Work is the amount of energy that a force would require to displace an object.
When a force acts on an object and, as a result, the object is displaced then it said that work was done on the object. The three components of work done are, displacement, force, and cause. IF either one of these three components are missing, then work was not done.
| Statement | Whether work was done or not |
|---|---|
| A teacher applies a force to a wall and becomes exhausted. | No (no displacement) |
| A book falls off a table and free falls to the ground. | Yes |
| A waiter carries a tray full of meals above his head by one arm straight across the room at constant speed. | No (no cause) |
| A rocket accelerates through space. | Yes |
$$ W = F\times d \times \cos\theta $$
Where W is work, F is force, d is displacement, and $\theta$ is the angle between the F and d vectors.
There are 3 cases:
$\theta = 0\degree$ . This means that the direction of force and direction of displacement are the same. In this case, $W = F\times d,\text{ }W\gt 0$
$\theta = 90\degree$ . This means that the direction of force and direction of displacement are perpendicular. In this case, $W = 0$
$\theta = 180\degree$ This means that the direction of force is opposite to the direction of displacement. In this case, $W = F \times d,\text{ }W\lt 0$.
Work is measured in Joules(J).
$$ 1\text{ Joule} = 1\text{ Newton} \times 1\text{ meter}\newline \text{J} = \text{N}\times\text{m} $$