Chapter Notes: Chapter -11 - Work and Energy, Class 9, Science Class 9 Notes | EduRev

Class 9 : Chapter Notes: Chapter -11 - Work and Energy, Class 9, Science Class 9 Notes | EduRev

 Page 1


 
 
WORK AND ENERGY
Work 
Work is said to be done when force produces motion.  
 
Example 
An engine pulling bogies of train, horse pulling a cart etc. 
 
The work done by a force on a body depends on two factors: - 
1. Magnitude of the force 
2. Distance through which the body moves 
 
In other words, we can say that work is said to be done when 
the point of application of a force moves. Work done in 
moving a body is equal to the product of force exerted on the 
body in the direction of force. 
 
Work = Force × Distance 
Or 
W = F × S 
          
 
S. I. Unit Of Work 
W = F × S 
W = N × m = Nm 
 
Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work 
will be Joule. 
 
1 Joule may be defined as, a force of 1N moving a body 
through a distance of 1 m in its own direction. In such 
case, the work done is known as 1 Joule. 
 
1 Joule = 1Newton × 1metre 
1J = 1Nm 
 
S.I. unit of work is joule denoted by J.  
 
Work is a scalar quantity. Note that work is said to be done 
only if there is a move in an object through some distance. If 
however, the distance moved is zero the work done on the 
body of man himself is not zero, because his muscles are 
stretched and his blood is displaced. 
 
Examples Of Work Done 
(i) Push a pebble lying on a surface. The pebble moves 
through a distance. You exerted the force on the pebble 
and the pebble is displaced. In this case the work is done. 
(ii) A girl pulls a trolley and the trolley moves through a 
distance. The girl has exerted a force and the trolley is 
displaced. The work is done. 
(iii) Lift a book through a height. The book rises up. There is a 
force applied on the book and the book has moved. The 
work is done. 
 
When Work Is Not Said To Be Done? 
(i) You are pushing a huge rock and the rock is not at all 
moving from its place. As there is no displacement in the 
rock even after applying force, work is not done. 
(ii) You stand still for a few minutes with a heavy load on 
your head. You get tired. No work is done on the load. 
Therefore work is not said to be done if there is no 
displacement even after the application of the force. 
 
Work Done Against Gravity 
Whenever work is done against gravity the amount of work 
done is equal to the product of weight of the body and the 
vertical distance through which the body is lifted. Work done 
by the person against gravity is positive. 
 
Work Done In Lifting A Body Upwards = Weight Of  
           Body × Vertical Distance 
Or 
W = m × g × h 
 
When a body of mass m is lifted to a height h above the 
ground, work equal to mgh is done on the body. 
 
Work Done When A Body Moves At An Angle To The 
Direction Of Force 
In such cases, we cannot use the formula W = F × S, because 
the distance moved S is not exactly in the direction of force 
applied. In such case, the force is applied at certain angle to 
the horizontal ground but the body moves horizontally on the 
ground. 
         
Calculating The Work Done When A Body Moves 
At An Angle To The Direction Of Force 
In this case, all force F is not utilized in pulling the body, only 
the horizontal component of force F is pulling the body along 
the ground. The horizontal component of force F is F Cos? and 
distance moved is S. 
Thus,  
W = FS Cos ? 
 
Work Done By Force When A Body Moves In A 
Direction Different From That Of Force 
1. When the displacement is in the direction of force i.e. 
when ?  = 0°   
 W=F S Cos ? 
 W=F S Cos 0° = F S × 1 = F× S 
  
 
Page 2


 
 
WORK AND ENERGY
Work 
Work is said to be done when force produces motion.  
 
Example 
An engine pulling bogies of train, horse pulling a cart etc. 
 
The work done by a force on a body depends on two factors: - 
1. Magnitude of the force 
2. Distance through which the body moves 
 
In other words, we can say that work is said to be done when 
the point of application of a force moves. Work done in 
moving a body is equal to the product of force exerted on the 
body in the direction of force. 
 
Work = Force × Distance 
Or 
W = F × S 
          
 
S. I. Unit Of Work 
W = F × S 
W = N × m = Nm 
 
Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work 
will be Joule. 
 
1 Joule may be defined as, a force of 1N moving a body 
through a distance of 1 m in its own direction. In such 
case, the work done is known as 1 Joule. 
 
1 Joule = 1Newton × 1metre 
1J = 1Nm 
 
S.I. unit of work is joule denoted by J.  
 
Work is a scalar quantity. Note that work is said to be done 
only if there is a move in an object through some distance. If 
however, the distance moved is zero the work done on the 
body of man himself is not zero, because his muscles are 
stretched and his blood is displaced. 
 
