Abhishek DhawanSenior Executive – Editorial
- What is Work-Energy Theorem?
- Derivation of Work-Energy Theorem
- Derivation of Work-Energy Theorem: Step-by-Step
- Illustrated Examples on Work-Energy Theorem
- FAQs on Work-Energy Theorem
What is Work-Energy Theorem?
The work-energy theorem defines the relation between kinetic energy and total work. The sum of all the work is equivalent to the changes that occur in the kinetic energy. It can be extended to describe the rotational kinetic energy of stiff bodies and the work of the kinetic energy. The kinetic energy of an object can be defined as the energy it possesses due to the external force of the object.
In simple words, it is the work that is required to accelerate the object or to move the object from rest to motion. Examples of kinetic energy include a walking person, an apple falling from the table, books falling from the shelf, thrown football, etc. It can be perceived from the movement of an object or a particle.
Derivation of Work-Energy Theorem
Work done is said to be done when an external force acts on an object. If the displacement is 0, it is assumed that no work has been done. Work is defined as the change in kinetic energy, and it includes both displacement and force.
The work-energy theorem can be expressed as:
Here, ΔK represents the change in kinetic energy,
W is the work done; the unit of work is the joule.
Derivation of Work-Energy Theorem: Step-by-Step
The equation of motion is written as:
Equation of Motion
V2 = u2 + 2 as
Acceleration (assumed as constant)
The above equation can be rewritten as
- V2 – u2 = 2 as
After multiplying both the sides by m/2, we get the following equation –
- ½ mv2 – ½ mu2 = m a.d = F.d
We already know that W = F.d and Kinetic Energy = (mv2)/2
The equation will be derived as:
- Kf – Ki = W
By this equation we get,
- ΔK = W
- ΔK = Kf – Ki (this equation shows the change in kinetic energy.
After calculating the work-energy theorem, we can say that the work is equivalent to the change in an object’s kinetic energy.
Derivation of the work-energy theorem in class 11
The chapter of 'work, energy, and power' holds a significant weightage of 6 marks. It consists of one objective type question of 1 mark, one very short question of 2 marks, and one short question of 3 marks bringing a total of up to 6 marks.
Illustrated Examples on Work-Energy Theorem
Example 1) Illustrate the work related to displacement and force acting on an object.
Answer – The illustration is as follows:
Example 2) State the formula of the work-energy theorem.
Answer – The formula of the work-energy theorem is W = ΔK.
Example 3) State the formula used for the work done by a variable force.
Answer – The formula is ∆W =F (x) ∆x.
[Image Courtesy: NCERT]
FAQs on Work-Energy Theorem
Q: What do you mean by Kinetic energy?
Q: What is the S.I. unit of Kinetic Energy?
Q: What is the principle of the work-energy theorem?
Q: What is the formula used to calculate work?
Q: What is the formula of Kinetic energy?