# Basic Physics lesson-8 : Force, work done and energy

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## Introduction

We had learnt some basic concepts of Physics in some earlier lessons in this series and if we recall we learnt about mass of a body and its acceleration. There is a relation between these two entities because when a force is applied on the body then an acceleration is produced in it. Now it is time to learn in details about the force, work done and energy in this lesson.

## What do we understand by force?

Force is defined as the entity which can try or make a stationary object move or try to stop or slow down an object which is already moving. Force can be momentary or continuous. Momentary force would have limited effect on the objects while continuous force will have a prolonged effect till force remains in action.

When a continuous force is applied on the object then its velocity increases. The increase in velocity is nothing but defined as acceleration. More the force, more the acceleration produced. It is also observed that for a smaller mass the same force would be able to produce more acceleration as compared to that produced in a bigger mass.

The relationship between force (F), mass (m) and acceleration (a) is given by the formula -

Force = mass x acceleration

or

F = ma

This as we all know is in accordance with the Newton's second law of motion. Actually Newton's second law is considered as the most useful and valuable out of three laws as it helps to quantitatively calculate the dynamics of bodies as how their velocities change and how it changes in a particular direction as directed by the force direction and things like that. In the above famous formula F and a are both vector quantities and the direction of acceleration and force are same.

Students often ask why it is so that when we throw a body up in the air it stops and comes back. The answer can be understood in a simple way like this - when we throw something up we apply a force on it and with that it starts moving up and as per Newton's first law of motion it should continue to move up. But here comes in between the force of gravity which pulls it downward and this force is nothing but equal to mg (mass x acceleration due to gravity). So due to this force applied by Earth on it in downward direction, it decelerates (retards) and it slows down and stops. But force by Earth is continuously applied on it and it starts falling back with an acceleration equal to g (which is actually about 9.8 metre / second square) on the surface of the Earth.

For a body already in motion any additional external force applied on it will deviate it from its direction depending upon the angle between that new force and the direction of motion of the body. So its trajectory and velocity will change in accordance with the resultant of earlier applied force and the new one now applied to it. Body would respond to each and every force applied on it. For example in a game of tug of war if both the sides exert same force then the tug would remain standstill till one side weakens.

## Unit of force

Force is defined as mass x acceleration and its M.K.S. unit is thereby becomes kg m/s2.

Sir Issac Newton was the scientist behind the famous equation F = ma and to honour him this M.K.S. unit is termed as Newton. So, 1 Newton = 1 kg m/s2.

1 Newton is the force which can accelerate 1 kg mass with acceleration of 1 meter/second square or also represented as 1 metre/second2.

Other common units of force are dyne, gram force, kg force, pound force etc. They are related to the Newton as follows -

1 dyne = 10-5 Newton

1 gram force = 9.8 milli Newton

1 Kg force = 9.8 Newton

1 Pound force = 4.45 Newton

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## Example of force

Let us take an example to understand the force and its effect on bodies. Suppose a body has a mass of 0.2 kilo gram (200 gram) and it is placed on a frictionless smooth surface. As the body is stationary its initial velocity is zero. Let us say we apply a force of 0.1 kg m/s2 (0.1 Newton) on it and it starts moving. Using the formula F = ma, we get a = 0.1/0.2 which equals to 0.5 m/s2. So the body moves ahead with an acceleration of 0.5 m/s2.

If we recall that in an earlier lesson Basic Physics lesson-3 : Acceleraton, we learnt about the relationship between final velocity v, initial velocity u, acceleration a, and time incurred t (in attaining velocity v from u). The relationship was given by -

v = u + at

Now we can use this equation to find out the velocity after some time in the above example. Let us say we want to find its velocity after 5 seconds.

So the velocity after 5 seconds would equal to 0 + (0.5 x 5) = 2.5 m/s.

What does this example tell us? It simply illustrates the fact that if a force is continuously applied on a body then it's velocity would go on increasing. This fact is utilised in launching rockets to Moon or Mars. The rocket is powered through multiple stage thrusting forces so that it attains enough velocity to leave the Earth's gravitational pull and enter the inter planetary space where it floats in a stage of almost weightlessness and then it depends on its thrust engine's firing direction to move it in a particular direction.

## What do we understand by work done?

When we apply a force on an object then it may move from its position and then we say that we have done some work depending upon how much force we exerted and how much the object moved away from its original position. Here we have to note that if the object does not move then work done would be zero. Someone might ask that even if the object did not move but one has tried and exerted and lost some energy in doing that then how come that work done is zero. The answer is that work done is seen from the perspective of result of applying force on the object. For example if a person slightly pushes an object so that it does not move and then repeats it hundred times then he would feel tired and exhausted but work done on the object is zero. So we have to remember that work done would only be there when the object moves from its original position. There is a difference between workout and work done.

