The basic concept of work is that it is force times distance. You do work on an object by applying a force over a certain distance. When you lift an object you apply a lifting force over the height that you lift the object. Machines are objects that allow us to do work more efficiently. For example, a ramp is what is called a simple machine. If you load objects into a truck, then a large ramp (large distance) allows you to apply less force to achieve the same work. All students should read my handout on simple machines. There it is clearly explained why work is defined as force × distance. Actually the proper physical definition of work is more complicated. The proper definition is

Writing

and

gives

Let's first look at the 1-dimensional case

If the force F_x is constant then it can be taken outside the integral to give

giving us back our original idea. The reason why we have an integral is in case the force depends on distance. The reason we have the scalar product .  is if the force and distance are at some angle, such as a tall person pulling a toy wagon along with a rope inclined at some angle. By the way, the units of work must be Newton × meter which is given a special name, Joule. Thus

Joule ≡ Newton meter

Example If I push a sled with a constant force of 100 N along a 5 m path, how much work do I do ?

Solution The force is constant and in only 1-dimension, so