We perform various activities like eating, studying, playing, walking, sleeping, jumping, and several others in our daily life. Some of these tasks require more energy than others.  Even the machines that we use to help us throughout the day require energy too!

Can you imagine driving your car without petrol or diesel? The concept of work and energy helps us understand which task will qualify as work and which will not and why we need the energy to perform all these tasks.

Work

Work is said to be done if a force acting on an object produces a displacement. Thus, according to physics, daily activities like humming a tune, watching a movie, standing, or talking might not quantify as work done. But if a person throws a ball, he applies force on the ball, and the ball gets displaced- is an example of work done.

That means, if you push against a wall and the wall does not move, no work will be done even though all your energy gets drained in the process.

Therefore, we can define work as the energy transfer that occurs as an object moves over a certain distance under the effect of an external force.

Work Done by a Constant Force

Consider a constant force \(F\) acting on an object such that the object is displaced through a certain distance \(s,\) under the action of this force, in the direction of the applied force. If \(W\) be the work done on the object during its displacement, then this work done is equal to the product of force and displacement, i.e.,

\({\rm{Workdone = Force \times displacement}}\)

\(W = F \cdot S\)

Where, 

\(F:\) is the applied external force

\(s:\) is the displacement

Work done is a scalar quantity; it has magnitude and no direction. The SI unit of work is the joule\((\rm{J})\) or newton-meter \((\rm{N-m}).\) The work done on an object will be \(1\,{\rm{J}}\) if a force of \(1\,{\rm{N}}\) displaces it through a distance of \(1\,{\rm{m}}\) in the direction of the applied force.

Work done is positive when the applied force and corresponding displacement are in the same direction. Work done is said to be negative if the applied force and the corresponding displacement are in opposite directions, and work done is said to be zero if either the force or the object’s displacement is zero.

Energy

Can you imagine running on a day you have not had food? Can you imagine a mixer grinder working without a battery or electric supply? For performing any task or doing some work, energy is required. Energy is the ability of a body to do work. Thus, an object which shows the capability of doing work must possess some energy. The object that does the work is said to lose energy, while the object on which work is done is said to gain energy. For example, you take a ball and place it at some height- you lost energy while doing the work while the ball gained energy.

The SI unit of energy is the same as that of work, i.e. joule \((\rm{J}).\) One joule is the amount of energy required to perform one joule of work.

It is important here to remember that energy can neither be created nor be destroyed. It gets transferred from one form into another. While running, the chemical energy from food gets converted into our kinetic energy; while singing, this energy gets converted into sound energy. In an electric heater, the electrical energy gets converted into heat energy and so on.

Kinetic Energy

Kinetic energy is the energy possessed by an object by virtue of its motion. We know that energy and work are co-related; thus, the kinetic energy of an object moving with a certain velocity can be defined as the work done on an object to achieve that velocity.

To determine the expression for kinetic energy: Take an object of mass \(m\) having a uniform velocity \(u.\) Let a constant force \(F\) displaces this object through a distance \(s\) along the direction of the force.

Thus, work done on the object, 

\(W=F.s —(1)\)

This work done will bring a change in the velocity of the object. Let the final velocity of the object be \(v.\) Since there is a change in its velocity, the object will accelerate and let \(a\) be the acceleration produced. 

Thus, the force acting on the object can be given as \(F=m.a……..(2)\)

From the equations of motion, we know that the initial and final velocity, acceleration, and displacement of an object are related as:

\({v^2} – {u^2} = 2as\)

\(s = \frac{{{v^2} – {u^2}}}{{2a}}…….\left( 3 \right)\)

Substituting the values of equations \((2)\) and \((3)\) in equation \((1),\) we get:

\(W = m.a \times \frac{{{v^2} – {u^2}}}{{2a}}\)

\(W = \frac{1}{2}m\left( {{v^2} – {u^2}} \right) = \frac{1}{2}m{v^2} – \frac{1}{2}m{u^2}…….\left( 4 \right)\)

Or, \(W = {\rm{Final}}\,{\rm{Kinetic}}\,{\rm{Energy}} – {\rm{Initial}}\,{\rm{Kinetic}}\,{\rm{Energy}}\)

Thus, work done on an object is equal to the change in its kinetic energy. If the object starts from rest, i.e. its initial velocity \(u=0,\) then:

\(W = {E_K} = \frac{1}{2}m{v^2}\)

This is the expression for kinetic energy possessed by an object of mass \(m\) moving with a uniform velocity \(v.\)

Potential Energy

Suppose that energy transferred to perform work on an object does not cause a change in the speed or velocity of the object; in such a case, the energy due to work done gets stored in the object. This energy is called the potential energy of the object. When a rubber band or a spring is stretched, the energy transferred to the rubber band or spring is stored in them as potential energy. Thus, we can define potential energy present in an object as the energy possessed by it by virtue of its position of configuration.

