Work and Energy

Life is impossible without ENERGY. The sun is the biggest natural source of energy. We often use the term 'ENERGY' in our day to day life, but science give it a definite and precise meaning.

ENERGY is defined as the capability or capacity of doing work.

Or, capability of doing work is called ENERGY.

An object having a capability to do work is said to possess ENERGY.

The object which does the work loses energy and the object on which the work is done gains energy.

Example

When a fast moving cricket ball hits a stationary wicket, the wicket is thrown away.

This fast moving ball can make a dent in a wall.

Here, after hitting the wicket fast moving ball loses energy and stationary wicket on which work is done gains energy.

Because of gain of energy stationary wicket is thrown away. This means stationary wicket starts moving.

Wicket is thrown away here, because fast moving ball is capable of doing some work. That means, a fast moving ball has some energy.

Similarly when a raised hammer falls on a nail placed on a piece of wood, it drives the nail into the wood.

This happens because; raised hammer has capability of doing work. This means raised hammer has energy. In this case, raised hammer loses energy and nail on which work is done gains energy and starts moving; resulting gets driven in the wood.

How does an object with energy do work?

An object that possesses energy can exert a force on another object. In this course energy is transformed from the former to the latter object. The second object may move as it receives energy and therefore do some work.

Thus, the first object which possessed energy initially has a capacity to do work.

Thus, we can say that Any object that possesses energy can do work.

Unit of Energy

Since, any object that possessed energy can do work. Thus, energy possessed by an object is measured in the terms of capacity of doing work.

Therefore, the unit of energy is the same as that of work, that is, joule (J).

Thus, SI unit of energy is joule (J).

What is 1 joule of Energy?

1 J is the energy required to do 1 joule of work.

Larger unit of Energy

Kilo joule (kJ) is the larger unit of energy.

1 kJ = 1000 J

Forms of Energy

There are various forms of energy. For example, mechanical energy, chemical energy, potential energy, kinetic energy, heat energy, light energy, sound energy, etc.

Potential energy and kinetic energy together can form mechanical energy.

Kinetic Energy

The word 'Kinetic' came from Greek word 'Kinesis' which means 'movement or to move or motion'. Consequently, the term 'Kinetic Energy' means energy due to motion or movement.

The energy possessed by an object due to its motion is called Kinetic Energy.

A moving object can do work. A faster moving object can do more work than an identical object moving slower.

Example, a moving bullet, a moving blade, blowing wind, a rotating wheel, a speeding stone, a flying bow, etc. can do work.

A moving bullet can pierce a target. A moving blade can cut an object. Blowing wind can blow many things which come in its way.

A Storm is fast moving wind. A storm can uproot many trees and damage houses and other many things. This happens because a moving wind possesses energy, i.e. can do work.

Wind energy is the result of moving wind.

Thus, object in motion possess energy, and this energy is called Kinetic Energy.

How much energy is possessed by a moving body by virtue of its motion?

The Kinetic Energy of a body moving with a certain velocity is equal to the work done on it to make it acquire that velocity.

Mathematical Form of Kinetic Energy

Let an object of mass m is moving with a uniform velocity u.

Let the object is displaced through a distance s when a constant force F acts on it in the direction of its displacement.

Now, we know that, work done W = F s

Let the velocity of object changes from u to v.

Let the acceleration produced in this course = a

Now, we know that,

Now, we know that, Work done (W) = Force (F) × Displacement (s)

Or, W = F s

Thus, by substituting, the value of s, we get,

Now, we know that, F = ma. Thus, by replacing F=m a in the above equation, we get

Now, if the object is starting from its stationary position, then u = 0

Thus,

--------- (i)

Now it is clear that the work done is equal to the change in the kinetic energy of an object.

And when, u = 0, then work done will be equal to

Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is

---------- (ii)

Example Question (1) If an object of 10 kg is moving with a uniform velocity 5 m ^{s– 1}, then what is the kinetic energy possessed by the object?

Solution

Here, given, mass (m) of the object = 10 kg

Velocity of the object, v = 5 m ^{s– 1}

Now, We know that,

= 125 J

Thus, kinetic energy of the object is 125 J Answer

Example Problem (2) A car having mass of 1000 kg is running at a velocity of 20 km/h. Find the work done to increase its velocity to 50 km/h.

Solution

Given, mass (m) of car = 1000 kg

Initial velocity, u = 20 km/h

Final velocity, v = 50 km/h

Thus, work done, i.e. change in kinetic energy =?

We know that,

= 81018.51 J

Thus, work done require to increase the speed of given car = 81018.51 J Answer

Potential Energy

The Energy possessed by an object because of the position or configuration of the object is called POTENTIAL ENERGY.

In other word, the energy possessed by an object because of change in position or configuration is called POTENTIAL ENERGY.

Example (1)

When a stretched rubber band is released, it gains its original position.

After stretching, the position of a rubber band is changed. While stretching, some work is done on the rubber band which stretched the rubber band. This work done is transferred in the form of some energy into the stretched rubber band. The stretched position of a rubber band is new position or configuration.

When the stretched rubber band is released, it gains its original position after releasing some energy.

Thus, a stretched rubber band possesses some energy because of its new position. This energy possessed by the rubber band because of position or configuration is called POTENTIAL ENERGY.

Example (2)

When work is done while binding the spring inside of a toy car. The energy is transferred to the spring inside is stored as potential energy. And when the spring is released or toy car is left free on the ground, it starts moving. Toy car moves because of potential energy stored in the spring inside.

Example (3)

When water is pumped on the overhead tank. Work is done on water, to lift the water to the overhead tank. In this case energy is transferred to the water because of work done on it. This energy is POTENTIAL ENERGY because of position of water.

And after opening the tap connected to the water tank, water starts flowing. This is a common method to store water in households. And get water available as per need.

Potential Energy of an Object at A Height

Gravitational Potential Energy

The energy possessed by an object at a point above the ground because of the work done in raising it from the ground to that point against gravity is called GRAVITATIONAL POTENTIAL ENERGY.

An object increases its energy when raised through a height. This happens because some work is done on the object against gravity while it is being raised. The energy present in such an object is called Gravitational Potential Energy.

Expression for the Gravitational Potential Energy of an Object at a height

Let an object of mass m is raised through a height h from the ground.

A force is required to raise the object. The minimum force required to raise the object is equal to the weight of the object, i.e. = mg

The object gains energy equal to the work done on it.

Let the work done on the object against gravity be W.

That is,

Work done, W = Force × Displacement

⇒ W = mg × h

⇒ W = mgh

Since, work done on the object is equal to mgh, an energy equal to mgh units is gained by the object.

This is the Potential Energy (E_P) of the object.

E_P = mgh

The work done by the gravity depends on the difference in vertical heights of the initial and final positions of the object and not on the path along with the object is moved.

Example Question (3) What is the energy possessed by an object of mass 50 kg when it is at a height of 10 m above the ground. [g = 9.8 m s^–2]

Solution

Given, the mass of the object, m = 50 kg

Displacement (height), h = 10 m

Acceleration due to gravity = 9.8 m s^{– 2}

Thus, potential energy, E_P = ?

We know that, E_P = mgh

= 50 kg × 9.8 m s^{– 2} × 10 m

= 4900 J

Thus, Potential Energy possessed by the object = 4800 J Answer