Examples Of Work Done 
(i) Push a pebble lying on a surface. The pebble moves 
through a distance. You exerted the force on the pebble 
and the pebble is displaced. In this case the work is done. 
(ii) A girl pulls a trolley and the trolley moves through a 
distance. The girl has exerted a force and the trolley is 
displaced. The work is done. 
(iii) Lift a book through a height. The book rises up. There is a 
force applied on the book and the book has moved. The 
work is done. 
 
When Work Is Not Said To Be Done? 
(i) You are pushing a huge rock and the rock is not at all 
moving from its place. As there is no displacement in the 
rock even after applying force, work is not done. 
(ii) You stand still for a few minutes with a heavy load on 
your head. You get tired. No work is done on the load. 
Therefore work is not said to be done if there is no 
displacement even after the application of the force. 
 
Work Done Against Gravity 
Whenever work is done against gravity the amount of work 
done is equal to the product of weight of the body and the 
vertical distance through which the body is lifted. Work done 
by the person against gravity is positive. 
 
Work Done In Lifting A Body Upwards = Weight Of  
           Body × Vertical Distance 
Or 
W = m × g × h 
 
When a body of mass m is lifted to a height h above the 
ground, work equal to mgh is done on the body. 
 
Work Done When A Body Moves At An Angle To The 
Direction Of Force 
In such cases, we cannot use the formula W = F × S, because 
the distance moved S is not exactly in the direction of force 
applied. In such case, the force is applied at certain angle to 
the horizontal ground but the body moves horizontally on the 
ground. 
         
Calculating The Work Done When A Body Moves 
At An Angle To The Direction Of Force 
In this case, all force F is not utilized in pulling the body, only 
the horizontal component of force F is pulling the body along 
the ground. The horizontal component of force F is F Cos? and 
distance moved is S. 
Thus,  
W = FS Cos ? 
 
Work Done By Force When A Body Moves In A 
Direction Different From That Of Force 
1. When the displacement is in the direction of force i.e. 
when ?  = 0°   
 W=F S Cos ? 
 W=F S Cos 0° = F S × 1 = F× S 
  
 
 
 Work done is equal to F×S.  It is positive work. 
 Example  
 A baby pulling a toy car parallel to the ground. 
 
2. When the displacement is at right angles to that of force 
i.e., when ? = 90
0
 
 W = F S Cos ? = F S Cos 90°  = F × S × 0 = 0 
 
No work is done by force. Also we can say that no work 
is done when a body is moving along a circular path. 
 
3. When displacement is in the opposite direction to that of 
the force i.e ?  =180°  
W=F S cos ?  =  F S cos 180° = F S×-1 = -F× S 
 
It is called negative work. 
Work done is negative or work done against the force is 
positive. 
 
POWER 
Power is the rate of doing work. 
 
Power = 
Taken Time
Done Work
 or  P = 
T
W
     
 
In other words, we can say that power is work done per unit 
time. Power is a scalar quantity. 
 
Units Of Power 
P = 
T
W
 = 
Second
Joules
  = 
s
J
 = J/s  or Js
-1 
 
Joules per second is called watt. The S.I. unit of power is 
watt. One watt is the rate of doing work at 1 joule per second. 
 
1 Watt=
Second 1
Joule 1
  Or 
1watt = 
s 1
J 1
  = 
s
J
 
 
Another unit of power is Horse Power (h.p.) 
1Horse Power = 746 Watts  Or 
1 h.p.  =  746 W 
 
Work 
From the formula of power another formula of work done can 
be derived that is, 
 
Power = 
Taken Time
Done Work
 
 
? Work Done = Power ×  Time 
 
Or          W = P × t 
 
ENERGY 
Energy is the ability or capacity to do work. The amount of 
work possessed by a body is equal to the amount of work it 
can do when its energy is released. Energy is utilized to do 
work. 
 
Forms Of Energy 
1. Mechanical Energy 
2. Chemical Energy 
3. Electrical Energy 
4. Light Energy 
5. Nuclear Energy 
6. Heat Or Thermal Energy 
 
How Does An Object With Energy Do Work? 
An object that possesses energy can exert force on another 
object. When this happens energy is transferred from one 
object to another. The second object may move as it receives 
energy and therefore do some work. Thus the first object has 
the capacity to do work. This implies that any object that 
possesses energy can do work. 
 
Unit Of Energy 
S.I. unit of energy is Joule (J). Energy is a scalar quantity. 
The energy possessed by an object is measured in terms of its 
capacity of doing work. Therefore the units of both energy and 
work are same. 
 
