NEET Exam > NEET Notes > Physics Class 11 > Revision Notes: Work, Energy & Power
Work, Energy & Power Class 11 Notes Physics Chapter 5
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
1. WORK
In Physics, work stands for ‘mechanical work’.
Work is said to be done by a force when the body is
displaced actually through some distance in the direction
of the applied force.
However, when there is no displacement in the direction
of the applied force, no work is said to be done, i.e., work
done is zero, when displacement of the body in the direction
of the force is zero.
Suppose a constant force
F
acting on a body produces a
displacement
s
in the body along the positive x-direction,
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 (F cos ). As work done
by the force is the product of component of force in the
direction of the displcement and the magnitude of the
displacement,
W Fcos s
...(1)
If displacement is in the direction of force applied, = 0°.
From (1), W = (F cos 0°) s = F s
Equation (1) can be rewritten as W F.s
...(2)
Thus, work done by a force is the dot product of force and
displacement.
In terms of rectangular cmponent,
F
and s,
may written as
x y z
ˆ ˆ ˆ
F i F jF kF
and
ˆ ˆ ˆ
s ix jy kz
From (2), W F.s
x y z
ˆ ˆ ˆ ˆ ˆ ˆ
W i F jF k F . i x jy k z
x y z
W x F y F zF
Obviously, work is a scalar quantity, i.e., it has magnitude
only and no direction. However, work done by a force can
be positive or negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance W = (M
1
L
1
T
–2
) × L
1 2 2
W M L T
This is the dimensional formula of work.
The units of work are of two types :
1. Absolute units 2. Gravitational units
(a) Absolute unit
1. Joule. It is the absolute unit of work on SI.
Work done is said to be one joule, when a force of one
newton actually moves a body through a distance of one
metre in the direction of applied force.
From W = F cos
1 joule = 1 newton × 1 metre × cos 0° = 1 N–m
2. Erg. It is the absolute unit of work on cgs system.
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.
From W = Fs cos
1 eg = 1 dyne × 1 cm × cos 0°
(b) Gravitational units
These are also called the practical units of work.
1. Kilogram-metre (kg–m). It is the gravitational unit of
work on SI.
Work done is said to be one kg–m, when a force of 1 kg f
move a body through a distance of 1 m in the direction of
the applied force.
From W = F s cos
1 kg–m = 1 kg f × 1 m × cos 0° = 9.8 N × 1 m = 9.8 joule, i.e.,
1kg m 9.8J
WORK, POWER & ENERGY
Page 2
1. WORK
In Physics, work stands for ‘mechanical work’.
Work is said to be done by a force when the body is
displaced actually through some distance in the direction
of the applied force.
However, when there is no displacement in the direction
of the applied force, no work is said to be done, i.e., work
done is zero, when displacement of the body in the direction
of the force is zero.
Suppose a constant force
F
acting on a body produces a
displacement
s
in the body along the positive x-direction,
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 (F cos ). As work done
by the force is the product of component of force in the
direction of the displcement and the magnitude of the
displacement,
W Fcos s
...(1)
If displacement is in the direction of force applied, = 0°.
From (1), W = (F cos 0°) s = F s
Equation (1) can be rewritten as W F.s
...(2)
Thus, work done by a force is the dot product of force and
displacement.
In terms of rectangular cmponent,
F
and s,
may written as
x y z
ˆ ˆ ˆ
F i F jF kF
and
ˆ ˆ ˆ
s ix jy kz
From (2), W F.s
x y z
ˆ ˆ ˆ ˆ ˆ ˆ
W i F jF k F . i x jy k z
x y z
W x F y F zF
Obviously, work is a scalar quantity, i.e., it has magnitude
only and no direction. However, work done by a force can
be positive or negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance W = (M
1
L
1
T
–2
) × L
1 2 2
W M L T
This is the dimensional formula of work.
The units of work are of two types :
1. Absolute units 2. Gravitational units
(a) Absolute unit
1. Joule. It is the absolute unit of work on SI.
Work done is said to be one joule, when a force of one
newton actually moves a body through a distance of one
metre in the direction of applied force.
From W = F cos
1 joule = 1 newton × 1 metre × cos 0° = 1 N–m
2. Erg. It is the absolute unit of work on cgs system.
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.
From W = Fs cos
1 eg = 1 dyne × 1 cm × cos 0°
(b) Gravitational units
These are also called the practical units of work.
1. Kilogram-metre (kg–m). It is the gravitational unit of
work on SI.
Work done is said to be one kg–m, when a force of 1 kg f
move a body through a distance of 1 m in the direction of
the applied force.
From W = F s cos
1 kg–m = 1 kg f × 1 m × cos 0° = 9.8 N × 1 m = 9.8 joule, i.e.,
1kg m 9.8J
WORK, POWER & ENERGY
2. Gram-centimetre (g-cm). It is the gravitational unit of
work on cgs system.
Work done is said to be one g-cm, when a force of 1 g f
moves a body through a distance of 1 cm. in the direction
of the applied force.