Another important thing in this respect is that if the direction of the force and direction of the displacement are same then we can calculate the work done (W) by multiplying the force (F) with displacement (d). Which means -

W = F x d

or simply -

W = Fd

What happens when the force applied is not in the direction of the displacement of the object. In that case we have to find out the part of the force that is actually applied on the object. Let us assume that the angle between the direction of force and displacement of the object is θ. So, the component of force (F) in the direction of displacement would be Fcosθ. To find the work done on the object we have to take this component force only and in this case the work done (W) would be -

W = F x d x cosθ

or simply -

W = Fdcosθ

## Units of work

Unit of work done is joule (J). If a force of 1 Newton is applied on an object and it moves a distance of 1 metre then it is said that 1 joule work is done.

So 1 joule = 1 Newton x 1 metre

There are other units of work done also -

Erg, Foot-pound, and kg m2/s2 etc. Erg is derived from dyne force and displacement in cm, Foot-pound is derived from pound force and displacement in foot, and kg m2/s2 is derived from kg force and displacement in meter.

## Example of work done

Suppose a few people are pushing a bad car towards the side of the road. They collectively apply say a force of 4000 Newton on the car and it moves about 6 meters almost in the same direction. The work done by the people on the car is equal to 4000 x 6 = 24000 joule.

Another example is that suppose I strike a billiard ball with a slight force of say 0.03 Newton and the ball moves say a total of 3 meters before coming to rest then work done is equal to 0.03 x 3 = 0.09 Joule. Interestingly pushing a car requires about 260000 times more work than displacing a billiard ball as in the example.

## What do we understand by energy?

Energy is very closely related to work done. We can push an object and move it when we have energy to do so. Let us ponder about some sources of energy. Sun rays heat the Earth and it's atmosphere and we feel hot. What is the source of this energy and how this energy reaches Earth? The water flows down the river and reaches sea. From where this energy comes to drive the water through such a long journey? A billiard ball collides with other balls and these move and then slow down and stop. From where this energy came and where to it has disappeared? To understand the answers to these questions we have to understand the basic concept of energy as explained in Physics.

Let us consider the simple case of pushing an object with some force and then object starts to move with some velocity. The question comes as what happened to the energy that we have imparted to it? Where it has gone? The answer is that the energy is converted to its kinetic energy which it has acquired by virtue of its mass and velocity. In mathematical terms this is presented as (mass x velocity2)/2 or in explicit formula form as mv2/2.

Another thing equally important is that just by the position of an object at rest, it can have some energy and that is known as potential energy. On the surface of the Earth it is basically derived from the Earth's gravitational field due to which an object has a weight. This weight is actually the force that can move a body from a height to the Earth surface and in common language we say that an object fell from such and such height and then rested on the ground. So the object possessed some energy at that height. What is that energy? It is gravitational potential energy. In mathematical terms it is given by mass x acceleration due to gravity x height from the surface of Earth. In formula form it is equal to mgh.

Kinetic energy and potential energy often change from one to another but they also change to other forms like heat, electricity etc depending on the machine designed to do so. Solar energy from sun reaches us and we can use it in solar cooker to cook food. Electrical energy is used in a electric bulb to create light. Those who have seen filament type electric bulb might know that its body, which is glass, heats up while giving light to us. So a large portion of electrical energy goes in that heat form. Incidentally, the efficiecy of these bulbs for converting electrical energy to light is quite low about 2-3 % only and now they have been replaced by the CFL types having efficiency of around 8-10 % only.

So far, we have neglected the amount of energy consumed against frictional forces when objects move on a surface or even go through the air, as air also has some resistance when something tries to move through it. Further, if a body moves through water then water would create more frictional force against the movement. So mediums and surface would also impede the motion and some energy would go to annul them and in common language these are known as frictional loss of energy. In strict sense it is not a loss as well said that loss of one is gain for other - this small energy is actually converted in heat in the adjacent areas. Please note that sometimes this heat is massive and significant. For example the meteorites which fall on Earth from outer space get burned and charred by frictional heat in the atmosphere once they enter the Earth's atmosphere. Only in case of bigger meteorites which do not burn fully, they reach the Earth surface and collide and sometimes create destruction also depending on their remaining size and where they fall.

