Quick Revision: Work, Energy & Power | Science & Technology for UPSC CSE PDF Download

 Page 1


 
                                                                                     
 
Physics 
Work, Energy and Power 
 
Work 
When an object is compelled to move from one spot to another, work is 
accomplished. Work is equal to force multiplied by displacement. Determining 
how far a body travels is termed displacement.  
? If the force F and the displacement d are both in the same direction, the 
work W can be calculated using the formula,  W F d ?? 
? Work is equal to the product of displacement and force. In SI (international 
system) units, unit of the force is Newton (N), and the distance & 
displacement unit is the metre (m) 
? A Newton-metre can thus be used to express the work unit. It's also known 
as a Joule, or J. Because the Newton is a composite unit, a Joule is also 
comparable to it. 
2
2
m
1J 1N m 1kg
s
? ? ? ? 
? The equation  W F d ?? depends on the same direction as force and 
displacement. 
? There are a variety of situations where, for example, someone pushing on 
a box near the floor is moving in a specific direction. 
? Although the box's resulting direction is forward, a portion of the force is 
directed down. In a case like this, only the force along the route of the 
displacement contributes to the job being done. If we treat force and 
displacement as vectors, then we can find the work by using the dot product 
(also known as the scalar product). 
W F d ?? 
cos W Fd ? ? 
? In the above formula, ? is the angle between the force and displacement 
vectors, and F and d  are the magnitudes of the vectors. 
Page 2


 
                                                                                     
 
Physics 
Work, Energy and Power 
 
Work 
When an object is compelled to move from one spot to another, work is 
accomplished. Work is equal to force multiplied by displacement. Determining 
how far a body travels is termed displacement.  
? If the force F and the displacement d are both in the same direction, the 
work W can be calculated using the formula,  W F d ?? 
? Work is equal to the product of displacement and force. In SI (international 
system) units, unit of the force is Newton (N), and the distance & 
displacement unit is the metre (m) 
? A Newton-metre can thus be used to express the work unit. It's also known 
as a Joule, or J. Because the Newton is a composite unit, a Joule is also 
comparable to it. 
2
2
m
1J 1N m 1kg
s
? ? ? ? 
? The equation  W F d ?? depends on the same direction as force and 
displacement. 
? There are a variety of situations where, for example, someone pushing on 
a box near the floor is moving in a specific direction. 
? Although the box's resulting direction is forward, a portion of the force is 
directed down. In a case like this, only the force along the route of the 
displacement contributes to the job being done. If we treat force and 
displacement as vectors, then we can find the work by using the dot product 
(also known as the scalar product). 
W F d ?? 
cos W Fd ? ? 
? In the above formula, ? is the angle between the force and displacement 
vectors, and F and d  are the magnitudes of the vectors. 
 
                                                                                     
? When work is performed against gravity, the amount of work performed 
equals the body's weight product plus the vertical distance lifted. 
? Work done in lifting body = Weight of Body ? Vertical Distance 
W mgh ?  
Where, W = Work Done  
M = Mass of body, g = acceleration due to gravity,  
h = Height through which the body is lifted 
? The quantity of work is a scalar quantity. Joule is the SI unit of work, and 
erg is the CGS unit of work. 
1 ? Joule 
7
10 erg ? 
? Its dimensional formula is 
22
ML T
?
??
??
. 
? Work done by a force is zero, if 
? Body is not displaced actually, i.e., 0 s ? . 
? The body is shifted perpendicular to the force direction. i.e., 90 ?
?
? . 
? When the angle between F and s is acute, the work done by a force is 
positive. 
? If the angle between F and s is obtuse, then the force's work is negative. 
? The work done by a constant force is dependent only on the initial and final 
places, not on the actual path taken between them. 
 
Work done in different conditions: 
Work done by a variable force is given by, 
W F ds ?
?
 
It corresponds to the area underneath the force-displacement graph with the 
proper sign. 
 
Energy 
Page 3


 
                                                                                     
 
Physics 
Work, Energy and Power 
 
Work 
When an object is compelled to move from one spot to another, work is 
accomplished. Work is equal to force multiplied by displacement. Determining 
how far a body travels is termed displacement.  
? If the force F and the displacement d are both in the same direction, the 
work W can be calculated using the formula,  W F d ?? 
? Work is equal to the product of displacement and force. In SI (international 
system) units, unit of the force is Newton (N), and the distance & 
displacement unit is the metre (m) 
? A Newton-metre can thus be used to express the work unit. It's also known 
as a Joule, or J. Because the Newton is a composite unit, a Joule is also 
comparable to it. 
2
2
m
1J 1N m 1kg
s
? ? ? ? 
? The equation  W F d ?? depends on the same direction as force and 
displacement. 
? There are a variety of situations where, for example, someone pushing on 
a box near the floor is moving in a specific direction. 
? Although the box's resulting direction is forward, a portion of the force is 
directed down. In a case like this, only the force along the route of the 
displacement contributes to the job being done. If we treat force and 
displacement as vectors, then we can find the work by using the dot product 
(also known as the scalar product). 
W F d ?? 
cos W Fd ? ? 
? In the above formula, ? is the angle between the force and displacement 
vectors, and F and d  are the magnitudes of the vectors. 
 