From W = F s cos
1 g-cm = 1 g f × 1 cm × cos 0°
1 g-cm = 980 dyne × 1 cm × 1
1g m 980ergs
3. NATURE OF WORK DONE
Although work done is a scalar quantity, its value may be
positive, negative, negative or even zero, as detailed below:
(a) Positive work
As W = F.s
= F s cos
when is acute (< 90°), cos is positive. Hence, work
done is positive.
For example :
(i) When a body falls freely under the action of gravity,
= 0°, cos = cos 0° = + 1. Therefore, work done by
gravity on a body falling freely is positive.
(b) Negative work
As W = F. s
= F s cos
When is obtuse (> 90°), cos is negative. Hence, work
done is negative.
For example :
(i) When a body is thrown up, its motion is opposed by
gravity. The angle between gravitational force
F
and
the displacement
s
is 180°. As cos = cos 180° = –1,
therefore, work done by gravity on a body moving
upwards is negative.
(c) Zero work
When force applied F
or the displacement
s
or both are
zero, work done W = F s cos is zero. Again, when angle
between F
and s
is 90°, cos = cos 90° = 0. Therefore
work done is zero.
For example :
When we push hard against a wall, the force we exert on
the wall does no work, because
s 0.
However, in this
process, our muscles are contracting and relaxing
alternately and internal energy is being used up. That 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. We can, therefore, learn to
calculate work done by a variable force, let us consider a
force acting along the fixed direction, say x–axis, but
having a variable magnitude.
We have to calculate work done in moving the body from
A to B under the action of this variable force. To do 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 figure from P to Q.
As the displacement PQ = dx is infinitesimally small, we
consider that all along this displacement, force is constant
in magnitude (= PS) as well in same direction.
Small amount of work done in moving the body from P to
Q is
dW = F × dx = (PS) (PQ) = area of strip PQRS
Total work done in moving the body from A to B is given by
W =
dW
W =
F × dx
If the displacement are allowed to approach zero, then the
number of terms in the sum increases without limit. And
the sum approaches a definite value equal to the area under
the curve CD.
A
B
WORK, POWER & ENERGY
Page 3
1. WORK
In Physics, work stands for ‘mechanical work’.
Work is said to be done by a force when the body is
displaced actually through some distance in the direction
of the applied force.
However, when there is no displacement in the direction
of the applied force, no work is said to be done, i.e., work
done is zero, when displacement of the body in the direction
of the force is zero.
Suppose a constant force
F
acting on a body produces a
displacement
s
in the body along the positive x-direction,
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 (F cos ). As work done
by the force is the product of component of force in the
direction of the displcement and the magnitude of the
displacement,
W Fcos s
...(1)
If displacement is in the direction of force applied, = 0°.
From (1), W = (F cos 0°) s = F s
Equation (1) can be rewritten as W F.s
...(2)
Thus, work done by a force is the dot product of force and
displacement.
In terms of rectangular cmponent,
F
and s,
may written as
x y z
ˆ ˆ ˆ
F i F jF kF
and
ˆ ˆ ˆ
s ix jy kz
From (2), W F.s
x y z
ˆ ˆ ˆ ˆ ˆ ˆ
W i F jF k F . i x jy k z
x y z
W x F y F zF
Obviously, work is a scalar quantity, i.e., it has magnitude
only and no direction. However, work done by a force can
be positive or negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance W = (M
1
L
1
T
–2
) × L
1 2 2
W M L T
This is the dimensional formula of work.
The units of work are of two types :
1. Absolute units 2. Gravitational units
(a) Absolute unit
1. Joule. It is the absolute unit of work on SI.
Work done is said to be one joule, when a force of one
newton actually moves a body through a distance of one
metre in the direction of applied force.
From W = F cos
1 joule = 1 newton × 1 metre × cos 0° = 1 N–m
2. Erg. It is the absolute unit of work on cgs system.
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.
From W = Fs cos
1 eg = 1 dyne × 1 cm × cos 0°
(b) Gravitational units
These are also called the practical units of work.
1. Kilogram-metre (kg–m). It is the gravitational unit of
work on SI.
Work done is said to be one kg–m, when a force of 1 kg f
move a body through a distance of 1 m in the direction of
the applied force.
From W = F s cos
1 kg–m = 1 kg f × 1 m × cos 0° = 9.8 N × 1 m = 9.8 joule, i.e.,
1kg m 9.8J
WORK, POWER & ENERGY
2. Gram-centimetre (g-cm). It is the gravitational unit of
work on cgs system.
Work done is said to be one g-cm, when a force of 1 g f
moves a body through a distance of 1 cm. in the direction
of the applied force.
From W = F s cos
1 g-cm = 1 g f × 1 cm × cos 0°
1 g-cm = 980 dyne × 1 cm × 1
1g m 980ergs
3. NATURE OF WORK DONE
Although work done is a scalar quantity, its value may be
positive, negative, negative or even zero, as detailed below:
(a) Positive work
As W = F.s
= F s cos
when is acute (< 90°), cos is positive. Hence, work
done is positive.
