Kinetic Energy and Work

In this post, we we will introduce the concepts of kinetic energy and work to you. The reason we eat food (chemical energy ) is a perfect example of the relationship between energy and work and how energy is converted into one form to another. When we eat food, we get “energy” and this energy can be used to do “work”. But if we keep lying at one place (That is also one kind of Work 😀 ) and be lazy , that would be our Potential Energy. However, if we do some Work or some exercise, that would be termed as Kinetic Energy.

Let us now talk about these quantities “scientifically”.

What is Energy?

Energy is a scalar quantity which is associated with the state of a system. It is very difficult to define energy in a usual way as it’s such a broad term. In a very generic way, we can say that energy is the ability to perform any work or heat an object. The beauty of energy is that it can’t be created or destroyed but can only be converted from one form to other. This universal law also forms the basis of first law of thermodynamics.

Energy can have numerous forms like potential energy, kinetic energy, electrical energy, chemical energy etc. Heat and work are two forms of energies which are not stored in system but are energies in transit, which means the form of energy which can be transferred. The former type of energy (heat) is of low quality and later (work)is of high quality. 

Units of energy in SI system is joules or N-m or kg-m²/s². Here we will talk about kinetic energy and work in following sections.

Kinetic energy

Kinetic energy is the energy of system due to its motion. Kinetic energy is directly proportional to mass of system as well as square of the velocity. For example a bullet has small mass but very high speed due to which it will have very high kinetic energy. On contrary, if you throw a big rock it will have lesser kinetic energy despite having much higher mass as compared to the bullet but very less velocity.

Work

Work is a form of energy that is transferred to or from a system by means of applied force. If a force f is applied on a body and it moves a distance s, then the work done on the body is given by

Which represents the dot product of force and displacement. Here θ represents the angle between force and work. Which means if a force is applied on a body vertically and body is moving in perfectly horizontal direction , the work done by the force will be zero as cos(90⁰) is 0.

Relation between Kinetic energy and Work

Let a bullet of mass m misses the aim and hits a wooden wall of thickness x, instead and passes through it. When it hits the wall, it has a velocity v_i and when it leaves the wall, it has a velocity v_o. It is obvious that velocity while hitting the wall will be greater than the velocity when the bullet leaves the wall because the wooden board exerts the resistance to the bullet. Let a constant retardation (negative acceleration) applied by wooden board on bullet is a, we can relate v_i and v_o as-

Multiplying equation by m,

From equation 1 and two we can see that change in kinetic energy of the bullet is equal to the work done by bullet on the wooden wall.

The above expression also verifies the energy conversion principle. It is to be noted that work (as well as heat) is the form that can only be transferred not stored while kinetic energy (or potential energy) can be stored in the system.

Also read our post on Newton’s Laws of Motions. Happy Reading 🙂