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Revision Notes: Work, Energy & Power
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Revision Notes
Class - 11 Physics
Chapter 6 – Work, Energy and Power
1. WORK
In Physics, work refers to ‘mechanical work’. Work is said to be done by a force
on a body when the body is actually displaced through some distance in the
direction of the applied force.
However, when there is no displacement in the direction of the applied force, there
is no work done, i.e., work done is zero, when displacement of the body in the
direction of the force is zero.
Consider a constant force ‘F’ acting on a body to produce a displacement ‘s’ in the
body along the positive x-direction as shown in the following figure:
If
?
is the angle which F makes with the positive x-direction of the displacement,
then the component of F in the direction of displacement is given by
Fco s ?
. Since
the work done by the force is the product of component of force in the direction of
the displacement and the magnitude of the displacement, we can write:
W (Fcos )s =?
Now, when the displacement is in the direction of force applied, i.e., when
0
0 ?=
;
( )
W Fcos0 s F .s ? = ? =
Page 2
Revision Notes
Class - 11 Physics
Chapter 6 – Work, Energy and Power
1. WORK
In Physics, work refers to ‘mechanical work’. Work is said to be done by a force
on a body when the body is actually displaced through some distance in the
direction of the applied force.
However, when there is no displacement in the direction of the applied force, there
is no work done, i.e., work done is zero, when displacement of the body in the
direction of the force is zero.
Consider a constant force ‘F’ acting on a body to produce a displacement ‘s’ in the
body along the positive x-direction as shown in the following figure:
If
?
is the angle which F makes with the positive x-direction of the displacement,
then the component of F in the direction of displacement is given by
Fco s ?
. Since
the work done by the force is the product of component of force in the direction of
the displacement and the magnitude of the displacement, we can write:
W (Fcos )s =?
Now, when the displacement is in the direction of force applied, i.e., when
0
0 ?=
;
( )
W Fcos0 s F .s ? = ? =
Clearly, work done by a force is the dot product of force and displacement.
In terms of rectangular components, F and s may be written as
x Y Z
ˆ ˆ ˆ
F iF jF kF = + + and
ˆ ˆ ˆ
s ix jy kz = + +
( ) ( ) x Y Z
ˆ ˆ ˆ ˆ ˆ ˆ
W iF jF kF . ix jy kz ? = + + + +
x y z
W xF yF zF ? = + +
Work is a scalar quantity, i.e., it has magnitude only and no direction. However,
work done by a force can be positive, negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance;
1 2 2
W (M L T ) L
-
? = ?
1 2 2
W [M L T ]
-
?=
This is the dimensional formula of work.
The units of work are of two kinds: a) Absolute units and b) Gravitational units
a) Absolute units
1. Joule: It is the absolute unit of work in the SI system of units. Work done is
said to be one joule, when a force of one newton actually moves a body
through a distance of one meter in the direction of applied force.
0
1joule 1newton 1metre cos0 1N.m ? = ? ? =
2. Erg: It is the absolute unit of work in the CGS system of units. Work done is
said to be one erg, when a force of one dyne actually moves a body through
a distance of one cm in the direction of applied force.
0
1erg 1dyne 1cm cos0 1dyne.cm ? = ? ? =
Page 3
Revision Notes
Class - 11 Physics
Chapter 6 – Work, Energy and Power
1. WORK
In Physics, work refers to ‘mechanical work’. Work is said to be done by a force
on a body when the body is actually displaced through some distance in the
direction of the applied force.
However, when there is no displacement in the direction of the applied force, there
is no work done, i.e., work done is zero, when displacement of the body in the
direction of the force is zero.
Consider a constant force ‘F’ acting on a body to produce a displacement ‘s’ in the
body along the positive x-direction as shown in the following figure:
If
?
is the angle which F makes with the positive x-direction of the displacement,
then the component of F in the direction of displacement is given by
Fco s ?
