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Important Work, Energy & Power Formulas for JEE and NEET
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Page 1
1.
Work
done
by
variable
force
Suppose
we
have
to
calculate
work
done
in
moving
a
body from a
point
A( )
to
a
point
B( )
under
the
action
of
a
variable
force.
So
the
work
done
by this
variable
force
in
displacing
a
body from point
to
is,
2.
Conservative
and
non-
conservative
forces
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
position
of
the
body,
and
not
on
the
natural
path
followed
between
the
initial
and
final
positions.
If
the
work
done
by or
against
a
force
in
moving
a
body from one
position
to
another
relies
on
the
path
taken
between
these
two
places,
the
force
is
said
to
be
non-conservative.
3.
Power
definition and
relation between work
and
power
Power
is
defined
as
the
rate
at
which
work
is
completed
in
a
given
amount
of
time.
The
relation
between
work
( )
and
power
( )
is
expressed
as
4.
Kinetic energy
and
linear
momentum
relation
The
energy of
a
body is
defined
as
the
capability or
ability of
the
body
to
do
the
work.
The
relation
between
kinetic
energy
(
)
and
linear
momentum( )
shows
that
a
body cannot
have
kinetic
energy
without
having
linear
momentum and
vice-versa.
Name of the Concept Key Points of the Concepts
Work, Energy and Power
Page 2
1.
Work
done
by
variable
force
Suppose
we
have
to
calculate
work
done
in
moving
a
body from a
point
A( )
to
a
point
B( )
under
the
action
of
a
variable
force.
So
the
work
done
by this
variable
force
in
displacing
a
body from point
to
is,
2.
Conservative
and
non-
conservative
forces
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
position
of
the
body,
and
not
on
the
natural
path
followed
between
the
initial
and
final
positions.
If
the
work
done
by or
against
a
force
in
moving
a
body from one
position
to
another
relies
on
the
path
taken
between
these
two
places,
the
force
is
said
to
be
non-conservative.
3.
Power
definition and
relation between work
and
power
Power
is
defined
as
the
rate
at
which
work
is
completed
in
a
given
amount
of
time.
The
relation
between
work
( )
and
power
( )
is
expressed
as
4.
Kinetic energy
and
linear
momentum
relation
The
energy of
a
body is
defined
as
the
capability or
ability of
the
body
to
do
the
work.
The
relation
between
kinetic
energy
(
)
and
linear
momentum( )
shows
that
a
body cannot
have
kinetic
energy
without
having
linear
momentum and
vice-versa.
Name of the Concept Key Points of the Concepts
Work, Energy and Power
5.
Work
energy
theorem
This
theorem states
that
if
some
work
( )
is
done
by the
body then
the
kinetic
energy( )
of
the
body also
increases
by the
same
amount.
Work
done
=
increase
in
K.E.
of
the
body
6.
Potential
energy
of
a
spring
The
potential
energy ( )
of
the
spring
is
the
energy associated
with
the
state
of
compression
or
expansion
of
an
elastic
spring.
It
is
given
as
Here,
=
spring
constant
and
=
stretch
or
compression
in
the
string
7.
Mechanical
energy
and
its
conservation
The
total
mechanical
energy of
the
system
is
conserved
if
the
forces
doing
work
on
the
system are
conservative
i.e,
when
net
work
done
by external
non-conservative
force
is
zero.
The
mechanical
energy ( )
of
a
body is
the
sum of
kinetic
energy ( )
and
potential
energy ( )
of
the
body.
Mathematically,
we
can
write
it
as
8.
Collision and
its
types When
two
things
bump
or
strike
against
each
other,
it
is
referred
to
as
a
collision.
There
are
two
types
of
collision,
Elastic collision:
A collision
in
which
there
is
no
kinetic
energy loss
at
all.
Inelastic collision:
A collision
that
results
in
some
loss
of
kinetic
energy.
The
basic characteristics
of
elastic
collision
are:
Linear
momentum is
conserved
Total
energy of
the
system is
conserved.
The
kinetic
energy is
conserved.