For example :
(i) When a body falls freely under the action of gravity,
= 0°, cos = cos 0° = + 1. Therefore, work done by
gravity on a body falling freely is positive.
(b) Negative work
As W = F. s
= F s cos
When is obtuse (> 90°), cos is negative. Hence, work
done is negative.
For example :
(i) When a body is thrown up, its motion is opposed by
gravity. The angle between gravitational force
F
and
the displacement
s
is 180°. As cos = cos 180° = –1,
therefore, work done by gravity on a body moving
upwards is negative.
(c) Zero work
When force applied F
or the displacement
s
or both are
zero, work done W = F s cos is zero. Again, when angle
between F
and s
is 90°, cos = cos 90° = 0. Therefore
work done is zero.
For example :
When we push hard against a wall, the force we exert on
the wall does no work, because
s 0.
However, in this
process, our muscles are contracting and relaxing
alternately and internal energy is being used up. That 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. We can, therefore, learn to
calculate work done by a variable force, let us consider a
force acting along the fixed direction, say x–axis, but
having a variable magnitude.
We have to calculate work done in moving the body from
A to B under the action of this variable force. To do 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 figure from P to Q.
As the displacement PQ = dx is infinitesimally small, we
consider that all along this displacement, force is constant
in magnitude (= PS) as well in same direction.
Small amount of work done in moving the body from P to
Q is
dW = F × dx = (PS) (PQ) = area of strip PQRS
Total work done in moving the body from A to B is given by
W =
dW
W =
F × dx
If the displacement are allowed to approach zero, then the
number of terms in the sum increases without limit. And
the sum approaches a definite value equal to the area under
the curve CD.
A
B
WORK, POWER & ENERGY WORK, POWER & ENERGY
Hence, we may rewrite, W =
dx x
limit F dx
In the language of integral calculus, we may write it as
B
A
x
x
W F dx
, where x
A
= O
A
and x
B
= OB
B
A
x
x
W area
of the strip PQRS
= total area under the curve between F and x-axis from
x = x
A
to x = x
B
W Area ABCDA
Hence, work done by a variable force is numerically equal
to the area under the force curve and the displacement axis.
Mathematical Treatment (of work done by a variable
force).
Suppose we have to calculate work done in moving a body
from a point A (S
A
) to point B (S
B
) under the action of a
varying force, figure. Here, S
A
and S
B
are the distance of
the points A and B with respect to some reference point.
At any stage, suppose the body is at P, where force on the
body is F
. Under the action of this force, let the body
undergo an infinitesimally small displacement
PQ ds
.
During such a small displacement, if we assume that the
force remains constant, then small amount of work done
in moving the body from P to Q is
dW F.ds
When ds 0,
total work done in moving the body from A A
to B can be obtained by integrating the above expression
between S
A
and S
B
.
B
A
S
S
W F.ds
5. CONSERVATIVE & NONCONSERVATIVE FORCES
Conservative force
A force is said to be conservative if work done by or against
the force in moving a body depends only on the initial and
final positions of the body, and not on the nature of path
followed between the initial and the final positions.
This means, work done by or against a conservative force
in moving a body over any path between fixed initial and
final positions will be the same.
For example, gravitational force is a conservative force.
Properties of Conservative forces :
1. Work done by or against a conservative force, in moving
a body from one position to the other depends only on
the initial position and final position of the body.
2. Work done by or against a conservative force does not
depend upon the nature of the path followed by the body
in going from initial position to the final position.
3. Work done by or against a conservative force in moving a
body through any round trip (i.e., closed path, where final
position coincides with the initial position of the body) is
always zero.
Non-conservative Forces
A force is said to be non-conservative, if work done by or
against the force in moving a body from one position to
another, depends on the path followed between these two
positions.
For example, frictional forces are non-conservative forces.
6. POWER
Power of a person or machine is defined as the time rate at
which work is done by it.
i.e., Power = Rate of doing work =
work done
time taken
Thus, power of a body measures how fast it can do the
work.
Page 4
1. WORK
In Physics, work stands for ‘mechanical work’.
Work is said to be done by a force when the body is
displaced actually through some distance in the direction
of the applied force.
However, when there is no displacement in the direction
of the applied force, no work is said to be done, i.e., work
done is zero, when displacement of the body in the direction
of the force is zero.
Suppose a constant force
F
acting on a body produces a
displacement
s
in the body along the positive x-direction,
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 (F cos ). As work done
by the force is the product of component of force in the
direction of the displcement and the magnitude of the
displacement,
W Fcos s
...(1)
If displacement is in the direction of force applied, = 0°.
From (1), W = (F cos 0°) s = F s
Equation (1) can be rewritten as W F.s
...(2)
Thus, work done by a force is the dot product of force and
displacement.
