Important Points and Formulas: Work and Energy | Science Class 9 PDF Download

 Page 1


1 
 
WORK AND ENERGY 
 
 
 Work and Energy 
• Work is said to be done if (i) a force is applied on the object and (ii) the object is 
displaced from its original position. 
• Work done by a force acting on an object is equal to the product of the force (F) and 
the displacement (s) of the object in the direction of the force, i.e., W = F × s = Fs.  
• Work done by a force is positive if the force and the displacement are in same 
direction. 
• Work done by a force is negative if the force and the displacement are in opposite 
direction. 
• Work done by a force is zero if the force is perpendicular to the displacement, i.e., if 
there is no displacement in the direction of force. Work done by a force is also zero, when 
there is no displacement at all. 
• Work is a scalar quantity. 
• The unit of work is joule (J). One joule work is said to be done on an object when a 
force of one newton displaces it by one metre along the line of action of the force. 
    1 J = 1 N × 1 m = 1 Nm 
    Further, 1 kilo joule (1 kJ) = 1000 J and 1 mega joule (1 MJ) = . 
 Energy 
• Energy of an object is defined as its capacity for doing work and it is measured by the 
total quantity of work it can do. It is a scalar quantity. 
• The unit of energy is the same as that of work, i.e., joule (J). 
 Forms of Energy 
• Kinetic energy of an object is defined as the energy, which it possesses by virtue of 
its motion. It is measured by the amount of work that the object can do against an opposing 
force before it comes to rest. 
 Derivation of kinetic energy 
 Now work done = F ´ s   … (i) 
  
 Thus, kinetic energy possessed by an object of mass, m and moving with a uniform 
velocity, v is 
    
• The kinetic energy  of an object is defined as half the product of its mass (m) and 
the square of the speed (v) of the object, i.e., . 
J 10
6
2
2
1
mv E
K
=
) (
k
E
2
2
1
mv E
k
=
Page 2


1 
 
WORK AND ENERGY 
 
 
 Work and Energy 
• Work is said to be done if (i) a force is applied on the object and (ii) the object is 
displaced from its original position. 
• Work done by a force acting on an object is equal to the product of the force (F) and 
the displacement (s) of the object in the direction of the force, i.e., W = F × s = Fs.  
• Work done by a force is positive if the force and the displacement are in same 
direction. 
• Work done by a force is negative if the force and the displacement are in opposite 
direction. 
• Work done by a force is zero if the force is perpendicular to the displacement, i.e., if 
there is no displacement in the direction of force. Work done by a force is also zero, when 
there is no displacement at all. 
• Work is a scalar quantity. 
• The unit of work is joule (J). One joule work is said to be done on an object when a 
force of one newton displaces it by one metre along the line of action of the force. 
    1 J = 1 N × 1 m = 1 Nm 
    Further, 1 kilo joule (1 kJ) = 1000 J and 1 mega joule (1 MJ) = . 
 Energy 
• Energy of an object is defined as its capacity for doing work and it is measured by the 
total quantity of work it can do. It is a scalar quantity. 
• The unit of energy is the same as that of work, i.e., joule (J). 
 Forms of Energy 
• Kinetic energy of an object is defined as the energy, which it possesses by virtue of 
its motion. It is measured by the amount of work that the object can do against an opposing 
force before it comes to rest. 
 Derivation of kinetic energy 
 Now work done = F ´ s   … (i) 
  
 Thus, kinetic energy possessed by an object of mass, m and moving with a uniform 
velocity, v is 
    
• The kinetic energy  of an object is defined as half the product of its mass (m) and 
the square of the speed (v) of the object, i.e., . 
J 10
6
2
2
1
mv E
K
=
) (
k
E
2
2
1
mv E
k
=
 
 
• Work-energy theorem states that net work done (W) by external forces on an object 
is equal to the change in its kinetic energy, i.e., W = change in kinetic energy.  
  
  
• The energy possessed by an object by virtue of its position or configuration (shape) is 
called its potential energy. It is measured by the amount of work that the object can do in 
passing from its present position or configuration (shape) to some standard position or 
configuration. 
• Potential energy is also termed as configuration energy or mutual energy. 
• Potential energy may be (i) gravitational potential energy (i.e., potential energy due to 
position of an object) or (ii) elastic potential energy (i.e., potential energy due to 
configuration of an object). 
• The potential energy of an object due to its height is called gravitational potential 
energy  
• Gravitational potential energy of an object of mass m at a height h is given by 
, where g is the acceleration due to gravity at the place under consideration. 
• Gravitational potential energy is due to the force of attraction (mg) between the Earth 
and the object. 
• Gravitational potential energy of an object depends on the difference in vertical heights 
of the initial and the final positions of the object and not on the path the object is moved, i.e., 
gravitational potential energy is path independent. 
 Law of Conservation of Energy and Its Transformation 
• Energy exists in nature in several forms such as solar energy, ocean energy, hydro 
energy, wind energy, mechanical energy, kinetic energy, potential energy, heat energy, 
chemical energy, light energy, sound energy etc. 
• Mechanical energy is the sum of the kinetic and potential energies. 
• One form of energy can be changed into another form – this process is called energy 
conversion or energy transformation. 
• Energy can neither be created nor destroyed, it can only be changed from one form to 
the other. This is called the Law of Conservation of Energy. 
• The total mechanical energy of a body throughout its free fall is conserved. 
• Gravitational potential energy depends on the choice of zero level. Positive 
gravitational potential energy implies that the body will do work while returning to zero level. 
Negative gravitational potential energy on the other hand implies that the work has to be 
done to bring the body back to the zero level. 
 Power 
• Power of an agent is the rate at which work is done by it. If W is the work done by an 
agent in time t, its power (P) is given by P = W/t. 
• The SI unit of power is called watt (W) where 
Ki Kf
E E W - =
2 2
2
1
2
1
mu mv W - =
). (
p
E
mgh E
p
=
Page 3