Mechanical Energy 
The energy by which the body can do some mechanical work 
is called mechanical energy. Two forms of mechanical energy 
are: - 
 
1. Kinetic Energy 
2. Potential Energy 
 
Mechanical energy is equal to sum of kinetic and potential 
energy 
 
M.E. = K.E. + P.E. 
 
1. Kinetic Energy 
The energy of a body due to its motion is called kinetic 
energy. A moving object possesses energy that is why it is 
capable of doing work. 
 
Example 
A fast moving ball, a stone thrown at a high speed high speed 
bullet, flowing wind and flowing water. 
 
Formula For Kinetic Energy 
To measure kinetic energy we have to measure the amount of 
work done because that is equal to kinetic energy. 
 
Work Done = Kinetic Energy ……………………………(i) 
 
Consider a body of mass m moving against the opposing force 
F with velocity v. Before its coming to rest after covering a 
certain distance work done by it will be given by  
 
W = F × S   ……………………………(ii) 
 
But, because work done is equal to Kinetic Energy from (i) and 
(ii), we can say 
 
K.E. = F × S 
 
Now, assume that 
Initial Velocity = 0 
Final Velocity = v 
Acceleration = a 
Distance = S 
(v)
2
 – (0)
2
 = 2aS  ……………………………(i) 
 
From Newton’s second law of motion 
F = m × a 
 
Page 3


 
 
WORK AND ENERGY
Work 
Work is said to be done when force produces motion.  
 
Example 
An engine pulling bogies of train, horse pulling a cart etc. 
 
The work done by a force on a body depends on two factors: - 
1. Magnitude of the force 
2. Distance through which the body moves 
 
In other words, we can say that work is said to be done when 
the point of application of a force moves. Work done in 
moving a body is equal to the product of force exerted on the 
body in the direction of force. 
 
Work = Force × Distance 
Or 
W = F × S 
          
 
S. I. Unit Of Work 
W = F × S 
W = N × m = Nm 
 
Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work 
will be Joule. 
 
1 Joule may be defined as, a force of 1N moving a body 
through a distance of 1 m in its own direction. In such 
case, the work done is known as 1 Joule. 
 
1 Joule = 1Newton × 1metre 
1J = 1Nm 
 
S.I. unit of work is joule denoted by J.  
 
Work is a scalar quantity. Note that work is said to be done 
only if there is a move in an object through some distance. If 
however, the distance moved is zero the work done on the 
body of man himself is not zero, because his muscles are 
stretched and his blood is displaced. 
 
Examples Of Work Done 
(i) Push a pebble lying on a surface. The pebble moves 
through a distance. You exerted the force on the pebble 
and the pebble is displaced. In this case the work is done. 
(ii) A girl pulls a trolley and the trolley moves through a 
distance. The girl has exerted a force and the trolley is 
displaced. The work is done. 
(iii) Lift a book through a height. The book rises up. There is a 
force applied on the book and the book has moved. The 
work is done. 
 
When Work Is Not Said To Be Done? 
(i) You are pushing a huge rock and the rock is not at all 
moving from its place. As there is no displacement in the 
rock even after applying force, work is not done. 
(ii) You stand still for a few minutes with a heavy load on 
your head. You get tired. No work is done on the load. 
Therefore work is not said to be done if there is no 
displacement even after the application of the force. 
 
Work Done Against Gravity 
Whenever work is done against gravity the amount of work 
done is equal to the product of weight of the body and the 
vertical distance through which the body is lifted. Work done 
by the person against gravity is positive. 
 
Work Done In Lifting A Body Upwards = Weight Of  
           Body × Vertical Distance 
Or 
W = m × g × h 
 
When a body of mass m is lifted to a height h above the 
ground, work equal to mgh is done on the body. 
 
Work Done When A Body Moves At An Angle To The 
Direction Of Force 
In such cases, we cannot use the formula W = F × S, because 
the distance moved S is not exactly in the direction of force 
applied. In such case, the force is applied at certain angle to 
the horizontal ground but the body moves horizontally on the 
ground. 
         
Calculating The Work Done When A Body Moves 
At An Angle To The Direction Of Force 
In this case, all force F is not utilized in pulling the body, only 
the horizontal component of force F is pulling the body along 
the ground. The horizontal component of force F is F Cos? and 
distance moved is S. 
Thus,  
W = FS Cos ? 
 