In terms of rectangular cmponent,
F
and s,
may written as
x y z
ˆ ˆ ˆ
F i F jF kF
and
ˆ ˆ ˆ
s ix jy kz
From (2), W F.s
x y z
ˆ ˆ ˆ ˆ ˆ ˆ
W i F jF k F . i x jy k z
x y z
W x F y F zF
Obviously, work is a scalar quantity, i.e., it has magnitude
only and no direction. However, work done by a force can
be positive or negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance W = (M
1
L
1
T
–2
) × L
1 2 2
W M L T
This is the dimensional formula of work.
The units of work are of two types :
1. Absolute units 2. Gravitational units
(a) Absolute unit
1. Joule. It is the absolute unit of work on SI.
Work done is said to be one joule, when a force of one
newton actually moves a body through a distance of one
metre in the direction of applied force.
From W = F cos
1 joule = 1 newton × 1 metre × cos 0° = 1 N–m
2. Erg. It is the absolute unit of work on cgs system.
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.
From W = Fs cos
1 eg = 1 dyne × 1 cm × cos 0°
(b) Gravitational units
These are also called the practical units of work.
1. Kilogram-metre (kg–m). It is the gravitational unit of
work on SI.
Work done is said to be one kg–m, when a force of 1 kg f
move a body through a distance of 1 m in the direction of
the applied force.
From W = F s cos
1 kg–m = 1 kg f × 1 m × cos 0° = 9.8 N × 1 m = 9.8 joule, i.e.,
1kg m 9.8J
WORK, POWER & ENERGY
2. Gram-centimetre (g-cm). It is the gravitational unit of
work on cgs system.
Work done is said to be one g-cm, when a force of 1 g f
moves a body through a distance of 1 cm. in the direction
of the applied force.
From W = F s cos
1 g-cm = 1 g f × 1 cm × cos 0°
1 g-cm = 980 dyne × 1 cm × 1
1g m 980ergs
3. NATURE OF WORK DONE
Although work done is a scalar quantity, its value may be
positive, negative, negative or even zero, as detailed below:
(a) Positive work
As W = F.s
= F s cos
when is acute (< 90°), cos is positive. Hence, work
done is positive.
For example :
(i) When a body falls freely under the action of gravity,
= 0°, cos = cos 0° = + 1. Therefore, work done by
gravity on a body falling freely is positive.
(b) Negative work
As W = F. s
= F s cos
When is obtuse (> 90°), cos is negative. Hence, work
done is negative.
For example :
(i) When a body is thrown up, its motion is opposed by
gravity. The angle between gravitational force
F
and
the displacement
s
is 180°. As cos = cos 180° = –1,
therefore, work done by gravity on a body moving
upwards is negative.
(c) Zero work
When force applied F
or the displacement
s
or both are
zero, work done W = F s cos is zero. Again, when angle
between F
and s
is 90°, cos = cos 90° = 0. Therefore
work done is zero.
For example :
When we push hard against a wall, the force we exert on
the wall does no work, because
s 0.
However, in this
process, our muscles are contracting and relaxing
alternately and internal energy is being used up. That 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. We can, therefore, learn to
calculate work done by a variable force, let us consider a
force acting along the fixed direction, say x–axis, but
having a variable magnitude.
We have to calculate work done in moving the body from
A to B under the action of this variable force. To do 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 figure from P to Q.
As the displacement PQ = dx is infinitesimally small, we
consider that all along this displacement, force is constant
in magnitude (= PS) as well in same direction.
Small amount of work done in moving the body from P to
Q is
dW = F × dx = (PS) (PQ) = area of strip PQRS
Total work done in moving the body from A to B is given by
W =
dW
W =
F × dx
If the displacement are allowed to approach zero, then the
number of terms in the sum increases without limit. And
the sum approaches a definite value equal to the area under
the curve CD.
A
B
WORK, POWER & ENERGY WORK, POWER & ENERGY
Hence, we may rewrite, W =
dx x
limit F dx
In the language of integral calculus, we may write it as
B
A
x
x
W F dx
, where x
A
= O
A
and x
B
= OB
B
A
x
x
W area
of the strip PQRS
= total area under the curve between F and x-axis from
x = x
A
to x = x
B
W Area ABCDA
Hence, work done by a variable force is numerically equal
to the area under the force curve and the displacement axis.
Mathematical Treatment (of work done by a variable
force).
Suppose we have to calculate work done in moving a body
from a point A (S
A
) to point B (S
B
) under the action of a
varying force, figure. Here, S
A
and S
B
are the distance of
the points A and B with respect to some reference point.
At any stage, suppose the body is at P, where force on the
body is F
. Under the action of this force, let the body
undergo an infinitesimally small displacement
PQ ds
.
During such a small displacement, if we assume that the
force remains constant, then small amount of work done
in moving the body from P to Q is
dW F.ds
When ds 0,
total work done in moving the body from A A
to B can be obtained by integrating the above expression
between S
A
and S
B
.