. Since
the work done by the force is the product of component of force in the direction of
the displacement and the magnitude of the displacement, we can write:
W (Fcos )s =?
Now, when the displacement is in the direction of force applied, i.e., when
0
0 ?=
;
( )
W Fcos0 s F .s ? = ? =
Clearly, work done by a force is the dot product of force and displacement.
In terms of rectangular components, F and s may be written as
x Y Z
ˆ ˆ ˆ
F iF jF kF = + + and
ˆ ˆ ˆ
s ix jy kz = + +
( ) ( ) x Y Z
ˆ ˆ ˆ ˆ ˆ ˆ
W iF jF kF . ix jy kz ? = + + + +
x y z
W xF yF zF ? = + +
Work is a scalar quantity, i.e., it has magnitude only and no direction. However,
work done by a force can be positive, negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance;
1 2 2
W (M L T ) L
-
? = ?
1 2 2
W [M L T ]
-
?=
This is the dimensional formula of work.
The units of work are of two kinds: a) Absolute units and b) Gravitational units
a) Absolute units
1. Joule: It is the absolute unit of work in the SI system of units. Work done is
said to be one joule, when a force of one newton actually moves a body
through a distance of one meter in the direction of applied force.
0
1joule 1newton 1metre cos0 1N.m ? = ? ? =
2. Erg: It is the absolute unit of work in the CGS system of units. Work done is
said to be one erg, when a force of one dyne actually moves a body through
a distance of one cm in the direction of applied force.
0
1erg 1dyne 1cm cos0 1dyne.cm ? = ? ? =
b) Gravitational units
These are also known as practical units of work.
1. Kilogram-meter (kg-m): It is the gravitational unit of work in the SI system
of units. Work done is said to be one kg-m, when a force of 1kgf moves a
body through a distance of 1m in the direction of the applied force.
0
1kg m 1kgf 1m cos0 9.8N 1m 9.8joules ? - = ? ? = ? = , i.e.,
1kg m 9.8J ? - =
2. Gram-centimeter (g-cm): It is the gravitational unit of work in the CGS
system of units. Work done is said to be one g-cm, when a force of 1gf
moves a body through a distance of 1cm in the direction of the applied force.
0
1g cm 1gf 1cm cos0 ? - = ? ?
1g cm 980dyne 1cm 1 ? - = ? ?
1g m 980ergs ? - =
3. NATURE OF WORK DONE
Although work done ( ) W (Fcos )s =? is a scalar quantity, its value may be
positive, negative, negative or even zero, as detailed below:
a) Positive work is said to be done on a body when
?
is acute (
0
90 ?
). Clearly,
cos ?
turns out to be positive and hence, the work done is positive.
For example, when a body falls freely under the action of gravity,
00
0 ;cos cos0 1 ? = ? = = + . Clearly, work done by gravity on a body falling
freely is positive.
b) Negative work is said to be done on a body when
?
is obtuse (
0
90 ?
).
Clearly,
cos ?
is negative and hence, the work done is negative.
For example, when a body is thrown up, its motion is opposed by gravity.
The angle
?
between gravitational force and the displacement is
0
180
. Since
0
cos cos180 1 ? = = -
; work done by gravity on a body moving upwards is
negative.
Page 4
Revision Notes
Class - 11 Physics
Chapter 6 – Work, Energy and Power
1. WORK
In Physics, work refers to ‘mechanical work’. Work is said to be done by a force
on a body when the body is actually displaced through some distance in the
direction of the applied force.
However, when there is no displacement in the direction of the applied force, there
is no work done, i.e., work done is zero, when displacement of the body in the
direction of the force is zero.
Consider a constant force ‘F’ acting on a body to produce a displacement ‘s’ in the
body along the positive x-direction as shown in the following figure:
If
?
is the angle which F makes with the positive x-direction of the displacement,
then the component of F in the direction of displacement is given by
Fco s ?
