Class 11 Exam > Class 11 Videos > Conservation of Momentum (Part - 9) - Laws of Motion, Physics
Conservation of Momentum (Part - 9) - Laws of Motion, Physics Video Lecture - Class 11
FAQs on Conservation of Momentum (Part - 9) - Laws of Motion, Physics Video Lecture - Class 11
| 1. What is the law of conservation of momentum? |  |
The law of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. This means that in a closed system, the total momentum before an event is equal to the total momentum after the event.
| 2. How is momentum calculated? | |
Momentum is calculated by multiplying an object's mass by its velocity. The formula for momentum is: momentum = mass x velocity. The SI unit for momentum is kilogram-meter per second (kg m/s).
| 3. Can momentum be lost or gained? | |
According to the law of conservation of momentum, momentum cannot be lost or gained in an isolated system. This means that if there are no external forces acting on the system, the total momentum of the system will remain constant.
| 4. What happens to the momentum when two objects collide? | |
When two objects collide, the total momentum of the system is conserved. If the collision is elastic (no loss of kinetic energy), the momentum of each object may change, but the total momentum before and after the collision will be the same. In an inelastic collision (some kinetic energy is lost), the total momentum is still conserved, but the momentum of each object may not be the same before and after the collision.
| 5. How does the law of conservation of momentum apply to everyday life? | |
The law of conservation of momentum is applicable in various everyday situations. For example, when a person jumps off a moving boat onto a dock, the boat will move backward due to the conservation of momentum. Similarly, in sports such as billiards or pool, the motion of the balls after a collision follows the principles of momentum conservation. Understanding this law helps explain and predict the behavior of objects in everyday scenarios.
Text Transcript from Video
hello friends this video on laws of
motion part 9 is brought to you by exam
feel calm no more fear from exam please
make sure that you have watched all the
videos from part 1 2 5 8 before going
ahead with part 9 now that we have
discussed Newton's first law Newton's
second law and Newton's third law of
motion we let us now study conservation
of momentum conservation of momentum
states that in an isolated system the
total momentum is conserved what do I
mean when I say isolated system isolated
system is something where no external
force is acting on the system that is
the external force acting on the system
is equal to zero so in an isolated
system the total momentum of the system
is conserved conserved in the sense that
the total momentum the value of total
momentum remains constant we will take
up an example so that the idea becomes
even more clearer let us take the
example of a spinning top if you look at
a top you see that it constantly keeps
revolving around its tip correct so what
do we see that however at every point of
time the momentum keeps changing in
direction but for every point later
suppose we have a momentum at this point
this point this point at all the points
you have a momentum but what happens
exactly is the momentum act somewhat
like this but at the same time on the
other end you have directions like this
so for every momentum you have an equal
in magnitude but opposite in direction
another momentum so they both cancel out
as a result the net momentum when you
calculate is found to be zero so what do
we see in this initially the vendor
system was at rest then the momentum was
equal to zero even after the it started
spinning the final momentum also the net
value of the final momentum also turns
out to be zero so we see that the
initial momentum of
the system and the final momentum of the
system is equal and that is what we want
we see in the law of conservation of
momentum it says that for the total
momentum of a system before any event
and the total momentum of the system
after the event remains the same so
that's what we observed in case of the
spinning top will take few more examples
to get things clear let us take the
example of a bullet fired from a rifle
if you see the first picture you see the
rifle is at rest so this is our initial
this system will tell us the initial
momentum of the system now the initial
momentum of the system is equal to 0 now
in the later stage what do we see when
the rifle is fired that is when the
trigger is moved somewhat in the in this
direction as you can see here the bullet
is fired in this direction correct so
now what would be the final momentum of
this system after the bullet is fired
what happened here was the trigger was
pulled in this direction that is in the
negative x direction and a bullet was
fired in the positive x direction so the
bullet gained some momentum because the
bullet had its own mass and it moved
with some velocity as you saw here so
the bullet had gained some momentum but
this momentum got canceled by the rifles
momentum in the backward direction so
the bullets momentum was in this
direction and the rifles momentum was in
this direction so the both thing equal
and opposite got cancelled therefore the
total momentum given in this case turned
out to be 0 therefore we find that the
momentum remains conserved conserved
that is before the firing and after the
firing the total momentum of the system
is zero now let us take up the next
example for conservation of momentum
here we take the example of a rocket
propulsion let us suppose
this is the rocket we say initially now
what does this initial time do noting it
is denoting the time when the rocket
just start moving so let us suppose the
mass of the rocket is M fine