B
A
S
S
W F.ds
5. CONSERVATIVE & NONCONSERVATIVE FORCES
Conservative force
A force is said to be conservative if work done by or against
the force in moving a body depends only on the initial and
final positions of the body, and not on the nature of path
followed between the initial and the final positions.
This means, work done by or against a conservative force
in moving a body over any path between fixed initial and
final positions will be the same.
For example, gravitational force is a conservative force.
Properties of Conservative forces :
1. Work done by or against a conservative force, in moving
a body from one position to the other depends only on
the initial position and final position of the body.
2. Work done by or against a conservative force does not
depend upon the nature of the path followed by the body
in going from initial position to the final position.
3. Work done by or against a conservative force in moving a
body through any round trip (i.e., closed path, where final
position coincides with the initial position of the body) is
always zero.
Non-conservative Forces
A force is said to be non-conservative, if work done by or
against the force in moving a body from one position to
another, depends on the path followed between these two
positions.
For example, frictional forces are non-conservative forces.
6. POWER
Power of a person or machine is defined as the time rate at
which work is done by it.
i.e., Power = Rate of doing work =
work done
time taken
Thus, power of a body measures how fast it can do the
work.
WORK, POWER & ENERGY
dW
P
dt
Now, dW = F.ds,
where
F
is the force applied and
ds
is
the small displacement.
F.ds
P
dt
But
ds
v,
dt
the instantaneous velocity. .
P F.v
Dimensions of power can be deduced as :
1 2
1 2 3
1
W M L T
P M L T
t T
Units of power
The absolute unit of power in SI is watt, which is denoted
by W.
From P = W/t
1 watt =
1 joule
,
1sec
i.e.,
1
1W 1Js
Power of a body is said to be one watt, if it can do one
joule of work in one second.
1 h.p. 746 W
7. ENERGY
Energy of a body is defined as the capacity or ability of
the body to do the work.
8. KINETIC ENERGY
The kinetic energy of a boyd is the energy possessed by
the body by virtue of its motion.
For example :
(i) A bullet fired from a gun can pierce through a target on
account of kinetic energy of the bullet.
(ii) Wind mills work on the kinetic energy of air. For example,
sailing ships use the kinetic energy of wind.
(iii) Water mills work on the kinetic energy of water. For
example, fast flowing stream has been used to grind corn.
(iv) A nail is driven into a wooden block on account of kinetic
energy of the hammer striking the nail.
Formula for Kinetic Energy
Kinetic Energy of a body can be obtained either from
(i) the amount of work done in stopping the moving body, or
from
(ii) the amount of work done in giving the present velocity
today he body from the state of rest.
Let us use the second method :
suppose m = mass of a body at rest (i.e., u = 0).
F = Force applied on the body
a = acceleration produced in the body in the direction of
force applied.
v = velocity acquired by the body in moving through a
distance s, figure
From v – u = 2 a s
v
2
– 0 = 2 as
v
a
2s
As F = m a using, F = m
2
v
2s
Work done on the body, W = Force × distance
v
W m s
2s
1
W m v
This work done on the body is a measure of kinetic energy
(K.E.) acquired by the body,
1
K.E. of body W m v
Alternative method
The formula for kinetic energy of a body is also obtained
by the method of calculus :
Let m = mass of a body, which is initially at rest
(i.e., u = 0)
F
= Force applied on the body, ,
Page 5
1. WORK
In Physics, work stands for ‘mechanical work’.
Work is said to be done by a force when the body is
displaced actually through some distance in the direction
of the applied force.
However, when there is no displacement in the direction
of the applied force, no work is said to be done, i.e., work
done is zero, when displacement of the body in the direction
of the force is zero.
Suppose a constant force
F
acting on a body produces a
displacement
s
in the body along the positive x-direction,
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 (F cos ). As work done
by the force is the product of component of force in the
direction of the displcement and the magnitude of the
displacement,
W Fcos s
...(1)
If displacement is in the direction of force applied, = 0°.
From (1), W = (F cos 0°) s = F s
Equation (1) can be rewritten as W F.s
...(2)
Thus, work done by a force is the dot product of force and
displacement.
In terms of rectangular cmponent,
F
and s,
may written as
x y z
ˆ ˆ ˆ
F i F jF kF
and
ˆ ˆ ˆ
s ix jy kz
From (2), W F.s
x y z
ˆ ˆ ˆ ˆ ˆ ˆ
W i F jF k F . i x jy k z
x y z
W x F y F zF
Obviously, work is a scalar quantity, i.e., it has magnitude
only and no direction. However, work done by a force can
be positive or negative or zero.
2. DIMENSIONS AND UNITS OF WORK
As work = force × distance W = (M
1
L
1
T
–2
) × L
1 2 2
W M L T
This is the dimensional formula of work.
The units of work are of two types :
1. Absolute units 2. Gravitational units
(a) Absolute unit
1. Joule. It is the absolute unit of work on SI.
Work done is said to be one joule, when a force of one
newton actually moves a body through a distance of one
metre in the direction of applied force.
