Work, Energy & Power Class 11 Notes Physics Chapter 5

 Page 1


89
4.1 Introduction
Work is said to be done when a force applied on the body displaces the body 
through a certain distance in the direction of force.
4.2 Work Done by a Constant Force
Let a constant force F be applied on the body such that it makes an angle 
? with the horizontal and body is displaced through a distance s.
Then work done by the force in displacing the body through a distance s is 
given by
W = (F cos ?) s = Fs cos ?  ?  W = (F cos ?) s = Fs cos ?
W = 
4.3 Nature of Work Done 
Positive work Negative work
Positive work means that force (or its Negative work means that force (or its 
component) is parallel to displacement  component) is opposite to displacement
0º = ? < 90º i.e., 90º < ? = 180º
The positive work sigmnes that the external The negative work sigmnes that the 
external force favours the motion   force opposes the motion of the body. 
of the body.
Page 2


89
4.1 Introduction
Work is said to be done when a force applied on the body displaces the body 
through a certain distance in the direction of force.
4.2 Work Done by a Constant Force
Let a constant force F be applied on the body such that it makes an angle 
? with the horizontal and body is displaced through a distance s.
Then work done by the force in displacing the body through a distance s is 
given by
W = (F cos ?) s = Fs cos ?  ?  W = (F cos ?) s = Fs cos ?
W = 
4.3 Nature of Work Done 
Positive work Negative work
Positive work means that force (or its Negative work means that force (or its 
component) is parallel to displacement  component) is opposite to displacement
0º = ? < 90º i.e., 90º < ? = 180º
The positive work sigmnes that the external The negative work sigmnes that the 
external force favours the motion   force opposes the motion of the body. 
of the body.
4.4 Work Done by aVariable Force
When the magnitude and direction of a force varies with position, the work  
 done by such a force for an infinite simal displacement is given by  
dW = . 
 The total work done in going from A to B is W = .
Area under force displacement curve with proper algebraic sign represents 
work done by the force.
4.5 Work Depends on Frame of Reference
With change of frame of reference (inertial) force does not change while  
 displacement may change. So the work done by a force will be different in 
different frames.
Examples : If a person is pushing a box inside a moving train, the work done 
in the frame of train will  while in the frame of earth will be 
where  is the displacement of the train relative to the ground.
4.6 Energy
The energy of a body is defined as its capacity for doing work.
(1) It is a scalar quantity.
(2) Dimension : [ML
2
T
2
] it is same as that of work or torque.
(3) Units : Joule [S.I.], erg [C.G.S.]
Practical units : electron volt (eV), Kilowatt hour (KWh), Calories (Cal) 
Relation between different units :
1 Joule = 10
7
 erg
1 eV = 1.6 × 10
–19
 Joule
1 KWh = 3.6 × 10
6
 Joule
1 Calorie = 4.18 Joule
(4) Mass energy equivalence : The relation between the mass of a particle 
m and its equivalent energy is given as E = mc
2
 where c = velocity of 
light in vacuum.
Page 3