Work Done By Force When A Body Moves In A 
Direction Different From That Of Force 
1. When the displacement is in the direction of force i.e. 
when ?  = 0°   
 W=F S Cos ? 
 W=F S Cos 0° = F S × 1 = F× S 
  
 
 
 Work done is equal to F×S.  It is positive work. 
 Example  
 A baby pulling a toy car parallel to the ground. 
 
2. When the displacement is at right angles to that of force 
i.e., when ? = 90
0
 
 W = F S Cos ? = F S Cos 90°  = F × S × 0 = 0 
 
No work is done by force. Also we can say that no work 
is done when a body is moving along a circular path. 
 
3. When displacement is in the opposite direction to that of 
the force i.e ?  =180°  
W=F S cos ?  =  F S cos 180° = F S×-1 = -F× S 
 
It is called negative work. 
Work done is negative or work done against the force is 
positive. 
 
POWER 
Power is the rate of doing work. 
 
Power = 
Taken Time
Done Work
 or  P = 
T
W
     
 
In other words, we can say that power is work done per unit 
time. Power is a scalar quantity. 
 
Units Of Power 
P = 
T
W
 = 
Second
Joules
  = 
s
J
 = J/s  or Js
-1 
 
Joules per second is called watt. The S.I. unit of power is 
watt. One watt is the rate of doing work at 1 joule per second. 
 
1 Watt=
Second 1
Joule 1
  Or 
1watt = 
s 1
J 1
  = 
s
J
 
 
Another unit of power is Horse Power (h.p.) 
1Horse Power = 746 Watts  Or 
1 h.p.  =  746 W 
 
Work 
From the formula of power another formula of work done can 
be derived that is, 
 
Power = 
Taken Time
Done Work
 
 
? Work Done = Power ×  Time 
 
Or          W = P × t 
 
ENERGY 
Energy is the ability or capacity to do work. The amount of 
work possessed by a body is equal to the amount of work it 
can do when its energy is released. Energy is utilized to do 
work. 
 
Forms Of Energy 
1. Mechanical Energy 
2. Chemical Energy 
3. Electrical Energy 
4. Light Energy 
5. Nuclear Energy 
6. Heat Or Thermal Energy 
 
How Does An Object With Energy Do Work? 
An object that possesses energy can exert force on another 
object. When this happens energy is transferred from one 
object to another. The second object may move as it receives 
energy and therefore do some work. Thus the first object has 
the capacity to do work. This implies that any object that 
possesses energy can do work. 
 
Unit Of Energy 
S.I. unit of energy is Joule (J). Energy is a scalar quantity. 
The energy possessed by an object is measured in terms of its 
capacity of doing work. Therefore the units of both energy and 
work are same. 
 
Mechanical Energy 
The energy by which the body can do some mechanical work 
is called mechanical energy. Two forms of mechanical energy 
are: - 
 
1. Kinetic Energy 
2. Potential Energy 
 
Mechanical energy is equal to sum of kinetic and potential 
energy 
 
M.E. = K.E. + P.E. 
 
1. Kinetic Energy 
The energy of a body due to its motion is called kinetic 
energy. A moving object possesses energy that is why it is 
capable of doing work. 
 
Example 
A fast moving ball, a stone thrown at a high speed high speed 
bullet, flowing wind and flowing water. 
 
Formula For Kinetic Energy 
To measure kinetic energy we have to measure the amount of 
work done because that is equal to kinetic energy. 
 
Work Done = Kinetic Energy ……………………………(i) 
 
Consider a body of mass m moving against the opposing force 
F with velocity v. Before its coming to rest after covering a 
certain distance work done by it will be given by  
 
W = F × S   ……………………………(ii) 
 
But, because work done is equal to Kinetic Energy from (i) and 
(ii), we can say 
 
K.E. = F × S 
 
Now, assume that 
Initial Velocity = 0 
Final Velocity = v 
Acceleration = a 
Distance = S 
(v)
2
 – (0)
2
 = 2aS  ……………………………(i) 
 
From Newton’s second law of motion 
F = m × a 
 
 
? a = 
m
F
   ……………………………(ii) 
 
By putting the value from (ii) in (i) we get  
v
2
- 0 = 
2FS
m
             
? v
2
 = 
2FS
m
 
? F × S =  
2
mv
2
       
 
Now, 
F × S = K.E. 
? K.E. = 
2
1
mv
2
 
Where 
m = mass of body 
v = velocity of the body  
Important Conclusion From The Formula 
K.E. = 
2
1
mv
2
  
 
(i) As K.E. ? m, therefore if mass of the body is doubled then 
its kinetic energy also gets doubled and if mass of the 
body is halved its kinetic energy also gets halved. 
 