From W = F cos
1 joule = 1 newton × 1 metre × cos 0° = 1 N–m
2. Erg. It is the absolute unit of work on cgs system.
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.
From W = Fs cos
1 eg = 1 dyne × 1 cm × cos 0°
(b) Gravitational units
These are also called the practical units of work.
1. Kilogram-metre (kg–m). It is the gravitational unit of
work on SI.
Work done is said to be one kg–m, when a force of 1 kg f
move a body through a distance of 1 m in the direction of
the applied force.
From W = F s cos
1 kg–m = 1 kg f × 1 m × cos 0° = 9.8 N × 1 m = 9.8 joule, i.e.,
1kg m 9.8J
WORK, POWER & ENERGY
2. Gram-centimetre (g-cm). It is the gravitational unit of
work on cgs system.
Work done is said to be one g-cm, when a force of 1 g f
moves a body through a distance of 1 cm. in the direction
of the applied force.
From W = F s cos
1 g-cm = 1 g f × 1 cm × cos 0°
1 g-cm = 980 dyne × 1 cm × 1
1g m 980ergs
3. NATURE OF WORK DONE
Although work done is a scalar quantity, its value may be
positive, negative, negative or even zero, as detailed below:
(a) Positive work
As W = F.s
= F s cos
when is acute (< 90°), cos is positive. Hence, work
done is positive.
For example :
(i) When a body falls freely under the action of gravity,
= 0°, cos = cos 0° = + 1. Therefore, work done by
gravity on a body falling freely is positive.
(b) Negative work
As W = F. s
= F s cos
When is obtuse (> 90°), cos is negative. Hence, work
done is negative.
For example :
(i) When a body is thrown up, its motion is opposed by
gravity. The angle between gravitational force
F
and
the displacement
s
is 180°. As cos = cos 180° = –1,
therefore, work done by gravity on a body moving
upwards is negative.
(c) Zero work
When force applied F
or the displacement
s
or both are
zero, work done W = F s cos is zero. Again, when angle
between F
and s
is 90°, cos = cos 90° = 0. Therefore
work done is zero.
For example :
When we push hard against a wall, the force we exert on
the wall does no work, because
s 0.
However, in this
process, our muscles are contracting and relaxing
alternately and internal energy is being used up. That 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. We can, therefore, learn to
calculate work done by a variable force, let us consider a
force acting along the fixed direction, say x–axis, but
having a variable magnitude.
We have to calculate work done in moving the body from
A to B under the action of this variable force. To do 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 figure from P to Q.
As the displacement PQ = dx is infinitesimally small, we
consider that all along this displacement, force is constant
in magnitude (= PS) as well in same direction.
Small amount of work done in moving the body from P to
Q is
dW = F × dx = (PS) (PQ) = area of strip PQRS
Total work done in moving the body from A to B is given by
W =
dW
W =
F × dx
If the displacement are allowed to approach zero, then the
number of terms in the sum increases without limit. And
the sum approaches a definite value equal to the area under
the curve CD.
A
B
WORK, POWER & ENERGY WORK, POWER & ENERGY
Hence, we may rewrite, W =
dx x
limit F dx
In the language of integral calculus, we may write it as
B
A
x
x
W F dx
, where x
A
= O
A
and x
B
= OB
B
A
x
x
W area
of the strip PQRS
= total area under the curve between F and x-axis from
x = x
A
to x = x
B
W Area ABCDA
Hence, work done by a variable force is numerically equal
to the area under the force curve and the displacement axis.
Mathematical Treatment (of work done by a variable
force).
Suppose we have to calculate work done in moving a body
from a point A (S
A
) to point B (S
B
) under the action of a
varying force, figure. Here, S
A
and S
B
are the distance of
the points A and B with respect to some reference point.
At any stage, suppose the body is at P, where force on the
body is F
. Under the action of this force, let the body
undergo an infinitesimally small displacement
PQ ds
.
During such a small displacement, if we assume that the
force remains constant, then small amount of work done
in moving the body from P to Q is
dW F.ds
When ds 0,
total work done in moving the body from A A
to B can be obtained by integrating the above expression
between S
A
and S
B
.
B
A
S
S
W F.ds
5. CONSERVATIVE & NONCONSERVATIVE FORCES
Conservative force
A force is said to be conservative if work done by or against
the force in moving a body depends only on the initial and
final positions of the body, and not on the nature of path
followed between the initial and the final positions.
This means, work done by or against a conservative force
in moving a body over any path between fixed initial and
final positions will be the same.
For example, gravitational force is a conservative force.
Properties of Conservative forces :
1. Work done by or against a conservative force, in moving
a body from one position to the other depends only on
the initial position and final position of the body.
2. Work done by or against a conservative force does not
depend upon the nature of the path followed by the body
in going from initial position to the final position.
3. Work done by or against a conservative force in moving a
body through any round trip (i.e., closed path, where final
position coincides with the initial position of the body) is
always zero.
Non-conservative Forces
A force is said to be non-conservative, if work done by or
against the force in moving a body from one position to
another, depends on the path followed between these two
positions.