                                                                                     
? When work is performed against gravity, the amount of work performed 
equals the body's weight product plus the vertical distance lifted. 
? Work done in lifting body = Weight of Body ? Vertical Distance 
W mgh ?  
Where, W = Work Done  
M = Mass of body, g = acceleration due to gravity,  
h = Height through which the body is lifted 
? The quantity of work is a scalar quantity. Joule is the SI unit of work, and 
erg is the CGS unit of work. 
1 ? Joule 
7
10 erg ? 
? Its dimensional formula is 
22
ML T
?
??
??
. 
? Work done by a force is zero, if 
? Body is not displaced actually, i.e., 0 s ? . 
? The body is shifted perpendicular to the force direction. i.e., 90 ?
?
? . 
? When the angle between F and s is acute, the work done by a force is 
positive. 
? If the angle between F and s is obtuse, then the force's work is negative. 
? The work done by a constant force is dependent only on the initial and final 
places, not on the actual path taken between them. 
 
Work done in different conditions: 
Work done by a variable force is given by, 
W F ds ?
?
 
It corresponds to the area underneath the force-displacement graph with the 
proper sign. 
 
Energy 
 
                                                                                     
Energy is the ability of a body to perform work. Energy is a scalar quantity, 
meaning it has magnitude and no direction. The joule is the S.I unit, while the 
erg is the CGS unit. Its dimensional formula is as follows:  
33
. ML T
?
??
??
 
Mechanical energy (kinetic and potential energy), chemical energy, light energy, 
heat energy, sound energy, nuclear energy, electric energy, and other types of 
energy exist. 
 
Potential Energy 
The ability to do work in a body because of its situation or setup or we can say a 
body's energy because of its position or shape change is called potential energy. 
For example, compressed string energy, gathered water energy at a height, spring 
energy in a watch, etc. 
? A body's energy is called gravitational potential energy because of its 
position above the floor. 
? A body's energy is called elastic potential energy due to changing its shape 
and size. 
 
 
Kinetic Energy 
An object's kinetic energy (K) is equal to the amount of work needed to accelerate 
the object from rest to speed (v) can be expressed as, 
2
1
0
2
W mv ?? 
This relationship between kinetic energy and work is called the theorem of work-
energy. An object's kinetic energy is a scalar value, which means it is not 
dependent on the direction in which the object moves. 
? The kinetic energy value is always positive or zero. 
? The kinetic energy unit is the same as the Joule (J) unit of work. 
 
Page 4


 
                                                                                     
 
Physics 
Work, Energy and Power 
 
Work 
When an object is compelled to move from one spot to another, work is 
accomplished. Work is equal to force multiplied by displacement. Determining 
how far a body travels is termed displacement.  
? If the force F and the displacement d are both in the same direction, the 
work W can be calculated using the formula,  W F d ?? 
? Work is equal to the product of displacement and force. In SI (international 
system) units, unit of the force is Newton (N), and the distance & 
displacement unit is the metre (m) 
? A Newton-metre can thus be used to express the work unit. It's also known 
as a Joule, or J. Because the Newton is a composite unit, a Joule is also 
comparable to it. 
2
2
m
1J 1N m 1kg
s
? ? ? ? 
? The equation  W F d ?? depends on the same direction as force and 
displacement. 
? There are a variety of situations where, for example, someone pushing on 
a box near the floor is moving in a specific direction. 
? Although the box's resulting direction is forward, a portion of the force is 
directed down. In a case like this, only the force along the route of the 
displacement contributes to the job being done. If we treat force and 
displacement as vectors, then we can find the work by using the dot product 
(also known as the scalar product). 
W F d ?? 
cos W Fd ? ? 
? In the above formula, ? is the angle between the force and displacement 
vectors, and F and d  are the magnitudes of the vectors. 
 
                                                                                     
? When work is performed against gravity, the amount of work performed 
equals the body's weight product plus the vertical distance lifted. 
? Work done in lifting body = Weight of Body ? Vertical Distance 
W mgh ?  
Where, W = Work Done  
M = Mass of body, g = acceleration due to gravity,  
h = Height through which the body is lifted 
? The quantity of work is a scalar quantity. Joule is the SI unit of work, and 
erg is the CGS unit of work. 
1 ? Joule 
7
10 erg ? 
? Its dimensional formula is 
22
ML T
?
??
??
. 
? Work done by a force is zero, if 
? Body is not displaced actually, i.e., 0 s ? . 
? The body is shifted perpendicular to the force direction. i.e., 90 ?
?
? . 
? When the angle between F and s is acute, the work done by a force is 
positive. 
? If the angle between F and s is obtuse, then the force's work is negative. 
? The work done by a constant force is dependent only on the initial and final 
places, not on the actual path taken between them. 
 