(ii) As K.E. ? v
2
, therefore if the velocity of the body is 
doubled then its kinetic energy becomes four times and if 
the velocity of body is halved, the kinetic energy become 
one fourth. 
 
2. Potential Energy 
The energy of a body due to its position or change in shape is 
known as potential energy. The potential energy exists in two 
types: - 
 
1. Gravitational Potential Energy 
The potential energy of a body due to its position above the 
ground is called gravitational potential energy. 
                    
2. Elastic Potential Energy 
The energy of a body due to a change in its shape and size is 
called elastic potential energy. 
           
Example 
(i) Water stored in an overhead tank. 
(ii) Coiled spring of a watch/clock. 
(iii) Raised hammer etc. 
 
The potential energy may be possessed by a body when it is 
not in motion, e.g. a stone lying on the top of the roof. 
 
Formula For Potential Energy 
Suppose a body of mass ‘m’ placed at a height ‘h’ above the 
ground and ‘g’ is the gravitational pull force acting on the body 
is gravitational pull of earth acting in downward direction is 
equal to m× g. Therefore, 
Force = m × g 
Displacement = h 
Work Done = Force × Distance 
 
W = m × g × h 
This work gets stored up in the body as potential energy. So,  
P.E. = m × g × h 
 
S. I. Unit Of Potential Energy 
P.E. = m × g × h 
P.E. = Kg × m/s
2
 × m  
 
But, 
Kg × m/s
2
 = N 
 
Therefore, 
P.E. = N × m = J 
S.I. unit of potential energy is Nm or J. 
 
Can a body possess both kinetic and potential energies 
at the same time? 
Certain bodies may possess both kinetic and potential energies 
at the same time. 
 
Examples  
(i) A man climbing a hill. 
(ii) An object rolling down a hill. 
(iii) A flying aeroplane. 
(iv) A flying bird. 
 
Transformation Of Energy 
The change of one form of energy into other form of energy is 
called transformation of energy. 
 
Example 
(i) When a body is released from a height then the potential 
energy of the body is gradually transformed into kinetic 
energy. 
(ii) The heat energy converted into K.E by a steam engine. 
(iii) The chemical energy of a firework is converted into 
thermal energy and light and sound energy when it 
explodes. 
(iv) A motor converts electrical energy into mechanical 
energy. 
 
Transformation In Case Of Mechanical Energy 
(i) When a body falls from a certain height its potential 
energy changes into kinetic energy. 
(ii) When a body is thrown upwards the kinetic energy of the 
body is changed into potential energy. 
 
Solar Energy 
The sun is a big store- house of energy. The solar energy gets 
changed into many other forms of energy which are very 
useful. 
 
Page 4


 
 
WORK AND ENERGY
Work 
Work is said to be done when force produces motion.  
 
Example 
An engine pulling bogies of train, horse pulling a cart etc. 
 
The work done by a force on a body depends on two factors: - 
1. Magnitude of the force 
2. Distance through which the body moves 
 
In other words, we can say that work is said to be done when 
the point of application of a force moves. Work done in 
moving a body is equal to the product of force exerted on the 
body in the direction of force. 
 
Work = Force × Distance 
Or 
W = F × S 
          
 
S. I. Unit Of Work 
W = F × S 
W = N × m = Nm 
 
Therefore, unit of work is Nm. 1Nm is 1 Joule. So, unit of work 
will be Joule. 
 
1 Joule may be defined as, a force of 1N moving a body 
through a distance of 1 m in its own direction. In such 
case, the work done is known as 1 Joule. 
 
1 Joule = 1Newton × 1metre 
1J = 1Nm 
 
S.I. unit of work is joule denoted by J.  
 
Work is a scalar quantity. Note that work is said to be done 
only if there is a move in an object through some distance. If 
however, the distance moved is zero the work done on the 
body of man himself is not zero, because his muscles are 
stretched and his blood is displaced. 
 
Examples Of Work Done 
(i) Push a pebble lying on a surface. The pebble moves 
through a distance. You exerted the force on the pebble 
and the pebble is displaced. In this case the work is done. 
(ii) A girl pulls a trolley and the trolley moves through a 
distance. The girl has exerted a force and the trolley is 
displaced. The work is done. 
(iii) Lift a book through a height. The book rises up. There is a 
force applied on the book and the book has moved. The 
work is done. 
 
When Work Is Not Said To Be Done? 
(i) You are pushing a huge rock and the rock is not at all 
moving from its place. As there is no displacement in the 
rock even after applying force, work is not done. 
(ii) You stand still for a few minutes with a heavy load on 
your head. You get tired. No work is done on the load. 
Therefore work is not said to be done if there is no 
displacement even after the application of the force. 
 