For example, frictional forces are non-conservative forces.
6. POWER
Power of a person or machine is defined as the time rate at
which work is done by it.
i.e., Power = Rate of doing work =
work done
time taken
Thus, power of a body measures how fast it can do the
work.
WORK, POWER & ENERGY
dW
P
dt
Now, dW = F.ds,
where
F
is the force applied and
ds
is
the small displacement.
F.ds
P
dt
But
ds
v,
dt
the instantaneous velocity. .
P F.v
Dimensions of power can be deduced as :
1 2
1 2 3
1
W M L T
P M L T
t T
Units of power
The absolute unit of power in SI is watt, which is denoted
by W.
From P = W/t
1 watt =
1 joule
,
1sec
i.e.,
1
1W 1Js
Power of a body is said to be one watt, if it can do one
joule of work in one second.
1 h.p. 746 W
7. ENERGY
Energy of a body is defined as the capacity or ability of
the body to do the work.
8. KINETIC ENERGY
The kinetic energy of a boyd is the energy possessed by
the body by virtue of its motion.
For example :
(i) A bullet fired from a gun can pierce through a target on
account of kinetic energy of the bullet.
(ii) Wind mills work on the kinetic energy of air. For example,
sailing ships use the kinetic energy of wind.
(iii) Water mills work on the kinetic energy of water. For
example, fast flowing stream has been used to grind corn.
(iv) A nail is driven into a wooden block on account of kinetic
energy of the hammer striking the nail.
Formula for Kinetic Energy
Kinetic Energy of a body can be obtained either from
(i) the amount of work done in stopping the moving body, or
from
(ii) the amount of work done in giving the present velocity
today he body from the state of rest.
Let us use the second method :
suppose m = mass of a body at rest (i.e., u = 0).
F = Force applied on the body
a = acceleration produced in the body in the direction of
force applied.
v = velocity acquired by the body in moving through a
distance s, figure
From v – u = 2 a s
v
2
– 0 = 2 as
v
a
2s
As F = m a using, F = m
2
v
2s
Work done on the body, W = Force × distance
v
W m s
2s
1
W m v
This work done on the body is a measure of kinetic energy
(K.E.) acquired by the body,
1
K.E. of body W m v
Alternative method
The formula for kinetic energy of a body is also obtained
by the method of calculus :
Let m = mass of a body, which is initially at rest
(i.e., u = 0)
F
= Force applied on the body, ,
WORK, POWER & ENERGY
ds
= small displacement produced in the body in the
direction of the force applied.
Small amount of work done by the force,
dW = F.ds
= F ds cos = 0° = F ds
If a is acceleration produced by the force, then from
F = m a = m
dv
dt
From, dW =
dv ds
m ds m dv
dt dt
dW = m v d v
ds
v
dt
Total work done by the force in increasing the velocity of
the body from zero to v is
v v
0 0 0
2
W m vd v m vd v m
2
1
W m v
Thus, kinetic energy of a body is half the product of mass
of the body and square of velocity of the body.
9. RELATION BETWEEN KINETIC ENERGY
AND LINEAR MOMENTUM
Let m = mass of a body, v = velocity of the body.
Linear momentum of the body, p = mv
and K.E. of the body
2
1 1
mv m v
2 m
p
K.E.
2 m
This is an important relation. It shows that a body cannot
have K.E. without having linear momentum. The reverse
is also true.
Further, if p = constant, K.E.
1
m
This is showin in figure (a)
If K.E. = constant, p
2
m or p m
This is shown in figure (b).
If m = constant, p
2
K.E. or p K.E.
This is shown in figure (c)
10. WORK ENERGY THEOREM OR
WORK ENERGY PRINCIPLE
According to this principle, work done by net force in
displacing a body is equal to change in kinetic energy of
the body.
Thus, when a force does some work on a body, the kinetic
energy of the body increases by the same amount.
Conversely, when an opposing (retarding) force is applied
on a body, its kinetic energy decreases. The decrease in
kinetic energy of the body is equal to the work done by
the body against the retarding force. Thus, according to
work energy principle, work and kinetic energy are
equivalent quantities.
Proof : To prove the work-energy theorem, we confine
ourselves to motion in one dimension.
Suppose m = mass of a body, u = initial velocity of the
body, F = force applied on the body along it direction of
motion, a = acceleration produced in the body, v = final
velocity of the body after t second.
Small amount of work done by the applied force on the
body, dW = F (ds) when ds is the small distance moved by
the body in the direction of the force applied.