Gravitational Potential Energy

The potential energy at any point above the earth’s surface is called gravitational potential energy. It is equal to the work done in raising an object from the ground to that point against gravity. Thus, as the height of an object from the ground increases, its gravitational potential energy increases.

To derive the expression for gravitational potential energy: Let there be an object of mass \(m.\) A force must be applied to the object against the force of gravity to raise it to a height \(h\) above the ground. Thus, the minimum force applied to the object must be equal to the weight of the object. 

Work done by force, \(W = {\rm{Force}} \times {\rm{displacement}} = F \cdot h\)

Force applied on the object, \(F=m.g\)

Thus, \(W=(m.g).h=mgh\)

The work done by the force to raise this object will get stored in the object in the form of energy, called the potential energy.

\({E_P} = mgh\)

Here, it is important to remember that the work done by gravity depends only on the vertical difference in the heights of the initial and final position and not on the path along which the object is moved to reach that height.

Law of Conservation of Energy

The law of conservation of energy states that energy can only be converted from one form to another. It means total energy before and after transformation remains the same. Thus, energy can neither be created nor be destroyed. The law of conservation of energy stays true in all kinds of transformations and is a universal law. If the total energy of an object is purely kinetic and potential, then the sum of the kinetic and potential energy of the object will remain constant throughout its motion.

The total mechanical energy of an object is the sum of its potential and kinetic energy. For an object infall- if there is a decrease in potential energy at any point in the motion of an object, it will result in an equal amount of increase in kinetic energy and vice-versa.

Rate of Doing Work

It is important to realize the speed at which work is being done by or on an object. The power of an agent is defined as the rate of doing work. It determines how fast or slow work is being done.

If \(W\) is the work being done by an object or on an object in time \(t,\) then the power generated can be given as:

\({\rm{Power = }}\frac{{{\rm{Work \,done }}}}{{{\rm{ time }}}} = \frac{W}{t}\)

The SI unit of power is the watt \((\rm{W}).\) One watt of power is generated by an agent when one joule of energy is consumed per second. An agent may perform work at different rates at different intervals of time; thus, instead of power, we calculate the average power of the agent.

Commercial Units of Energy

Joule, at times, is insufficient to measure usable energy. In our daily lives, we use bigger units of energy called kilowatt hour \((\rm{kW}\,\rm{h}).\)

One kilowatt-hour is the energy used in an hour at the rate of \(1000\;{\rm{J}}{{\rm{s}}^{ – 1}}\)

\(1\,{\rm{kW}}\,{\rm{h}} = 1\,{\rm{kW}} \times 1\,{\rm{h}}\)

\( = 1000\,{\rm{W}} \times 3600\;{\rm{s}}\)

\( = 3600000\,{\rm{Ws}}\)

\( = 3.6 \times {10^6}\;{\rm{J}}\)

Summary

Work is said to be done if a force acting on an object produces a displacement. If \(W\) be the work done on the object during its displacement, then it is equal to the product of force and displacement i.e, \(W = F \cdot s\). An object which shows the capability of doing work must possess some energy. Kinetic energy is the energy possessed by an object by virtue of its motion. The potential energy is defined as the energy possessed by it by virtue of its position of configuration. The potential energy at any point above the earth’s surface is called gravitational potential energy. It is equal to the work done in raising an object from the ground to that point against gravity. The law of conservation of energy states that energy can only be converted from one form to another.

Frequently Asked Questions on Work and Energy

Q.1. What is kinetic energy?
Ans: The energy possessed by an object by virtue of its motion is defined as kinetic energy.

Q.2. Define work done.
Ans: Work is done when an external force displaces an object in the direction of applied force.

Q.3. State the law of conservation of energy.
Ans: According to the conservation of energy, the energy can only be transformed from one form of energy to another; it can neither be created nor destroyed.

Q.4. If the displacement due to an applied external force is in the opposite direction, work done is: Positive or Negative?
Ans: Work done is negative when force and displacement are in opposite directions.

Q.5. What is the gravitational potential energy of an object kept on the ground?
Ans: The gravitational potential energy at the surface of the earth, i.e., ground, is zero.

We hope you find this article on ‘Work and Energy‘ helpful. In case of any queries, you can reach back to us in the comments section, and we will try to solve them.