Work done in different conditions: 
Work done by a variable force is given by, 
W F ds ?
?
 
It corresponds to the area underneath the force-displacement graph with the 
proper sign. 
 
Energy 
 
                                                                                     
Energy is the ability of a body to perform work. Energy is a scalar quantity, 
meaning it has magnitude and no direction. The joule is the S.I unit, while the 
erg is the CGS unit. Its dimensional formula is as follows:  
33
. ML T
?
??
??
 
Mechanical energy (kinetic and potential energy), chemical energy, light energy, 
heat energy, sound energy, nuclear energy, electric energy, and other types of 
energy exist. 
 
Potential Energy 
The ability to do work in a body because of its situation or setup or we can say a 
body's energy because of its position or shape change is called potential energy. 
For example, compressed string energy, gathered water energy at a height, spring 
energy in a watch, etc. 
? A body's energy is called gravitational potential energy because of its 
position above the floor. 
? A body's energy is called elastic potential energy due to changing its shape 
and size. 
 
 
Kinetic Energy 
An object's kinetic energy (K) is equal to the amount of work needed to accelerate 
the object from rest to speed (v) can be expressed as, 
2
1
0
2
W mv ?? 
This relationship between kinetic energy and work is called the theorem of work-
energy. An object's kinetic energy is a scalar value, which means it is not 
dependent on the direction in which the object moves. 
? The kinetic energy value is always positive or zero. 
? The kinetic energy unit is the same as the Joule (J) unit of work. 
 
 
                                                                                     
An object's kinetic energy can be associated with its mass and velocity with the 
formula, 
2
1
2
K mv ? 
If the force is in the same direction as the displacement of the object, this formula 
for kinetic energy can be discovered from the equation for work. This formula 
relies on the formula of kinematic. 
? ?
22
2 1 0
2
x
v v a x x ? ? ? 
The position change ? ?
0
xx ? is equivalent to the magnitude of the displacement, 
d.  
The formula can be rearranged for acceleration, a; 
22
21
2
vv
a
d
?
? 
Force is equal to the mass of an object multiplied by its acceleration, so the force 
is, F = ma.  
? This force formula can be replaced by the work formula,  W F d ?? 
22
21
2
vv
W m d
d
?? ?
??
??
??
   
? ?
22
21
1
2
W m v v ? ? ?   
22
21
11
22
W mv mv ? ? ? 
? The work performed by force on an object is therefore equivalent to the 
shift in the kinetic energy of the object,  
21
W K K ?? , WK ?? . 
The Greek uppercase letter ("delta") is used in this formula to mean 
"change in."   
? Work can be used to comprehend the energy of many objects experiencing 
forces. The work needed to extend a spring is one instance. If the object's 
displacement magnitude is marked x, and this represents the displacement 
away from a position of equilibrium 0 x ? , the force required to pull the 
object on the spring to a position x is,   F kx ? 
Page 5


 
                                                                                     
 
Physics 
Work, Energy and Power 
 
Work 
When an object is compelled to move from one spot to another, work is 
accomplished. Work is equal to force multiplied by displacement. Determining 
how far a body travels is termed displacement.  
? If the force F and the displacement d are both in the same direction, the 
work W can be calculated using the formula,  W F d ?? 
? Work is equal to the product of displacement and force. In SI (international 
system) units, unit of the force is Newton (N), and the distance & 
displacement unit is the metre (m) 
? A Newton-metre can thus be used to express the work unit. It's also known 
as a Joule, or J. Because the Newton is a composite unit, a Joule is also 
comparable to it. 
2
2
m
1J 1N m 1kg
s
? ? ? ? 
? The equation  W F d ?? depends on the same direction as force and 
displacement. 
? There are a variety of situations where, for example, someone pushing on 
a box near the floor is moving in a specific direction. 
? Although the box's resulting direction is forward, a portion of the force is 
directed down. In a case like this, only the force along the route of the 
displacement contributes to the job being done. If we treat force and 
displacement as vectors, then we can find the work by using the dot product 
(also known as the scalar product). 
W F d ?? 
cos W Fd ? ? 
? In the above formula, ? is the angle between the force and displacement 
vectors, and F and d  are the magnitudes of the vectors. 
 