Work Done Against Gravity 
Whenever work is done against gravity the amount of work 
done is equal to the product of weight of the body and the 
vertical distance through which the body is lifted. Work done 
by the person against gravity is positive. 
 
Work Done In Lifting A Body Upwards = Weight Of  
           Body × Vertical Distance 
Or 
W = m × g × h 
 
When a body of mass m is lifted to a height h above the 
ground, work equal to mgh is done on the body. 
 
Work Done When A Body Moves At An Angle To The 
Direction Of Force 
In such cases, we cannot use the formula W = F × S, because 
the distance moved S is not exactly in the direction of force 
applied. In such case, the force is applied at certain angle to 
the horizontal ground but the body moves horizontally on the 
ground. 
         
Calculating The Work Done When A Body Moves 
At An Angle To The Direction Of Force 
In this case, all force F is not utilized in pulling the body, only 
the horizontal component of force F is pulling the body along 
the ground. The horizontal component of force F is F Cos? and 
distance moved is S. 
Thus,  
W = FS Cos ? 
 
Work Done By Force When A Body Moves In A 
Direction Different From That Of Force 
1. When the displacement is in the direction of force i.e. 
when ?  = 0°   
 W=F S Cos ? 
 W=F S Cos 0° = F S × 1 = F× S 
  
 
 
 Work done is equal to F×S.  It is positive work. 
 Example  
 A baby pulling a toy car parallel to the ground. 
 
2. When the displacement is at right angles to that of force 
i.e., when ? = 90
0
 
 W = F S Cos ? = F S Cos 90°  = F × S × 0 = 0 
 
No work is done by force. Also we can say that no work 
is done when a body is moving along a circular path. 
 
3. When displacement is in the opposite direction to that of 
the force i.e ?  =180°  
W=F S cos ?  =  F S cos 180° = F S×-1 = -F× S 
 
It is called negative work. 
Work done is negative or work done against the force is 
positive. 
 
POWER 
Power is the rate of doing work. 
 
Power = 
Taken Time
Done Work
 or  P = 
T
W
     
 
In other words, we can say that power is work done per unit 
time. Power is a scalar quantity. 
 
Units Of Power 
P = 
T
W
 = 
Second
Joules
  = 
s
J
 = J/s  or Js
-1 
 
Joules per second is called watt. The S.I. unit of power is 
watt. One watt is the rate of doing work at 1 joule per second. 
 
1 Watt=
Second 1
Joule 1
  Or 
1watt = 
s 1
J 1
  = 
s
J
 
 
Another unit of power is Horse Power (h.p.) 
1Horse Power = 746 Watts  Or 
1 h.p.  =  746 W 
 
Work 
From the formula of power another formula of work done can 
be derived that is, 
 
Power = 
Taken Time
Done Work
 
 
? Work Done = Power ×  Time 
 
Or          W = P × t 
 
ENERGY 
Energy is the ability or capacity to do work. The amount of 
work possessed by a body is equal to the amount of work it 
can do when its energy is released. Energy is utilized to do 
work. 
 
Forms Of Energy 
1. Mechanical Energy 
2. Chemical Energy 
3. Electrical Energy 
4. Light Energy 
5. Nuclear Energy 
6. Heat Or Thermal Energy 
 
How Does An Object With Energy Do Work? 
An object that possesses energy can exert force on another 
object. When this happens energy is transferred from one 
object to another. The second object may move as it receives 
energy and therefore do some work. Thus the first object has 
the capacity to do work. This implies that any object that 
possesses energy can do work. 
 
Unit Of Energy 
S.I. unit of energy is Joule (J). Energy is a scalar quantity. 
The energy possessed by an object is measured in terms of its 
capacity of doing work. Therefore the units of both energy and 
work are same. 
 
Mechanical Energy 
The energy by which the body can do some mechanical work 
is called mechanical energy. Two forms of mechanical energy 
are: - 
 
1. Kinetic Energy 
2. Potential Energy 
 
Mechanical energy is equal to sum of kinetic and potential 
energy 
 
M.E. = K.E. + P.E. 
 
1. Kinetic Energy 
The energy of a body due to its motion is called kinetic 
energy. A moving object possesses energy that is why it is 
capable of doing work. 
 
Example 
A fast moving ball, a stone thrown at a high speed high speed 
bullet, flowing wind and flowing water. 
 
Formula For Kinetic Energy 
To measure kinetic energy we have to measure the amount of 
work done because that is equal to kinetic energy. 
 