89
4.1 Introduction
Work is said to be done when a force applied on the body displaces the body 
through a certain distance in the direction of force.
4.2 Work Done by a Constant Force
Let a constant force F be applied on the body such that it makes an angle 
? with the horizontal and body is displaced through a distance s.
Then work done by the force in displacing the body through a distance s is 
given by
W = (F cos ?) s = Fs cos ?  ?  W = (F cos ?) s = Fs cos ?
W = 
4.3 Nature of Work Done 
Positive work Negative work
Positive work means that force (or its Negative work means that force (or its 
component) is parallel to displacement  component) is opposite to displacement
0º = ? < 90º i.e., 90º < ? = 180º
The positive work sigmnes that the external The negative work sigmnes that the 
external force favours the motion   force opposes the motion of the body. 
of the body.
4.4 Work Done by aVariable Force
When the magnitude and direction of a force varies with position, the work  
 done by such a force for an infinite simal displacement is given by  
dW = . 
 The total work done in going from A to B is W = .
Area under force displacement curve with proper algebraic sign represents 
work done by the force.
4.5 Work Depends on Frame of Reference
With change of frame of reference (inertial) force does not change while  
 displacement may change. So the work done by a force will be different in 
different frames.
Examples : If a person is pushing a box inside a moving train, the work done 
in the frame of train will  while in the frame of earth will be 
where  is the displacement of the train relative to the ground.
4.6 Energy
The energy of a body is defined as its capacity for doing work.
(1) It is a scalar quantity.
(2) Dimension : [ML
2
T
2
] it is same as that of work or torque.
(3) Units : Joule [S.I.], erg [C.G.S.]
Practical units : electron volt (eV), Kilowatt hour (KWh), Calories (Cal) 
Relation between different units :
1 Joule = 10
7
 erg
1 eV = 1.6 × 10
–19
 Joule
1 KWh = 3.6 × 10
6
 Joule
1 Calorie = 4.18 Joule
(4) Mass energy equivalence : The relation between the mass of a particle 
m and its equivalent energy is given as E = mc
2
 where c = velocity of 
light in vacuum.
4.7 Kinetic Energy
The energy possessed by a body by virtue of its motion is called kinetic 
energy.
Let m = mass of the body, v = velocity of the body then K.E. = .
(1) Kinetic energy depends on frame of reference : The kinetic energy 
of a person of mass m, sitting in a train moving with speed v, is zero in 
the frame of train but  in the frame of the earth.
(2) Work-energy theorem : It states that work done by a force acting on a 
body is equal to the change produced in the kinetic energy of the body.
This theorem is valid for a system in presence of all types of forces 
(external or internal, conservative or non-conservative).
(3) Relation of kinetic energy with linear momentum : As we know 
       
E= p= 2mE  
p2
2m
(4) Various graphs of kinetic energy
4.8 Potential Energy
4.9 Potential Energy
Potential energy is defined only for conservative forces. In the space occupied 
by conservative forces every point is associated with certain energy which is 
called the energy of position or potential energy. Potential energy generally 
are of three types : Elastic potential energy and Gravitational potential energy 
Page 4


89
4.1 Introduction
Work is said to be done when a force applied on the body displaces the body 
through a certain distance in the direction of force.
4.2 Work Done by a Constant Force
Let a constant force F be applied on the body such that it makes an angle 
? with the horizontal and body is displaced through a distance s.
Then work done by the force in displacing the body through a distance s is 
given by
W = (F cos ?) s = Fs cos ?  ?  W = (F cos ?) s = Fs cos ?
W = 
4.3 Nature of Work Done 
Positive work Negative work
Positive work means that force (or its Negative work means that force (or its 
component) is parallel to displacement  component) is opposite to displacement
0º = ? < 90º i.e., 90º < ? = 180º
The positive work sigmnes that the external The negative work sigmnes that the 
external force favours the motion   force opposes the motion of the body. 
of the body.
4.4 Work Done by aVariable Force
When the magnitude and direction of a force varies with position, the work  
 done by such a force for an infinite simal displacement is given by  
dW = . 
 The total work done in going from A to B is W = .
Area under force displacement curve with proper algebraic sign represents 
work done by the force.
4.5 Work Depends on Frame of Reference
With change of frame of reference (inertial) force does not change while  
 displacement may change. So the work done by a force will be different in 
different frames.
Examples : If a person is pushing a box inside a moving train, the work done 
in the frame of train will  while in the frame of earth will be 
where  is the displacement of the train relative to the ground.
4.6 Energy
The energy of a body is defined as its capacity for doing work.
(1) It is a scalar quantity.
(2) Dimension : [ML
2
T
2
] it is same as that of work or torque.
(3) Units : Joule [S.I.], erg [C.G.S.]
Practical units : electron volt (eV), Kilowatt hour (KWh), Calories (Cal) 
Relation between different units :
1 Joule = 10
7
 erg
1 eV = 1.6 × 10
–19
 Joule
1 KWh = 3.6 × 10
6
 Joule
1 Calorie = 4.18 Joule
(4) Mass energy equivalence : The relation between the mass of a particle 
m and its equivalent energy is given as E = mc
2
 where c = velocity of 
light in vacuum.
4.7 Kinetic Energy
The energy possessed by a body by virtue of its motion is called kinetic 
energy.
Let m = mass of the body, v = velocity of the body then K.E. = .
(1) Kinetic energy depends on frame of reference : The kinetic energy 
of a person of mass m, sitting in a train moving with speed v, is zero in 
the frame of train but  in the frame of the earth.
(2) Work-energy theorem : It states that work done by a force acting on a 
body is equal to the change produced in the kinetic energy of the body.
This theorem is valid for a system in presence of all types of forces 
(external or internal, conservative or non-conservative).
(3) Relation of kinetic energy with linear momentum : As we know 
       