Read More
|
97 videos|379 docs|103 tests
|
FAQs on Work, Energy & Power Class 11 Notes Physics Chapter 5
| 1. What is work and how is it related to energy and power? |  |
Ans. Work is defined as the transfer of energy that occurs when a force is applied to an object and it causes the object to move in the direction of the force. In the context of physics, work is calculated by multiplying the force applied to an object by the distance the object moves. This work done on an object is directly related to the energy transferred to the object. Power, on the other hand, is the rate at which work is done or energy is transferred. It is calculated by dividing the amount of work done by the time taken to do the work.
| 2. How does the conservation of energy apply to work and power? | |
Ans. The conservation of energy states that energy cannot be created or destroyed, it can only be transferred or converted from one form to another. In the context of work and power, this means that the total amount of energy used to do work or transfer energy remains constant. For example, if a certain amount of work is done on an object, the energy used to do that work is transferred to the object in the form of kinetic energy. Similarly, in terms of power, the total power output is equal to the power input, as energy is conserved.
| 3. How can we calculate the amount of work done on an object? | |
Ans. The amount of work done on an object can be calculated by multiplying the force applied to the object by the distance the object moves in the direction of the force. This can be represented by the equation W = F × d, where W is the work done, F is the force applied, and d is the distance moved. The unit of work is joules (J).
| 4. What is the relationship between work, energy, and power? | |
Ans. Work, energy, and power are interconnected concepts in physics. Work is the transfer of energy that occurs when a force is applied to an object and it causes the object to move. Energy is the capacity to do work or transfer heat. Power, on the other hand, is the rate at which work is done or energy is transferred. The relationship between these three concepts can be represented by the equation Power = Work / Time, where Power is measured in watts (W), Work in joules (J), and Time in seconds (s).
| 5. How does the concept of power relate to everyday life? | |
Ans. The concept of power is relevant in various aspects of everyday life. For example, electrical appliances in our homes are rated in terms of their power consumption, which determines how much energy they use per unit of time. The power output of vehicles, such as cars and motorcycles, is an important factor in determining their performance. In industries, power is a crucial factor in determining the efficiency and productivity of machines and processes. Understanding power helps us make informed decisions about energy usage and efficiency in our daily lives.
About this Document
1.2K Views
4.80/5
Rating
Feb 16, 2025
Last updated
Document Description: Revision Notes: Work, Energy & Power for NEET 2025 is part of Physics Class 11 preparation.
The notes and questions for Revision Notes: Work, Energy & Power have been prepared according to the NEET exam syllabus. Information about Revision Notes: Work, Energy & Power covers topics
like and Revision Notes: Work, Energy & Power Example, for NEET 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Revision Notes: Work, Energy & Power.
Introduction of Revision Notes: Work, Energy & Power in English is available as part of our Physics Class 11
for NEET & Revision Notes: Work, Energy & Power in Hindi for Physics Class 11 course.
Download more important topics related with notes, lectures and mock test series for NEET
Exam by signing up for free. NEET: Work, Energy & Power Class 11 Notes Physics Chapter 5
Description
Full syllabus notes, lecture & questions for Work, Energy & Power Class 11 Notes Physics Chapter 5 - NEET | Plus excerises question with solution to help you revise complete syllabus for Physics Class 11 | Best notes, free PDF download
Information about Revision Notes: Work, Energy & Power
In this doc you can find the meaning of Revision Notes: Work, Energy & Power defined & explained in the simplest way possible. Besides explaining types of
Revision Notes: Work, Energy & Power theory, EduRev gives you an ample number of questions to practice Revision Notes: Work, Energy & Power tests, examples and also practice NEET
tests
Related Searches
ppt
,Exam
,Energy & Power Class 11 Notes Physics Chapter 5
,shortcuts and tricks
,Work
,practice quizzes
,Viva Questions
,mock tests for examination
,Important questions
,Work
,Summary
,Extra Questions
,Sample Paper
,past year papers
,study material
,Objective type Questions
,Previous Year Questions with Solutions
,Work
,Free
,MCQs
,Energy & Power Class 11 Notes Physics Chapter 5
,Semester Notes
,video lectures
,Energy & Power Class 11 Notes Physics Chapter 5
;
Additional Information about Revision Notes: Work, Energy & Power for NEET Preparation
Revision Notes: Work, Energy & Power Free PDF Download
The Revision Notes: Work, Energy & Power is an invaluable resource that delves deep into the core of the NEET exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the Revision Notes: Work, Energy & Power now and kickstart your journey towards success in the NEET exam.
Importance of Revision Notes: Work, Energy & Power
The importance of Revision Notes: Work, Energy & Power cannot be overstated, especially for NEET aspirants.
This document holds the key to success in the NEET exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
Revision Notes: Work, Energy & Power
Revision Notes: Work, Energy & Power Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to Revision Notes: Work, Energy & Power.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, Revision Notes: Work, Energy & Power Notes on EduRev are your ultimate resource for success.
Revision Notes: Work, Energy & Power NEET Questions
The "Revision Notes: Work, Energy & Power NEET Questions" guide is a valuable resource for all aspiring students preparing for the
NEET exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study Revision Notes: Work, Energy & Power on the App
Students of NEET can study Revision Notes: Work, Energy & Power alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Revision Notes: Work, Energy & Power,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Revision Notes: Work, Energy & Power is prepared as per the latest NEET syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup