Work and Energy

Work

Work is done when a force moves an object over a distance. It can be calculated as the product of the force (F), the distance moved (s) and the cosine of the angle between them: Work = Fs cos θ.
When the force and displacement are in the same direction, the angle taken is 0 degree and cos 0 = 1. So, Work = Fs.
Work done against gravity is given by the product of the weight of the object (mg) and the vertical height it’s raised (h): Work Done = mgh.
Negative work is done by a force when its direction is opposite to the direction of displacement.
In the case of a variable force, the work done can be given by the area under the force-distance graph.

Energy is the capacity to do work. It’s a scalar quantity and its Unit is the Joule (J).
There are different types of energy, among which are Potential Energy (due to an object’s position), Kinetic Energy (due to an object’s motion), and Mechanical Energy (Total Energy) which is the sum of potential and kinetic energy.
The Potential Energy (PE) of an object is the energy it possesses due to its position relative to others or due to its configuration. For an object under the effect of gravity, PE = mgh.
Kinetic Energy (KE) of an object is the energy it possesses due to its motion defined by: KE = 1/2 mv^2.
The Total Mechanical Energy in an isolated system remains constant if only conservative forces are doing work (Principle of Conservation of Mechanical Energy).

The Work-Energy Theorem states that the work done on a system is equal to the change in kinetic energy of the system. This is a special application of Newton’s Second Law of Motion.

Power is the rate at which work is done, expressed as the amount of work per unit time. It’s calculated by the equation Power = Work / Time. The unit of power is the Watt, where 1 Watt equals 1 Joule/second.
When dealing with rotational motion, we use torque instead of force and angular displacement instead of straight-line displacement in our calculations.

An important principle of physics is that energy can neither be created nor destroyed; it can only be transformed from one form to another. This principle is known as the Law of Conservation of Energy.
Energy transformations are common in many everyday situations. For example, the potential energy of a roller coaster car at the top of a hill is transformed into kinetic energy as it speeds down the hill. Knowing how to calculate these transformations can be very useful in solving real-world problems.