now let us suppose the velocity with
which the rocket is moving is V so what
could be the initial momentum of the
system it will be mass into velocity
that is MV now what happens is when the
as the rocket starts moving the gases
keeps eject gets ejecting in the
opposite direction that is the rocket
moves in this direction and the gases
are ejected in the opposite direction
now these gases which are ejected in the
opposite direction gives a kind of
forward push which helps the rocket to
move upward because these are ejected in
the downward direction so when busy the
later situation what happens the mass of
the rocket is now reduced by the mass of
this ejected gases let us suppose the
mass of the ejected gases is denoted by
small n that is this much of this much
mass of the gases are ejected in
downward direction and let us suppose
that the velocity of the gases in the
downward direction is denoted by say in
fee - so this is denoted by B - and this
is denoted by mass of the rocket is goes
Capital m initially and now the mass of
the gas is ejected its small n so what
will happen now the mass of the rocket
will become Capital m which was
initially the mass of the rocket minus
small M because the gases were initially
inside the rocket and now they are
ejected so the mass of the rocket is
reduced by small M now what will be the
velocity of the rocket now the velocity
of the rocket would
be feel that is the initial velocity of
the rocket + V - because the velocity of
the gasses are relative to the rocket in
the opposite direction since both our
B&B - are in opposite direction
so they will add up that is V Plus V -
so what do we find the final momentum is
equal to mass into velocity so mass is M
- 4 m velocity is V Plus V - now what
did we observe we find that M gets
reduced mass is reduced but at the same
time velocity is increased so this shows
that momentum remains constant
now initial momentum was mass into
velocity final momentum was in the final
momentum the mass got reduced but the
velocity got increased so keeping the
total value as constant one quantity was
reduced and the other quantity was
increased so the product remains the
same so we find that P final that is the
final momentum is equal to the initial
momentum and that is how the law of
conservation of momentum holds true for
a rocket propulsion I hope it is clear
to you initially the mass of the rocket
was em and since them rocket just
started moving the velocity of the
rocket was P so initial momentum was M V
now as the rocket kept moving the gases
were ejected in the opposite direction
with a velocity relative to the velocity
of the rocket so what happened now the
mass of the rocket was reduced by small
M because this is the mass of the gases
which are ejected and the velocity of
the rocket increased view to the
relative velocity of the gases which are
ejected as a result we find that in
momentum the mass were reduced but at
the same time the velocity got increased
so keeping the product of mass and
velocity constant so the initial
momentum and the final
remain the same thus it proves the
conservation of a moment we will now
look at a very important application of
conservation of moment and that is
collision between two bodies it is a
very important application of
conservation of momentum let us suppose
we have two bodies one and two and these
two bodies collide so what is the event
here collision is the event so what we
will do we will try to prove that the
initial momentum before collision is the
same as the final momentum after
collision so we will calculate the total
momentum of the system before collision
then they will calculate the total
momentum of the system after police let
us consider at initial initial means
before collision let us suppose before
collision the momentum of godî one was P
1 and the momentum of body 2 was heat
and let us suppose that after collision
that is the final values after collision
the momentum of 1 is P 1 dash and
momentum of 2 is P 2 dash now by
Newton's second law we know that force
is equal to rate of change of momentum
that is f is equal to DP by DT or we can
also write it as Delta P by Delta P now
for the first body that is for body 1 we
can write that the force exerted on body
1 by body to because when we are
considering two bodies even before
collision also there will be some force
exerted by two one one and as a result
there will be some force exerted by one
on two right now we are considering only
body 1 so the force exerted on one by 2
this will be equal to that the change
rate of change of momentum per unit time
so this will be the change in momentum
on body 1 so change in momentum will be
final value of momentum
- initial value of momentum divided by
delta T similarly for body - the force
acting on body 2 by body 1 will be equal
to the change in momentum in body 2 per
unit time right
also by Newton's third law we know that
F 1 2 is equal to minus F 2 1 that means
the force exerted on 1 by 2 is equal to
negative of force exerted on 2 by 1
because the forces are equal and
opposite in nature so we can put the
value of F 1 2 and F 2 1 in this
equation so we will get P 1 dash minus P
1 divided by Delta e is equal to e 2
dash minus P 2 divided by delta T so
delta T delta T will cancel out so we
get P 1 dash minus P 1 is equal to P 2
dash minus P 2 so from here we can write
P 1 dash minus P 2 dash is equal to P 1
minus P I am sorry I missed out the
minus sign over here there was a minus
sign here as we said minus F of T 1 so
this would be minus and this would be
plus so we get e 1 dash plus P dash is
equal to e 1 plus P so what does this
show P 1 plus P 2 is the total initial
momentum of the system P 1 plus P 2 is
the total initial momentum and P 1 dash
plus P 2 dash is the total final