. Since
the work done by the force is the product of component of force in the direction of
the displacement and the magnitude of the displacement, we can write:
W (Fcos )s =?
Now, when the displacement is in the direction of force applied, i.e., when
0
0 ?=
;
( )
W Fcos0 s F .s ? = ? =
Clearly, work done by a force is the dot product of force and displacement.
In terms of rectangular components, F and s may be written as
x Y Z
ˆ ˆ ˆ
F iF jF kF = + + and
ˆ ˆ ˆ
s ix jy kz = + +
( ) ( ) x Y Z
ˆ ˆ ˆ ˆ ˆ ˆ
W iF jF kF . ix jy kz ? = + + + +
x y z
W xF yF zF ? = + +
Work is a scalar quantity, i.e., it has magnitude only and no direction. However,
work done by a force can be positive, negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance;
1 2 2
W (M L T ) L
-
? = ?
1 2 2
W [M L T ]
-
?=
This is the dimensional formula of work.
The units of work are of two kinds: a) Absolute units and b) Gravitational units
a) Absolute units
1. Joule: It is the absolute unit of work in the SI system of units. Work done is
said to be one joule, when a force of one newton actually moves a body
through a distance of one meter in the direction of applied force.
0
1joule 1newton 1metre cos0 1N.m ? = ? ? =
2. Erg: It is the absolute unit of work in the CGS system of units. Work done is
said to be one erg, when a force of one dyne actually moves a body through
a distance of one cm in the direction of applied force.
0
1erg 1dyne 1cm cos0 1dyne.cm ? = ? ? =
b) Gravitational units
These are also known as practical units of work.
1. Kilogram-meter (kg-m): It is the gravitational unit of work in the SI system
of units. Work done is said to be one kg-m, when a force of 1kgf moves a
body through a distance of 1m in the direction of the applied force.
0
1kg m 1kgf 1m cos0 9.8N 1m 9.8joules ? - = ? ? = ? = , i.e.,
1kg m 9.8J ? - =
2. Gram-centimeter (g-cm): It is the gravitational unit of work in the CGS
system of units. Work done is said to be one g-cm, when a force of 1gf
moves a body through a distance of 1cm in the direction of the applied force.
0
1g cm 1gf 1cm cos0 ? - = ? ?
1g cm 980dyne 1cm 1 ? - = ? ?
1g m 980ergs ? - =
3. NATURE OF WORK DONE
Although work done ( ) W (Fcos )s =? is a scalar quantity, its value may be
positive, negative, negative or even zero, as detailed below:
a) Positive work is said to be done on a body when
?
is acute (
0
90 ?
). Clearly,
cos ?
turns out to be positive and hence, the work done is positive.
For example, when a body falls freely under the action of gravity,
00
0 ;cos cos0 1 ? = ? = = + . Clearly, work done by gravity on a body falling
freely is positive.
b) Negative work is said to be done on a body when
?
is obtuse (
0
90 ?
).
Clearly,
cos ?
is negative and hence, the work done is negative.
For example, when a body is thrown up, its motion is opposed by gravity.
The angle
?
between gravitational force and the displacement is
0
180
. Since
0
cos cos180 1 ? = = -
; work done by gravity on a body moving upwards is
negative.
c) Zero work is said to be done on a body when force applied on it or the
displacement caused or both of them are zero. Here, when angle
?
between
force and displacement is
0
90
;
0
cos cos90 0 ? = =
and hence, the work done
is zero.
For example, when we push hard against a wall, the force we exert on
the wall does no work because displacement is zero in this case. However, in
this process, our muscles are contracting and relaxing alternately and
internal energy is being used up. This is why we do get tired.
4. WORK DONE BY A VARIABLE FORCE
a) Graphical Method:
A constant force is rare. It is the variable force which is encountered more
commonly.
To evaluate the work done by a variable force, let us consider a force acting
along a fixed direction, say x–axis, but having a variable magnitude.
We have to compute work done in moving the body from A to B under the
action of this variable force.
To facilitate this, we assume that the entire displacement from A to B is
made up of a large number of infinitesimal displacements.
One such displacement shown in the following figure from P to Q.
Page 5
Revision Notes
Class - 11 Physics
Chapter 6 – Work, Energy and Power
1. WORK
In Physics, work refers to ‘mechanical work’. Work is said to be done by a force
on a body when the body is actually displaced through some distance in the
direction of the applied force.
However, when there is no displacement in the direction of the applied force, there
is no work done, i.e., work done is zero, when displacement of the body in the
direction of the force is zero.
Consider a constant force ‘F’ acting on a body to produce a displacement ‘s’ in the
body along the positive x-direction as shown in the following figure:
If
?
is the angle which F makes with the positive x-direction of the displacement,
then the component of F in the direction of displacement is given by
Fco s ?
. Since
the work done by the force is the product of component of force in the direction of
the displacement and the magnitude of the displacement, we can write:
W (Fcos )s =?
Now, when the displacement is in the direction of force applied, i.e., when
0
0 ?=
;
( )
W Fcos0 s F .s ? = ? =
Clearly, work done by a force is the dot product of force and displacement.
In terms of rectangular components, F and s may be written as
x Y Z
ˆ ˆ ˆ
F iF jF kF = + + and
ˆ ˆ ˆ
s ix jy kz = + +
( ) ( ) x Y Z
ˆ ˆ ˆ ˆ ˆ ˆ
W iF jF kF . ix jy kz ? = + + + +
x y z
W xF yF zF ? = + +
Work is a scalar quantity, i.e., it has magnitude only and no direction. However,
work done by a force can be positive, negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance;
1 2 2
W (M L T ) L
-
? = ?
1 2 2
W [M L T ]
-
?=
This is the dimensional formula of work.
The units of work are of two kinds: a) Absolute units and b) Gravitational units
a) Absolute units
1. Joule: It is the absolute unit of work in the SI system of units. Work done is
said to be one joule, when a force of one newton actually moves a body
through a distance of one meter in the direction of applied force.
0
1joule 1newton 1metre cos0 1N.m ? = ? ? =
2. Erg: It is the absolute unit of work in the CGS system of units. Work done is
said to be one erg, when a force of one dyne actually moves a body through
a distance of one cm in the direction of applied force.
0
1erg 1dyne 1cm cos0 1dyne.cm ? = ? ? =
b) Gravitational units
These are also known as practical units of work.
1. Kilogram-meter (kg-m): It is the gravitational unit of work in the SI system
of units. Work done is said to be one kg-m, when a force of 1kgf moves a
body through a distance of 1m in the direction of the applied force.
0
1kg m 1kgf 1m cos0 9.8N 1m 9.8joules ? - = ? ? = ? = , i.e.,
1kg m 9.8J ? - =
2. Gram-centimeter (g-cm): It is the gravitational unit of work in the CGS
system of units. Work done is said to be one g-cm, when a force of 1gf
moves a body through a distance of 1cm in the direction of the applied force.
0
1g cm 1gf 1cm cos0 ? - = ? ?
1g cm 980dyne 1cm 1 ? - = ? ?
1g m 980ergs ? - =
3. NATURE OF WORK DONE
Although work done ( ) W (Fcos )s =? is a scalar quantity, its value may be
positive, negative, negative or even zero, as detailed below:
a) Positive work is said to be done on a body when
?
is acute (
0
90 ?
). Clearly,
cos ?
turns out to be positive and hence, the work done is positive.
For example, when a body falls freely under the action of gravity,
00
0 ;cos cos0 1 ? = ? = = + . Clearly, work done by gravity on a body falling
freely is positive.
b) Negative work is said to be done on a body when
?
is obtuse (
0
90 ?
).