E= p= 2mE  
p2
2m
(4) Various graphs of kinetic energy
4.8 Potential Energy
4.9 Potential Energy
Potential energy is defined only for conservative forces. In the space occupied 
by conservative forces every point is associated with certain energy which is 
called the energy of position or potential energy. Potential energy generally 
are of three types : Elastic potential energy and Gravitational potential energy 
etc.
(1) Change in potential energy : Change in potential energy between any 
two points  is defined in terms of the work done by the fo rce in displacing 
the particle between these two points without any change in kinetic 
energy. 
U
2
 – U
1
 = ...(1)
(2) Potential energy curve : A graph plotted between the potential energy of 
a particle and its displacement from the centre of force is called potential 
energy curve. Negative gradient of the potential energy gives force.
 = F
(5) Types of equilibrium : If net force acting on a particle is zero, it is said 
to be in equilibrium.
For equilibrium,  = 0, but the equilibrium of particle can be of three 
types :
Stable Unstable Neutral
When a particle is displaced 
slightly from a position, then 
a force acting on it brings it 
back to the initial position, 
it is said to be in stable 
equilibrium position.
Potential energy is minimum.
i.e., rate of change of is 
positive.
Example : A marble placed 
at the bottom of a hemi-
spherical bowl.
4.10 Elastic Potential Energy
When a particle is displaced 
slightly from a position, then 
a force acting on it tries to 
displace the particle further 
away from the equilibrium 
position, it is said to be in 
unstable equilibrium.
Potential energy is maximum.
i.e., rate of change of
is negative.
Example : A marble 
balanced on top of a hemi-
spherical bowl.
When a particle is slightly 
displaced from a position 
then it does not experience 
any force acting on it and 
continues to be in equili-
brium in the displaced 
position, it is said to be in 
neutral equilibrium.
Potential energy is constant.
i.e., rate of change of
is zero.
Example : A marble placed 
on horizontal table.
Page 5


89
4.1 Introduction
Work is said to be done when a force applied on the body displaces the body 
through a certain distance in the direction of force.
4.2 Work Done by a Constant Force
Let a constant force F be applied on the body such that it makes an angle 
? with the horizontal and body is displaced through a distance s.
Then work done by the force in displacing the body through a distance s is 
given by
W = (F cos ?) s = Fs cos ?  ?  W = (F cos ?) s = Fs cos ?
W = 
4.3 Nature of Work Done 
Positive work Negative work
Positive work means that force (or its Negative work means that force (or its 
component) is parallel to displacement  component) is opposite to displacement
0º = ? < 90º i.e., 90º < ? = 180º
The positive work sigmnes that the external The negative work sigmnes that the 
external force favours the motion   force opposes the motion of the body. 
of the body.
4.4 Work Done by aVariable Force
When the magnitude and direction of a force varies with position, the work  
 done by such a force for an infinite simal displacement is given by  
dW = . 
 The total work done in going from A to B is W = .
Area under force displacement curve with proper algebraic sign represents 
work done by the force.
4.5 Work Depends on Frame of Reference
With change of frame of reference (inertial) force does not change while  
 displacement may change. So the work done by a force will be different in 
different frames.
Examples : If a person is pushing a box inside a moving train, the work done 
in the frame of train will  while in the frame of earth will be 
where  is the displacement of the train relative to the ground.
4.6 Energy
The energy of a body is defined as its capacity for doing work.
(1) It is a scalar quantity.
(2) Dimension : [ML
2
T
2
] it is same as that of work or torque.
(3) Units : Joule [S.I.], erg [C.G.S.]
Practical units : electron volt (eV), Kilowatt hour (KWh), Calories (Cal) 
Relation between different units :
1 Joule = 10
7
 erg
1 eV = 1.6 × 10
–19
 Joule
1 KWh = 3.6 × 10
6
 Joule
1 Calorie = 4.18 Joule
(4) Mass energy equivalence : The relation between the mass of a particle 
m and its equivalent energy is given as E = mc
2
 where c = velocity of 
light in vacuum.
4.7 Kinetic Energy
The energy possessed by a body by virtue of its motion is called kinetic 
energy.
Let m = mass of the body, v = velocity of the body then K.E. = .
(1) Kinetic energy depends on frame of reference : The kinetic energy 
of a person of mass m, sitting in a train moving with speed v, is zero in 
the frame of train but  in the frame of the earth.
(2) Work-energy theorem : It states that work done by a force acting on a 
body is equal to the change produced in the kinetic energy of the body.
This theorem is valid for a system in presence of all types of forces 
(external or internal, conservative or non-conservative).
(3) Relation of kinetic energy with linear momentum : As we know 
       