momentum of the system so we have proved
that the total initial momentum is equal
to the total final momentum that is the
momentum is conserved in case of a
collision so what we see here is we
consider two systems now the two systems
together will constitute the system when
I use the word system here I'm going to
see the system including both the
particles one an T now let us suppose
before they collide the initial more'd
numbers t1 and people for both of them
after they collide the momentum was p1 -
p2 - now my Newton second law we knew F
is equal to DP by DT that is change in
momentum with time so for body 1 the
force exerted on one by 2 is equal to
the change in momentum of 1 divided by
delta T similarly for what you do now we
know that Newton's third law says F 1 2
is equal to minus F 1 so what we did is
we just replace the value of F 1 2 and F
2 1 with these values and we believe and
we got V 1 dash plus V 2 dashed is equal
to P 1 plus P 2 that is the total final
momentum is defining the total initial
momentum of the system thank you
visit exam viacom to watch free
educational videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and much more thanks once again
motion part 9 is brought to you by exam
feel calm no more fear from exam please
make sure that you have watched all the
videos from part 1 2 5 8 before going
ahead with part 9 now that we have
discussed Newton's first law Newton's
second law and Newton's third law of
motion we let us now study conservation
of momentum conservation of momentum
states that in an isolated system the
total momentum is conserved what do I
mean when I say isolated system isolated
system is something where no external
force is acting on the system that is
the external force acting on the system
is equal to zero so in an isolated
system the total momentum of the system
is conserved conserved in the sense that
the total momentum the value of total
momentum remains constant we will take
up an example so that the idea becomes
even more clearer let us take the
example of a spinning top if you look at
a top you see that it constantly keeps
revolving around its tip correct so what
do we see that however at every point of
time the momentum keeps changing in
direction but for every point later
suppose we have a momentum at this point
this point this point at all the points
you have a momentum but what happens
exactly is the momentum act somewhat
like this but at the same time on the
other end you have directions like this
so for every momentum you have an equal
in magnitude but opposite in direction
another momentum so they both cancel out
as a result the net momentum when you
calculate is found to be zero so what do
we see in this initially the vendor
system was at rest then the momentum was
equal to zero even after the it started
spinning the final momentum also the net
value of the final momentum also turns
out to be zero so we see that the
initial momentum of
the system and the final momentum of the
system is equal and that is what we want
we see in the law of conservation of
momentum it says that for the total
momentum of a system before any event
and the total momentum of the system
after the event remains the same so
that's what we observed in case of the
spinning top will take few more examples
to get things clear let us take the
example of a bullet fired from a rifle
if you see the first picture you see the
rifle is at rest so this is our initial
this system will tell us the initial
momentum of the system now the initial
momentum of the system is equal to 0 now
in the later stage what do we see when
the rifle is fired that is when the
trigger is moved somewhat in the in this
direction as you can see here the bullet
is fired in this direction correct so
now what would be the final momentum of
this system after the bullet is fired
what happened here was the trigger was
pulled in this direction that is in the
negative x direction and a bullet was
fired in the positive x direction so the
bullet gained some momentum because the
bullet had its own mass and it moved
with some velocity as you saw here so
the bullet had gained some momentum but
this momentum got canceled by the rifles
momentum in the backward direction so
the bullets momentum was in this
direction and the rifles momentum was in
this direction so the both thing equal
and opposite got cancelled therefore the
total momentum given in this case turned
out to be 0 therefore we find that the
momentum remains conserved conserved
that is before the firing and after the
firing the total momentum of the system
is zero now let us take up the next
example for conservation of momentum
here we take the example of a rocket
propulsion let us suppose
this is the rocket we say initially now
what does this initial time do noting it
is denoting the time when the rocket
just start moving so let us suppose the
mass of the rocket is M fine
now let us suppose the velocity with
which the rocket is moving is V so what
could be the initial momentum of the
system it will be mass into velocity
that is MV now what happens is when the
as the rocket starts moving the gases
keeps eject gets ejecting in the
opposite direction that is the rocket
moves in this direction and the gases
are ejected in the opposite direction
now these gases which are ejected in the
opposite direction gives a kind of
forward push which helps the rocket to
move upward because these are ejected in
the downward direction so when busy the
later situation what happens the mass of
the rocket is now reduced by the mass of
this ejected gases let us suppose the
mass of the ejected gases is denoted by
small n that is this much of this much
mass of the gases are ejected in
downward direction and let us suppose
that the velocity of the gases in the
downward direction is denoted by say in
