The work-energy principle states that:
The net work done on an object is equal to the change in kinetic energy of that object
This principle is as a result of the conservation of energy and in equation form can be written as:
Where W is the net work done and ΔKE is the change in kinetic energy.
Derivation of the Work-Energy Principle
Newton’s second law can be used to derive the work-energy principle.
Imagine an object of mass m, travelling with constant acceleration, a. The distance, d, travelled by the particle can be calculated using the following SUVAT equation:
Where vf is the final velocity of the object and vi is the initial velocity of the object. We can rearrange to make the d the subject:
The acceleration on the particle is caused by a resultant force, F, acting on the object. We can calculate the net work done, W, on the object using the following equation:
From Newton’s second law we know that the resultant force and acceleration have a relationship given by the following equation:
If we substitute this along with the distance d into the work equation we get:
This simplifies to:
As you can see we now have an equation in which the net work done on the object is equal to the change in kinetic energy of the object:
Where KEf is the final kinetic energy of the object and KEi is the initial kinetic energy of the object.
Worked Examples
Example 1
The net work done on an object is 100J. It’s final kinetic energy is 137J. Calculate the initial kinetic energy of the object.
Example 2
The initial velocity of an object of mass 5kg is 3ms-1. The net work done on the object is 50J. Calculate the final velocity of the object giving your answer to 1 decimal place.
Example 3
An object of mass 3kg travels 10m. The initial velocity of the object is 0ms-1 and it’s final velocity is 2.5ms-1. Calculate the net force that acted on the object giving your answer to 1 decimal place.
If you have any questions please leave them in the comments section below. You can stay up to date with the latest posts and news by following us on Instagram and Pinterest. For more posts use the search bar at the bottom of the page or click on one of the categories below.