The most interesting thing about energy is that it is not wasted. It only changes it's form. It transforms from one stage to another. For example if we heat water then the heating energy has converted a part of itself to the heat energy that is now there in that water. Of couse some energy might have gone in the surrounding throgh radiation of heat in the air around the heating device. Some of it has gone to the pot also in which we are heating the water. So all the energy of the heating device or stove will not be converted to the heat in the hot water. This concept can be used to find the efficiecy of the heating device. In big power generating dams we use falling waters to rotate mightier turbines to produce electricity. In that system, some of the energy of falling water has transformed to the electrical energy. Water falling from a height has immense kinetic energy and when it falls on turbine blades, it rotates the turbine and electricity is produced. It is to be understood that only a part of the falling water energy gets converted to electricity and rest goes ahead as embedded in the used water as well as in the frictional interactions in the turbine system. All these concepts lead to the theory of conservation of energy which says that total energy in a system remains same albeit in different forms.

## Units of Energy

We use energy to do some work and so it is closely related and have similar units. Because of the thermal effect of energy, it has got another unit also which is known as calorie. One calorie heat or energy is that which can raise the temperature of 1 gram of water by 1 degree centigrade. Generally in food and nutrition related matters kilo calorie (denoted by kcal) is used. One has to take care while calculating the calorie value of the foods as some places it is common to use calorie in place of kcal. Some people use capital c in calorie to represent kcal by it. This is a bit ambiguous situation but a thing which is in use for a long time and somehow has to be accepted by the users.

## Conclusion

Understanding of force, work, and energy helps us in understanding the principles of Physics related to these entities. We can use the formulas and equations to quantify these things in a particular situation.

1. https://byjus.com/physics/unit-of-force/

2. https://en.m.wikibooks.org/wiki/Units_of_Measurement/Force

3. http://physics.bu.edu/

4. https://en.m.wikipedia.org/wiki/Calorie

5. https://www.physicsclassroom.com/class/energy/Lesson-1/Potential-Energy

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2020 Umesh Chandra Bhatt

Umesh Chandra Bhatt (author) from Kharghar, Navi Mumbai, India on September 03, 2020:

SKMUNSHI, thanks a lot, Sir.

SKMUNSHI on September 03, 2020:

This article is very well written and introduces the three important concepts in physics namely Force, Work and energ & touches upon important concepts of law of conservation of energ.just by going through it one can refresh his understanding of these concepts .It equally heps beginner's in easy understanding of these important concepts.

Well done sir.

Umesh Chandra Bhatt (author) from Kharghar, Navi Mumbai, India on August 06, 2020:

Mary, thanks a lot for your visit and encouraging comment.

Mary Norton from Ontario, Canada on August 06, 2020:

I find this very interesting. I don't think I understood much in my high school physics. I find your explanation of energy fascinating.

Umesh Chandra Bhatt (author) from Kharghar, Navi Mumbai, India on July 14, 2020:

Ruby Jean, thanks a lot for your encouraging comment.

Ruby Jean Richert from Southern Illinois on July 14, 2020:

Umesh, I remember having some physics in school, and learning about Newton's apple. It's good to get a refresher course. This article took a lot of work on your part, and I commend you. Great learning article!

Umesh Chandra Bhatt (author) from Kharghar, Navi Mumbai, India on July 12, 2020:

Flourish, thanks for your kind words. Highly appreciate.

FlourishAnyway from USA on July 12, 2020:

My husband is an engineer who started out as a physics major so I get some of this at home. The last physics class I personally had was in high school, however—an honors class. you provide a good explanation.

Umesh Chandra Bhatt (author) from Kharghar, Navi Mumbai, India on July 11, 2020:

Manatita, thanks for your comment. Highly appreciate.

Umesh Chandra Bhatt (author) from Kharghar, Navi Mumbai, India on July 11, 2020:

Nell, thanks a lot for your interest in the article.

manatita44 from london on July 11, 2020:

Didn't do this at school, but I commend you. Visually, it looks like a lot of work. But I see the protagonist using this quite effectively in Chinese movies. Shalom!

Nell Rose from England on July 11, 2020:

Great information Umesh! I love physics. I never learned at school but have tried to learn as much as possible at home.

Umesh Chandra Bhatt (author) from Kharghar, Navi Mumbai, India on July 11, 2020:

Eric, great to see that our junior Eric would be benefited by this. Feel so nice. And thanks a lot.

Eric Dierker from Spring Valley, CA. U.S.A. on July 11, 2020:

Thanks I needed this. My son is just about ready for about 4 of these concepts/definitions.