physics teacher might be doing before class. The same could be said for a mechanically inclined person repairing a gadget.
The scalar product of the magnitude of force and the distance travelled is the work that is relevant to this equation. The most obvious way to calculate this is to multiply the force by the distance travelled. Another more complicated calculation is to integrate the magnitude of the power over the trajectory of the point of application. The resulting equation is a good starting point.
The other stipulation is that the most interesting way to define work is not to think about the most efficient way to carry out a task. For example, carrying a heavy load over level ground is not the most efficient way to do it. The same could be said for a long-term force, such as a weightlifter holding 150 kg for 30 seconds. In the case of the Atwood machine, internal forces on the rope do not contribute to the work.
The most significant feature of work is its relationship to energy. A joule is a good approximation to the power of the energy. It is important to note that the SI unit of joule is not the taoist of the work unit. This is because the unit of joule is the unit of energy, not the unit of time.