E= p= 2mE  
p2
2m
(4) Various graphs of kinetic energy
4.8 Potential Energy
4.9 Potential Energy
Potential energy is defined only for conservative forces. In the space occupied 
by conservative forces every point is associated with certain energy which is 
called the energy of position or potential energy. Potential energy generally 
are of three types : Elastic potential energy and Gravitational potential energy 
etc.
(1) Change in potential energy : Change in potential energy between any 
two points  is defined in terms of the work done by the fo rce in displacing 
the particle between these two points without any change in kinetic 
energy. 
U
2
 – U
1
 = ...(1)
(2) Potential energy curve : A graph plotted between the potential energy of 
a particle and its displacement from the centre of force is called potential 
energy curve. Negative gradient of the potential energy gives force.
 = F
(5) Types of equilibrium : If net force acting on a particle is zero, it is said 
to be in equilibrium.
For equilibrium,  = 0, but the equilibrium of particle can be of three 
types :
Stable Unstable Neutral
When a particle is displaced 
slightly from a position, then 
a force acting on it brings it 
back to the initial position, 
it is said to be in stable 
equilibrium position.
Potential energy is minimum.
i.e., rate of change of is 
positive.
Example : A marble placed 
at the bottom of a hemi-
spherical bowl.
4.10 Elastic Potential Energy
When a particle is displaced 
slightly from a position, then 
a force acting on it tries to 
displace the particle further 
away from the equilibrium 
position, it is said to be in 
unstable equilibrium.
Potential energy is maximum.
i.e., rate of change of
is negative.
Example : A marble 
balanced on top of a hemi-
spherical bowl.
When a particle is slightly 
displaced from a position 
then it does not experience 
any force acting on it and 
continues to be in equili-
brium in the displaced 
position, it is said to be in 
neutral equilibrium.
Potential energy is constant.
i.e., rate of change of
is zero.
Example : A marble placed 
on horizontal table.
93
(1) Restoring force and spring constant : When a spring is stretched or 
compressed from its normal position (x = 0) by a small distance x, a 
restoring froce is produced in the spring to bring it to the normal position. 
According to Hooke’s law this restoring force is proportional to the 
displacement x and its direction is always opposite to the displacement.
i.e., a 
 or  = ...(i)
 where k is called spring constant.
(2) Expression for elastic potential energy :
Elastic potential energy    U = 
Note : 
• If spring is stretched from initial position x
1
 to final position x
2
 then
work done = Increment in elastic potential energy
 = 
(3) Energy graph for a spring : It mean kinetic energy changes parabolically 
w.r.t. position but total energy remain always constant irrespective to 
position of the mass.
4.11 Law of Conservation of Energy 
(1) Law of conservation of energy : For an isolated system or body in 
presence of conservative forces the sum of kinetic and potential energies 
at any point remains constant throughout the motion. It does not depends 
upon time. This is known as the law of conservation of mechanical energy.
(2) Law of conservation of total energy : If the forces are conservative 
and non-conservative both, it is not the mechanical energy alone which 
is conserved, but it is the total energy, may be heat, light, sound or