The
basic characteristics
of
inelastic
collision
are:
Linear
momentum is
conserved.
Total
energy is
conserved.
Name of the Concept Key Points of the Concepts
Page 3
1.
Work
done
by
variable
force
Suppose
we
have
to
calculate
work
done
in
moving
a
body from a
point
A( )
to
a
point
B( )
under
the
action
of
a
variable
force.
So
the
work
done
by this
variable
force
in
displacing
a
body from point
to
is,
2.
Conservative
and
non-
conservative
forces
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
position
of
the
body,
and
not
on
the
natural
path
followed
between
the
initial
and
final
positions.
If
the
work
done
by or
against
a
force
in
moving
a
body from one
position
to
another
relies
on
the
path
taken
between
these
two
places,
the
force
is
said
to
be
non-conservative.
3.
Power
definition and
relation between work
and
power
Power
is
defined
as
the
rate
at
which
work
is
completed
in
a
given
amount
of
time.
The
relation
between
work
( )
and
power
( )
is
expressed
as
4.
Kinetic energy
and
linear
momentum
relation
The
energy of
a
body is
defined
as
the
capability or
ability of
the
body
to
do
the
work.
The
relation
between
kinetic
energy
(
)
and
linear
momentum( )
shows
that
a
body cannot
have
kinetic
energy
without
having
linear
momentum and
vice-versa.
Name of the Concept Key Points of the Concepts
Work, Energy and Power
5.
Work
energy
theorem
This
theorem states
that
if
some
work
( )
is
done
by the
body then
the
kinetic
energy( )
of
the
body also
increases
by the
same
amount.
Work
done
=
increase
in
K.E.
of
the
body
6.
Potential
energy
of
a
spring
The
potential
energy ( )
of
the
spring
is
the
energy associated
with
the
state
of
compression
or
expansion
of
an
elastic
spring.
It
is
given
as
Here,
=
spring
constant
and
=
stretch
or
compression
in
the
string
7.
Mechanical
energy
and
its
conservation
The
total
mechanical
energy of
the
system
is
conserved
if
the
forces
doing
work
on
the
system are
conservative
i.e,
when
net
work
done
by external
non-conservative
force
is
zero.
The
mechanical
energy ( )
of
a
body is
the
sum of
kinetic
energy ( )
and
potential
energy ( )
of
the
body.
Mathematically,
we
can
write
it
as
8.
Collision and
its
types When
two
things
bump
or
strike
against
each
other,
it
is
referred
to
as
a
collision.
There
are
two
types
of
collision,
Elastic collision:
A collision
in
which
there
is
no
kinetic
energy loss
at
all.
Inelastic collision:
A collision
that
results
in
some
loss
of
kinetic
energy.
The
basic characteristics
of
elastic
collision
are:
Linear
momentum is
conserved
Total
energy of
the
system is
conserved.
The
kinetic
energy is
conserved.
The
basic characteristics
of
inelastic
collision
are:
Linear
momentum is
conserved.
Total
energy is
conserved.
Name of the Concept Key Points of the Concepts
List
of
Important
Formulas
for
Work
Energy
and
Power
Chapter
S.No. Name
of
the
Concept Formula
1.
Work
done
by variable
force
The
work
done
formula
by variable
force
is
The
work
done
formula
for
non-
variable
force
is
2.
Kinetic
energy and
linear
momentum relation.
The
kinetic
energy
formula
( )
is
The
expression
of
linear
momentum ( )
is
The
relationship
between
kinetic
energy and
linear
momentum is
as
follows:
3.
Work
energy theorem
According
to
this
theorem,
=
increase
in
of
the
body
Here,
and
are
the
final
and
initial
kinetic
energy of
the
body.
4.
Potential
energy of
a
spring
The
potential
energy
formula
of
a
spring
is
The
maximum velocity ( )
of
a
block
of
mass
upon
maximum
displacement
( )
is
5.
Mechanical
energy and
its
conservation.
According
to
conservation
of
mechanical
energy,
Page 4
1.
