11. Work and Energy

Introduction:

• All living beings need food. Living beings have to perform several basic activities to survive. We call such activities ‘life processes’.
• The energy for these processes comes from food. We need energy for other activities like playing, singing, reading, writing, thinking, jumping, cycling and running. Activities that are strenuous require more energy.
• Machines also require energy to work, for which diesel and petrol are used.

Work: The work done on a body is defined by the result of the force applied on it and the product of the distance fixed by it in the direction of the force.

Work = Force × Displacement

W = F × S 

S.I Unit of Work: 

Force is measured in newtons (N) and displacement is measured in meters (m). 

By the above formula we gets 

S.I unit of works => N (Newtons) × m (meter) = Nm 

This Nm is known as Joule (J). 

Therefore work is a type of energy so S.I Unit of work is Joule (J).

Work is a scalar quantity: by the definition of work, Work is the product of force (a vector quantity) and displacement (a vector quantity). Whereas work is a scalar quantity because work has magnitude but does not have direction. It is a scalar quantity similar to energy.

Note: All works done by you are not scientifically work.

Our Which actions are work? 

Activities like preparing for examination, reading books, drawing a picture, discussing on problems etc use a large amount of energy but according to scientific definition you can see there happens a very few work. 

Examples of some our activities: 

(i) Suppose you are pushing a very large rock with force, if in spite of your millions of efforts, the rock does not move, then this work will not be considered because the force applied did not cause the displacement of the object while the energy was spent too much.

(ii) We do many physical and mental tasks in daily life such as - playing in the field, interacting with friends, humming a tune, watching cinema, deep discussion on a subject etc. But all these tasks will not be understood as work.

(iii) Push a pebble lying on a surface. The pebble moves through a distance. You exerted a force on the pebble and the pebble got displaced. In this situation work is done.
(iv) A girl pulls a trolley and the trolley moves through a distance. The girl has exerted a force on the trolley and it is displaced. Therefore, work is done.

(v) Lift a book through a height. To do this you must apply a force. The book rises up. There is a force applied on the book and the book has moved. Hence, work is done.

SCIENTIFIC CONCEPTION OF WORK:

When we displace an object to apply a force then work will be done. 

Therefore, two conditions need to be satisfied for work to be done:

Conditions for work:

(i) a force should act on an object, and

(ii) the object must be displaced.

If any one of the above conditions does not exist, work is not done. This is the way we view work in science.

Define 1 Joule of Work:

When an object is displaced 1 m applying 1 N of force along the line of action of
the force it is called 1 Joule of work has done.

1 J = 1 N x 1 m

1 J = 1 Nm

Positive Work, Negative Work and Zero Work

Equation of Work: 

Mathematically work is expressed by the following equation. 

W = F . S . cos θ 

F = force, S = displacement, θ is the angle between force vector and displacement vector. 

There are three situation for work done:

Positive Work: Work done is positive when the force is in the
direction of displacement.

Example of positive work: 

The baby has exerted a force in the direction of displacement of the car. In this situation, the work done will be equal to the product of the force and displacement. In such situations, the work done by the force is taken as positive.

Zero Work: When after applying an amount of force but there is no displacement. Then the angle between these two vectors is 90^o. 

Example: A large and heavy rock is moved by applying force but no displacement noticed, in this case work will be calculate zero. 

Negative Work: Work done is negative when the force acts
opposite to the direction of displacement.

Consider a situation in which an object is being displaced by the action of forces and we identify one of the forces, F acting opposite to the direction of the displacement s, that is, the angle between the two directions is 180º. In such a situation, the work done by the force, F is taken as negative and denoted by the minus sign. The work done by the force is F × (–s) or (–F × s).

Positive force and Negative force:

When we lift an object, the force we exert on the object will be considered positive. At the same time, there is another force working there which is called the force of gravity. The force of gravity works opposite to the force applied by us, so this force will be considered negative.

Since when we apply force on an object, we have to exert more force than the result of the force of gravity to displace the object, hence the resultant force becomes positive. For example, suppose we applied 20 N force to lift an object while the measure of gravity is 10 N there.

Resultant force = 20 - 10 = 10 N

In this situation, we applied a total of 10 N force to displace the object.

Example1: A person displaces a stone by 3 meters by applying 100 Newton force. So find out the work done by him.

solution:

Force applied here (F) = 100 N

               Displacement (s) = 3 m

Work done (W) = F × s

                            = 100 × 3 = 300 joules

Example 2: A boy is unable to move a table by applying 20 N force and gets tired. So calculate the work done by him.

solution:

Force applied here (F) = 20 N

               Displacement (s) = 0 m

Work done (W) = F × s

                            = 20 × 0 = 0 joules

The work done here is zero. Therefore, this work will not be considered.

Example 3: Suppose you lifted a heavy burden with force and placed it on your head. Displacement occurred in the load. Till this work was done, but if you keep this burden on your head and stand for a long time. So force is being felt by you, gravity is also working opposite to it, but there is no displacement in the object. Therefore, in this situation no work will be considered here.