Clearly,
cos ?
is negative and hence, the work done is negative.
For example, when a body is thrown up, its motion is opposed by gravity.
The angle
?
between gravitational force and the displacement is
0
180
. Since
0
cos cos180 1 ? = = -
; work done by gravity on a body moving upwards is
negative.
c) Zero work is said to be done on a body when force applied on it or the
displacement caused or both of them are zero. Here, when angle
?
between
force and displacement is
0
90
;
0
cos cos90 0 ? = =
and hence, the work done
is zero.
For example, when we push hard against a wall, the force we exert on
the wall does no work because displacement is zero in this case. However, in
this process, our muscles are contracting and relaxing alternately and
internal energy is being used up. This is why we do get tired.
4. WORK DONE BY A VARIABLE FORCE
a) Graphical Method:
A constant force is rare. It is the variable force which is encountered more
commonly.
To evaluate the work done by a variable force, let us consider a force acting
along a fixed direction, say x–axis, but having a variable magnitude.
We have to compute work done in moving the body from A to B under the
action of this variable force.
To facilitate this, we assume that the entire displacement from A to B is
made up of a large number of infinitesimal displacements.
One such displacement shown in the following figure from P to Q.
Since the displacement PQ dx = is infinitesimally small, we consider that all
along this displacement, force is constant in magnitude as well in the same
direction.
Now, a small amount of work done in moving the body from P to Q is given
by,
dW F dx (PS)(PQ) area of strip PQRS = ? = =
Therefore, the total work done in moving the body from A to B is given by
W dW ?=
?
W F dx ? = ?
?
Here, when the displacement is allowed to approach zero, then the number
of terms in the sum increases without a limit. And the sum approaches a
definite value equal to the area under the curve CD.
Thus, we may rewrite that
dx x
W lim F(dx)
?
?=
?
Read MoreFAQs on Revision Notes: Work, Energy & Power
| 1. What's the difference between work and energy in physics, and why does it matter for NEET? |  |
Ans. Work is the process of transferring energy by applying force over distance, while energy is the capacity to do that work. Work measures the action; energy measures the potential or actual ability to cause change. For NEET, distinguishing these prevents calculation errors in thermodynamics and mechanics problems where energy conservation applies but work varies based on force direction and displacement.
| 2. How do I figure out if work is positive, negative, or zero in different situations? | |
Ans. Work depends on the angle between force and displacement vectors. When force aligns with motion, work is positive; opposing force creates negative work; perpendicular force produces zero work. Students often mistake this relationship, especially in circular motion where centripetal force does zero work. Using W = F·d·cosθ clarifies whether energy transfers into or out of a system during NEET problem-solving.
| 3. Why do kinetic energy and potential energy always seem to trade off with each other? | |
Ans. The law of conservation of mechanical energy states that kinetic and potential energy interchange when no external forces (like friction) act on a system. As an object falls, gravitational potential energy converts to kinetic energy; climbing upward reverses this. Understanding this trade-off is essential for solving motion problems in NEET where total mechanical energy remains constant throughout the process.
| 4. What exactly is power, and how is it different from energy and work? | |
Ans. Power measures how quickly work is done or energy is transferred-it's the rate at which work occurs, expressed as P = W/t. Energy is total capacity; work is energy transfer; power is speed of transfer. In NEET exams, calculating power requires identifying time intervals. Two machines can do identical work but differ in power output based on duration, which appears frequently in numerical problems.
| 5. How do I apply work-energy theorem to solve tough NEET physics problems? | |
Ans. The work-energy theorem states net work equals change in kinetic energy: W_net = ΔKE. Instead of tracking individual forces, sum all work contributions then equate to kinetic energy change. This shortcut bypasses force analysis entirely. For NEET candidates, this theorem simplifies complex multi-force scenarios-friction, gravity, applied force-into a single algebraic equation, significantly reducing calculation time and error likelihood.
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