Work
done
by
variable
force
Suppose
we
have
to
calculate
work
done
in
moving
a
body from a
point
A( )
to
a
point
B( )
under
the
action
of
a
variable
force.
So
the
work
done
by this
variable
force
in
displacing
a
body from point
to
is,
2.
Conservative
and
non-
conservative
forces
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
position
of
the
body,
and
not
on
the
natural
path
followed
between
the
initial
and
final
positions.
If
the
work
done
by or
against
a
force
in
moving
a
body from one
position
to
another
relies
on
the
path
taken
between
these
two
places,
the
force
is
said
to
be
non-conservative.
3.
Power
definition and
relation between work
and
power
Power
is
defined
as
the
rate
at
which
work
is
completed
in
a
given
amount
of
time.
The
relation
between
work
( )
and
power
( )
is
expressed
as
4.
Kinetic energy
and
linear
momentum
relation
The
energy of
a
body is
defined
as
the
capability or
ability of
the
body
to
do
the
work.
The
relation
between
kinetic
energy
(
)
and
linear
momentum( )
shows
that
a
body cannot
have
kinetic
energy
without
having
linear
momentum and
vice-versa.
Name of the Concept Key Points of the Concepts
Work, Energy and Power
5.
Work
energy
theorem
This
theorem states
that
if
some
work
( )
is
done
by the
body then
the
kinetic
energy( )
of
the
body also
increases
by the
same
amount.
Work
done
=
increase
in
K.E.
of
the
body
6.
Potential
energy
of
a
spring
The
potential
energy ( )
of
the
spring
is
the
energy associated
with
the
state
of
compression
or
expansion
of
an
elastic
spring.
It
is
given
as
Here,
=
spring
constant
and
=
stretch
or
compression
in
the
string
7.
Mechanical
energy
and
its
conservation
The
total
mechanical
energy of
the
system
is
conserved
if
the
forces
doing
work
on
the
system are
conservative
i.e,
when
net
work
done
by external
non-conservative
force
is
zero.
The
mechanical
energy ( )
of
a
body is
the
sum of
kinetic
energy ( )
and
potential
energy ( )
of
the
body.
Mathematically,
we
can
write
it
as
8.
Collision and
its
types When
two
things
bump
or
strike
against
each
other,
it
is
referred
to
as
a
collision.
There
are
two
types
of
collision,
Elastic collision:
A collision
in
which
there
is
no
kinetic
energy loss
at
all.
Inelastic collision:
A collision
that
results
in
some
loss
of
kinetic
energy.
The
basic characteristics
of
elastic
collision
are:
Linear
momentum is
conserved
Total
energy of
the
system is
conserved.
The
kinetic
energy is
conserved.
The
basic characteristics
of
inelastic
collision
are:
Linear
momentum is
conserved.
Total
energy is
conserved.
Name of the Concept Key Points of the Concepts
List
of
Important
Formulas
for
Work
Energy
and
Power
Chapter
S.No. Name
of
the
Concept Formula
1.
Work
done
by variable
force
The
work
done
formula
by variable
force
is
The
work
done
formula
for
non-
variable
force
is
2.
Kinetic
energy and
linear
momentum relation.
The
kinetic
energy
formula
( )
is
The
expression
of
linear
momentum ( )
is
The
relationship
between
kinetic
energy and
linear
momentum is
as
follows:
3.
Work
energy theorem
According
to
this
theorem,
=
increase
in
of
the
body
Here,
and
are
the
final
and
initial
kinetic
energy of
the
body.
4.
Potential
energy of
a
spring
The
potential
energy
formula
of
a
spring
is
The
maximum velocity ( )
of
a
block
of
mass
upon
maximum
displacement
( )
is
5.
Mechanical
energy and
its
conservation.
According
to
conservation
of
mechanical
energy,
6. Collision and its types
The expression of coefficient of
restitution ( ) is
Here, and are the initial and
final velocities of the object.
The expressions of final velocities,
after elastic collision of two object,
are
The expression of common velocity
( ) when two object collide
inelastically is
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