                                                                                     
? When work is performed against gravity, the amount of work performed 
equals the body's weight product plus the vertical distance lifted. 
? Work done in lifting body = Weight of Body ? Vertical Distance 
W mgh ?  
Where, W = Work Done  
M = Mass of body, g = acceleration due to gravity,  
h = Height through which the body is lifted 
? The quantity of work is a scalar quantity. Joule is the SI unit of work, and 
erg is the CGS unit of work. 
1 ? Joule 
7
10 erg ? 
? Its dimensional formula is 
22
ML T
?
??
??
. 
? Work done by a force is zero, if 
? Body is not displaced actually, i.e., 0 s ? . 
? The body is shifted perpendicular to the force direction. i.e., 90 ?
?
? . 
? When the angle between F and s is acute, the work done by a force is 
positive. 
? If the angle between F and s is obtuse, then the force's work is negative. 
? The work done by a constant force is dependent only on the initial and final 
places, not on the actual path taken between them. 
 
Work done in different conditions: 
Work done by a variable force is given by, 
W F ds ?
?
 
It corresponds to the area underneath the force-displacement graph with the 
proper sign. 
 
Energy 
 
                                                                                     
Energy is the ability of a body to perform work. Energy is a scalar quantity, 
meaning it has magnitude and no direction. The joule is the S.I unit, while the 
erg is the CGS unit. Its dimensional formula is as follows:  
33
. ML T
?
??
??
 
Mechanical energy (kinetic and potential energy), chemical energy, light energy, 
heat energy, sound energy, nuclear energy, electric energy, and other types of 
energy exist. 
 
Potential Energy 
The ability to do work in a body because of its situation or setup or we can say a 
body's energy because of its position or shape change is called potential energy. 
For example, compressed string energy, gathered water energy at a height, spring 
energy in a watch, etc. 
? A body's energy is called gravitational potential energy because of its 
position above the floor. 
? A body's energy is called elastic potential energy due to changing its shape 
and size. 
 
 
Kinetic Energy 
An object's kinetic energy (K) is equal to the amount of work needed to accelerate 
the object from rest to speed (v) can be expressed as, 
2
1
0
2
W mv ?? 
This relationship between kinetic energy and work is called the theorem of work-
energy. An object's kinetic energy is a scalar value, which means it is not 
dependent on the direction in which the object moves. 
? The kinetic energy value is always positive or zero. 
? The kinetic energy unit is the same as the Joule (J) unit of work. 
 
 
                                                                                     
An object's kinetic energy can be associated with its mass and velocity with the 
formula, 
2
1
2
K mv ? 
If the force is in the same direction as the displacement of the object, this formula 
for kinetic energy can be discovered from the equation for work. This formula 
relies on the formula of kinematic. 
? ?
22
2 1 0
2
x
v v a x x ? ? ? 
The position change ? ?
0
xx ? is equivalent to the magnitude of the displacement, 
d.  
The formula can be rearranged for acceleration, a; 
22
21
2
vv
a
d
?
? 
Force is equal to the mass of an object multiplied by its acceleration, so the force 
is, F = ma.  
? This force formula can be replaced by the work formula,  W F d ?? 
22
21
2
vv
W m d
d
?? ?
??
??
??
   
? ?
22
21
1
2
W m v v ? ? ?   
22
21
11
22
W mv mv ? ? ? 
? The work performed by force on an object is therefore equivalent to the 
shift in the kinetic energy of the object,  
21
W K K ?? , WK ?? . 
The Greek uppercase letter ("delta") is used in this formula to mean 
"change in."   
? Work can be used to comprehend the energy of many objects experiencing 
forces. The work needed to extend a spring is one instance. If the object's 
displacement magnitude is marked x, and this represents the displacement 
away from a position of equilibrium 0 x ? , the force required to pull the 
object on the spring to a position x is,   F kx ? 
 
                                                                                     
? The expression of work done in extending the spring from position 
1
x to 
2
x is given as 
22
21
11
22
W kx kx ?? . 
? The constant k in this equation is the spring constant, which is different for 
every spring. The spring constant has units Newton per metre, N/m.  
 
Power 
Power is a measure of work rate. It is a measurement of how fast work is 
performed. For a quantity of work W performed in time t, the power performed 
is 
W
P
t
? . 
? The Power unit is the Watt (W), which equals one Joule per second. 1 W 
= 1 J/s 
? Power P can also be expressed as force F times velocity v. Since work is 
provided by force times displacement,   W F d ?? , then we know that, 
W
P
t
? 
() Fd
P
t
?? 
d
PF
t
??
??
??
??
 
P Fv ?? 
? Power is a scalar quantity. Its SI unit is watt and its dimensional formula is 
23
ML T
?
??
??
. 
? Its other units are kilowatt and horsepower, 
1 kilowatt 1000 ? watt 
1 horsepower 746 ? watt. 
 
Spring potential energy