Work Done = Kinetic Energy ……………………………(i) 
 
Consider a body of mass m moving against the opposing force 
F with velocity v. Before its coming to rest after covering a 
certain distance work done by it will be given by  
 
W = F × S   ……………………………(ii) 
 
But, because work done is equal to Kinetic Energy from (i) and 
(ii), we can say 
 
K.E. = F × S 
 
Now, assume that 
Initial Velocity = 0 
Final Velocity = v 
Acceleration = a 
Distance = S 
(v)
2
 – (0)
2
 = 2aS  ……………………………(i) 
 
From Newton’s second law of motion 
F = m × a 
 
 
? a = 
m
F
   ……………………………(ii) 
 
By putting the value from (ii) in (i) we get  
v
2
- 0 = 
2FS
m
             
? v
2
 = 
2FS
m
 
? F × S =  
2
mv
2
       
 
Now, 
F × S = K.E. 
? K.E. = 
2
1
mv
2
 
Where 
m = mass of body 
v = velocity of the body  
Important Conclusion From The Formula 
K.E. = 
2
1
mv
2
  
 
(i) As K.E. ? m, therefore if mass of the body is doubled then 
its kinetic energy also gets doubled and if mass of the 
body is halved its kinetic energy also gets halved. 
 
(ii) As K.E. ? v
2
, therefore if the velocity of the body is 
doubled then its kinetic energy becomes four times and if 
the velocity of body is halved, the kinetic energy become 
one fourth. 
 
2. Potential Energy 
The energy of a body due to its position or change in shape is 
known as potential energy. The potential energy exists in two 
types: - 
 
1. Gravitational Potential Energy 
The potential energy of a body due to its position above the 
ground is called gravitational potential energy. 
                    
2. Elastic Potential Energy 
The energy of a body due to a change in its shape and size is 
called elastic potential energy. 
           
Example 
(i) Water stored in an overhead tank. 
(ii) Coiled spring of a watch/clock. 
(iii) Raised hammer etc. 
 
The potential energy may be possessed by a body when it is 
not in motion, e.g. a stone lying on the top of the roof. 
 
Formula For Potential Energy 
Suppose a body of mass ‘m’ placed at a height ‘h’ above the 
ground and ‘g’ is the gravitational pull force acting on the body 
is gravitational pull of earth acting in downward direction is 
equal to m× g. Therefore, 
Force = m × g 
Displacement = h 
Work Done = Force × Distance 
 
W = m × g × h 
This work gets stored up in the body as potential energy. So,  
P.E. = m × g × h 
 
S. I. Unit Of Potential Energy 
P.E. = m × g × h 
P.E. = Kg × m/s
2
 × m  
 
But, 
Kg × m/s
2
 = N 
 
Therefore, 
P.E. = N × m = J 
S.I. unit of potential energy is Nm or J. 
 
Can a body possess both kinetic and potential energies 
at the same time? 
Certain bodies may possess both kinetic and potential energies 
at the same time. 
 
Examples  
(i) A man climbing a hill. 
(ii) An object rolling down a hill. 
(iii) A flying aeroplane. 
(iv) A flying bird. 
 
Transformation Of Energy 
The change of one form of energy into other form of energy is 
called transformation of energy. 
 
Example 
(i) When a body is released from a height then the potential 
energy of the body is gradually transformed into kinetic 
energy. 
(ii) The heat energy converted into K.E by a steam engine. 
(iii) The chemical energy of a firework is converted into 
thermal energy and light and sound energy when it 
explodes. 
(iv) A motor converts electrical energy into mechanical 
energy. 
 
Transformation In Case Of Mechanical Energy 
(i) When a body falls from a certain height its potential 
energy changes into kinetic energy. 
(ii) When a body is thrown upwards the kinetic energy of the 
body is changed into potential energy. 
 
Solar Energy 
The sun is a big store- house of energy. The solar energy gets 
changed into many other forms of energy which are very 
useful. 
 
 
(i) Transformation of solar energy into wind energy. 
(ii) Transformation of solar energy into electrical energy. 
(iii) Transformation of solar energy into food energy. 
 
Law Of Conservation Of Energy 
Energy can neither be created nor destroyed; it is only 
transformed from one form into other. Whenever energy 
changes from one form to another, the total amount of energy 
remains constant or conserved. Whenever one form of energy 
disappears, an equivalent amount of energy in another form 
appears. Or we can say that whenever the energy gets 
transformed, the total energy before and after the 
transformation remains unchanged. 
 
