Mechanics: Work Done

Definition of Work Done

Work Done is a quantity which represents energy transferred between systems and is only done when a force moves something.
Express mathematically, Work Done = Force × Distance moved in direction of Force.
The SI unit for Work Done is the Joule (J), same as energy.

When force and displacement are in the same direction, the calculation of work done is simple multiplication of force and displacement.
If force and displacement are at an angle, the work done is the force multiplied by the displacement multiplied by the cosine of the angle between force and displacement.

Since work done is a type of energy, it’s important to remember the Law of Conservation of Energy: energy cannot be created or destroyed, only transferred or transformed.
Therefore, when work is done, energy is transferred from one form to another. Typical examples are from potential energy to kinetic energy and vice versa.
In situations where energy is lost due to work done against friction, the lost energy is transformed into heat energy.

Understanding the relationship between potential energy and work done is essential for calculating the work done in lifting an object to a height, it’s mgh, where m is mass, g acceleration due to gravity and h is height.
In scenarios involving springs, the work done can be calculated using the formula: Work Done = 1/2kx², where x is the amount of displacement or compression, and k is the spring constant.

Force-Displacement Graphs are often used to demonstrate work done. The area under the graph represents the work done.
In the context of changing forces, like springs, the work done needs to be calculated as the integral of force with respect to distance. In these instances, the area under the Force-Displacement graph isn’t a perfect rectangle, but the area still represents work done.