Example 4: A porter carries a 25 kg load on his head 2 meters above. So calculate the work done by him on that burden.

solution :

Mass of burden m = 25 kg

              Displacement = 2 m and

Force on object F = mg = 25 kg × 10 m s-2

                                      = 250 kg / m s-2 or 250 N

Work on burden (W) = F × s

                          = 250 × 2 N m

                          = 500 N m = 500 J

1 joule work: When an object is displaced 1 meter in the direction of force by applying 1 N force, it will be said that 1 joule work has been done.

Energy and its Forms

Energy: The Capacity of doing work is known as energy.

Energy is a scaler quantity. 

S.I unit of energy is joule (J) and biggest unit is kilo Joule (kj) 

                      1 kJ = 1000 J 

• Life is impossible without energy.
• The demand for energy is ever increasing.
• The Sun is the biggest natural source of energy to us.
• Many of our energy sources are derived from the Sun.
• We can also get energy from the nuclei of atoms, the interior of the earth, and the tides.

Energy possess object:

- 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.

How does work happens by using Energy? 

An object that possesses energy can exert a force on another object. When this happens, energy is transferred from the former to the latter. The second object may move as it receives energy and therefore do some work. Thus, the first object had a capacity to do work. This implies that any object that possesses energy can do work.

The capacity of doing work is  measured in Joule. 

Forms of Energy: 

There are different forms of energy: 

(1) Mechanical Energy: The sum of potential energy and kinetic energy is called mechanical energy. 

 Mechanical Energy = Potential Enrgy + Kinetic Enrgy 

In other words: The energy possess by a body on Account of its potition or motion is called mechanical energy.  

     (i) Potential Energy: The energy possessed by the object is the energy present in it by virtue of its position or configuration is called potential energy. 

     Or   The stored energy in an object due to change in its position is called potential energy. 

     (ii) Kinetic Energy: The energy possess by an object due to its motion is called kinetic energy. 

(2) Sound Energy : The energy possess an object during vibration and produce sound such energy is called sound energy. Sound energy has capacity to do work.   

(3) Heat Energy: Heat is also an energy. When a matter is heated its tiny particles vibrate or move. it has capacity to do work. 

(4) Chemical Energy: The energy released or produced during chemical reactions is called chemical energy. 

(5) Electrical Energy: Electrical energy is a form of energy resulting from the flow of electric charge. Electric energy has ability to do work or apply force to move an object. The force is electrical attraction or repulsion between charged particles.

(6) Light/Solar Energy: The sun is the begest source of energy on the Earth. We use the sunlight as energy. 

(7) Nuclear Energy: The energy released by fussion and fission of nucleuos of an atom is called nuclear energy. 

Potential Energy: The energy stored in an object by changing its position is called potential energy. 

It is a type of mechanical energy. 

Examples of potential energy: 

(I) Stored water in dam

(II) Wound up spring of a toy  car

(III) Stretched the string of a bow with arrow

(IV) Stretched a rubber band

(V) Lifted up a hammer

(VI) Lifeted up any object at height

Factors which affecting the potential energy: 

(i)  Mass : Increasing of mass of an object causes greater potential energy. 

(ii) Height from ground: Increasing the height of an object gives greater potential energy. 

(iii) Change in shape: Streching, bending or twisting an object gives greater potential energy. 

The Gravitational Potential Energy: 

An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy.

(i) When an object is lifted up or raised up it works against the gravity. As it raised up at height it gains the potential energy. 

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

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

POTENTIAL ENERGY OF AN OBJECT AT A HEIGHT

Consider an object of mass, m. Let it be raised through a height, h from the ground.

displacement = h 

mass of the object = m 

The minimum force required to raise the object is equal to the weight of the object = mg ( f = ma or mg) g is the acceleration due to gravity. 

work done, W = force × displacement

                       = mg × h 

                       = 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 

Example1: Find the energy possessed by an object of mass 10 kg when it is at
a height of 6 m above the ground. Given, g = 9.8 m s–².

Solution: 

Mass of the object, m = 10 kg,
displacement (height), h = 6 m, and
acceleration due to gravity, g = 9.8 m s–².
Potential energy = mgh
= 10 kg × 9.8 m s–² × 6 m
= 588 J.
The potential energy is 588 J.

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

Example of Kinetic Energy: 

(i) A falling coconut

(ii) a speeding car

(iii) a rolling stone

(iv) a flying aircraft

(v) flowing water

(vi) blowing wind

(vii) a running athlete

(viii) A moving cricket ball

Main-points:

• A moving object can do work.
• An object moving faster can do more work than an identical object moving relatively slow.
• 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.

Formula for Kinetic Energy:

Consider an object of mass, 'm' moving with a uniform velocity, 'u'. Let it now be displaced through a distance 's' when a constant force, F acts on it in the direction of its displacement. 

Its velocity changes from 'u' to 'v'. Then accelaration is 'a'.

Work done, W = f × s                  ......... (i) 

and              f = ma                      ......... (ii) 

Now           W = ma × s               .......... (iii) 

According to third equation of motion 

                2as =  v² - u² 

So,              s =  v² - u² / 2a          ......... (iv) 

Now putting the value of s from (iv) in equation (iii) 

if u = 0 (When the body or an object starts moving from rest) 

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