Proof Of The Law Of Conservation Of Energy 
To prove this principle, let us consider kinetic energy, potential 
energy and T.E. (total energy) of the body falling freely under 
gravity. 
Consider an object of mass m, kept at rest at point A, which is 
height h, above the ground. We take the potential energy of 
the object at the ground to be zero. The potential energy of 
the object at A is 
 U
A
   =  mgh 
K.E.
 A
   =   0  
[Q  v = 0, it is not moving] 
? total energy (T.E.)
 A
   =   U
A
   +   K.E.
 A
 
           =  mgh +   0 
           = mgh 
The object is now allowed to fall freely under the action of 
gravity. It gains velocity as it comes down and its kinetic 
energy increases due to increase in the velocity. 
 
 Let us consider a point C at any instant between A 
and B such that AC = x and v is the velocity of object at C. 
Then its kinetic energy will be 
1
2
mv
2
 and potential energy will 
be mg (h-x). 
 
Therefore total energy of the body will be 
T.E.  =  K.E.  +   P.E. 
T.E. = 
1
2
mv
2 
+ mg (h-x) 
Using the third equation of motion v
2
 = u
2
 + 2gx; v
2
= 0 + 2gx   
?    v
2
 = 2gx 
? T.E.  =  
1
2
m 2gx  +  mg (h-x) 
         =  mgx  +  mgh  –  mgx 
                     =  mgh 
And finally when the object reaches the ground, height from 
the ground is zero and therefore the potential energy (U
B
) = 
0. If the velocity of body on reaching the ground is v, then 
K.E. = 
1
2
mv
2
B 
Now from the 3
rd
 equation of motion 
 v
B
2  
  =  u
2  
 –  2 as 
 v
B
2
   =  (0)
2
   +  2gh 
 v
B
2
   =  2gh 
?at B   K.E. =  
1
2
mv
2
B
 
       =  
1
2
m (2gh) 
       = 
1
2
. 2 mgh 
?      T.E.
B
  =  v
B
   +  K.E.
B 
                  =  0  +  mgh   
      =  mgh 
Therefore the total energy of the object during the free fall 
remains constant at all positions. The form of energy however 
keeps on changing. At A the energy is entirely potential and at 
B it is entirely kinetic. In between A and B the energy is 
partiallt potential partially kinetic. But total energy remains 
constant throughout. 
When the body hits the ground and comes to rest, it looses all 
its kinetic energy, the loss of kinetic energy appears as sound, 
light and heat. When it hits the ground it produces sound, 
sparkling (light) and the point of contact becomes hot(heat). 
 
Example 
(i) Conservation of energy during the free fall of a body: As 
the ball falls downward its potential energy goes on 
decreasing whereas the kinetic energy increases in equal 
amount. So, total energy remains conserved. 
(ii) Energy of a ball thrown upwards is also conserved. 
(iii) A swinging simple pendulum is an example of 
conservation of energy. 
(iv) If a batsman hits a ball, the ball gets some velocity and at 
the same time the batsman looses some energy. 
 
The some total of energy in this universe is a constant 
quantity. 
 
Commercial Unit Of Energy 
The unit joule is too small and hence it is inconvenient to 
express large quantities of energy. A bigger unit of energy can 
be used that is kilowatt hour (kW h). The energy used in 
households, industries, and commercial establishments are 
usually expressed in kilowatt hour. For example electrical 
energy used during a month is expressed in terms of ‘units’. 
Here one ‘unit ‘ means 1 killowatt hour. 
 
1 kW h is the energy used in one hour at the rate of one 
thousand joules per second or 1 kW. 
 
1kW  =  1000 W ? 1 h 
   = 1000 W ? 3600 s 
   =  3600000 Ws 
   =  3600000 J 
 
1kW  =  3.6 ? 10
6
 J 
 
 
Read More
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Complete Syllabus of Class 9

Content Category

Related Searches

past year papers

,

mock tests for examination

,

Chapter Notes: Chapter -11 - Work and Energy

,

shortcuts and tricks

,

Chapter Notes: Chapter -11 - Work and Energy

,

Extra Questions

,

Semester Notes

,

Important questions

,

Class 9

,

video lectures

,

Science Class 9 Notes | EduRev

,

Class 9

,

Summary

,

Class 9

,

Exam

,

Chapter Notes: Chapter -11 - Work and Energy

,

Science Class 9 Notes | EduRev

,

MCQs

,

Previous Year Questions with Solutions

,

practice quizzes

,

pdf

,

ppt

,

Objective type Questions

,

Free

,

Viva Questions

,

Sample Paper

,

Science Class 9 Notes | EduRev

,

study material

;