1 
 
WORK AND ENERGY 
 
 
 Work and Energy 
• Work is said to be done if (i) a force is applied on the object and (ii) the object is 
displaced from its original position. 
• Work done by a force acting on an object is equal to the product of the force (F) and 
the displacement (s) of the object in the direction of the force, i.e., W = F × s = Fs.  
• Work done by a force is positive if the force and the displacement are in same 
direction. 
• Work done by a force is negative if the force and the displacement are in opposite 
direction. 
• Work done by a force is zero if the force is perpendicular to the displacement, i.e., if 
there is no displacement in the direction of force. Work done by a force is also zero, when 
there is no displacement at all. 
• Work is a scalar quantity. 
• The unit of work is joule (J). One joule work is said to be done on an object when a 
force of one newton displaces it by one metre along the line of action of the force. 
    1 J = 1 N × 1 m = 1 Nm 
    Further, 1 kilo joule (1 kJ) = 1000 J and 1 mega joule (1 MJ) = . 
 Energy 
• Energy of an object is defined as its capacity for doing work and it is measured by the 
total quantity of work it can do. It is a scalar quantity. 
• The unit of energy is the same as that of work, i.e., joule (J). 
 Forms of Energy 
• Kinetic energy of an object is defined as the energy, which it possesses by virtue of 
its motion. It is measured by the amount of work that the object can do against an opposing 
force before it comes to rest. 
 Derivation of kinetic energy 
 Now work done = F ´ s   … (i) 
  
 Thus, kinetic energy possessed by an object of mass, m and moving with a uniform 
velocity, v is 
    
• The kinetic energy  of an object is defined as half the product of its mass (m) and 
the square of the speed (v) of the object, i.e., . 
J 10
6
2
2
1
mv E
K
=
) (
k
E
2
2
1
mv E
k
=
 
 
• Work-energy theorem states that net work done (W) by external forces on an object 
is equal to the change in its kinetic energy, i.e., W = change in kinetic energy.  
  
  
• The energy possessed by an object by virtue of its position or configuration (shape) is 
called its potential energy. It is measured by the amount of work that the object can do in 
passing from its present position or configuration (shape) to some standard position or 
configuration. 
• Potential energy is also termed as configuration energy or mutual energy. 
• Potential energy may be (i) gravitational potential energy (i.e., potential energy due to 
position of an object) or (ii) elastic potential energy (i.e., potential energy due to 
configuration of an object). 
• The potential energy of an object due to its height is called gravitational potential 
energy  
• Gravitational potential energy of an object of mass m at a height h is given by 
, where g is the acceleration due to gravity at the place under consideration. 
• Gravitational potential energy is due to the force of attraction (mg) between the Earth 
and the object. 
• Gravitational potential energy of an object depends on the difference in vertical heights 
of the initial and the final positions of the object and not on the path the object is moved, i.e., 
gravitational potential energy is path independent. 
 Law of Conservation of Energy and Its Transformation 
• Energy exists in nature in several forms such as solar energy, ocean energy, hydro 
energy, wind energy, mechanical energy, kinetic energy, potential energy, heat energy, 
chemical energy, light energy, sound energy etc. 
• Mechanical energy is the sum of the kinetic and potential energies. 
• One form of energy can be changed into another form – this process is called energy 
conversion or energy transformation. 
• Energy can neither be created nor destroyed, it can only be changed from one form to 
the other. This is called the Law of Conservation of Energy. 
• The total mechanical energy of a body throughout its free fall is conserved. 
• Gravitational potential energy depends on the choice of zero level. Positive 
gravitational potential energy implies that the body will do work while returning to zero level. 
Negative gravitational potential energy on the other hand implies that the work has to be 
done to bring the body back to the zero level. 
 Power 
• Power of an agent is the rate at which work is done by it. If W is the work done by an 
agent in time t, its power (P) is given by P = W/t. 
• The SI unit of power is called watt (W) where 
Ki Kf
E E W - =
2 2
2
1
2
1
mu mv W - =
). (
p
E
mgh E
p
=
3 
 
1 watt (W) =  i.e., 1 W = 1 J/s = 1 Js
–1
 
• Power is also defined as the product of force (F) and velocity (v), i.e., P = F × v. 
• The commercial unit of energy is called kilowatt hour (kWh) or simply a unit. 
1 kWh = 1 kW × 1 h = 3.6 MJ =  
 
,
(s) second 1
(J) joule 1
J 10 6 . 3
6
´