fee - so this is denoted by B - and this
is denoted by mass of the rocket is goes
Capital m initially and now the mass of
the gas is ejected its small n so what
will happen now the mass of the rocket
will become Capital m which was
initially the mass of the rocket minus
small M because the gases were initially
inside the rocket and now they are
ejected so the mass of the rocket is
reduced by small M now what will be the
velocity of the rocket now the velocity
of the rocket would
be feel that is the initial velocity of
the rocket + V - because the velocity of
the gasses are relative to the rocket in
the opposite direction since both our
B&B - are in opposite direction
so they will add up that is V Plus V -
so what do we find the final momentum is
equal to mass into velocity so mass is M
- 4 m velocity is V Plus V - now what
did we observe we find that M gets
reduced mass is reduced but at the same
time velocity is increased so this shows
that momentum remains constant
now initial momentum was mass into
velocity final momentum was in the final
momentum the mass got reduced but the
velocity got increased so keeping the
total value as constant one quantity was
reduced and the other quantity was
increased so the product remains the
same so we find that P final that is the
final momentum is equal to the initial
momentum and that is how the law of
conservation of momentum holds true for
a rocket propulsion I hope it is clear
to you initially the mass of the rocket
was em and since them rocket just
started moving the velocity of the
rocket was P so initial momentum was M V
now as the rocket kept moving the gases
were ejected in the opposite direction
with a velocity relative to the velocity
of the rocket so what happened now the
mass of the rocket was reduced by small
M because this is the mass of the gases
which are ejected and the velocity of
the rocket increased view to the
relative velocity of the gases which are
ejected as a result we find that in
momentum the mass were reduced but at
the same time the velocity got increased
so keeping the product of mass and
velocity constant so the initial
momentum and the final
remain the same thus it proves the
conservation of a moment we will now
look at a very important application of
conservation of moment and that is
collision between two bodies it is a
very important application of
conservation of momentum let us suppose
we have two bodies one and two and these
two bodies collide so what is the event
here collision is the event so what we
will do we will try to prove that the
initial momentum before collision is the
same as the final momentum after
collision so we will calculate the total
momentum of the system before collision
then they will calculate the total
momentum of the system after police let
us consider at initial initial means
before collision let us suppose before
collision the momentum of godî one was P
1 and the momentum of body 2 was heat
and let us suppose that after collision
that is the final values after collision
the momentum of 1 is P 1 dash and
momentum of 2 is P 2 dash now by
Newton's second law we know that force
is equal to rate of change of momentum
that is f is equal to DP by DT or we can
also write it as Delta P by Delta P now
for the first body that is for body 1 we
can write that the force exerted on body
1 by body to because when we are
considering two bodies even before
collision also there will be some force
exerted by two one one and as a result
there will be some force exerted by one
on two right now we are considering only
body 1 so the force exerted on one by 2
this will be equal to that the change
rate of change of momentum per unit time
so this will be the change in momentum
on body 1 so change in momentum will be
final value of momentum
- initial value of momentum divided by
delta T similarly for body - the force
acting on body 2 by body 1 will be equal
to the change in momentum in body 2 per
unit time right
also by Newton's third law we know that
F 1 2 is equal to minus F 2 1 that means
the force exerted on 1 by 2 is equal to
negative of force exerted on 2 by 1
because the forces are equal and
opposite in nature so we can put the
value of F 1 2 and F 2 1 in this
equation so we will get P 1 dash minus P
1 divided by Delta e is equal to e 2
dash minus P 2 divided by delta T so
delta T delta T will cancel out so we
get P 1 dash minus P 1 is equal to P 2
dash minus P 2 so from here we can write
P 1 dash minus P 2 dash is equal to P 1
minus P I am sorry I missed out the
minus sign over here there was a minus
sign here as we said minus F of T 1 so
this would be minus and this would be
plus so we get e 1 dash plus P dash is
equal to e 1 plus P so what does this
show P 1 plus P 2 is the total initial
momentum of the system P 1 plus P 2 is
the total initial momentum and P 1 dash
plus P 2 dash is the total final
momentum of the system so we have proved
that the total initial momentum is equal
to the total final momentum that is the
momentum is conserved in case of a
collision so what we see here is we
consider two systems now the two systems
together will constitute the system when
I use the word system here I'm going to
see the system including both the
particles one an T now let us suppose
before they collide the initial more'd
numbers t1 and people for both of them
after they collide the momentum was p1 -
p2 - now my Newton second law we knew F
is equal to DP by DT that is change in
momentum with time so for body 1 the
force exerted on one by 2 is equal to
the change in momentum of 1 divided by
delta T similarly for what you do now we
know that Newton's third law says F 1 2
is equal to minus F 1 so what we did is
we just replace the value of F 1 2 and F
2 1 with these values and we believe and
we got V 1 dash plus V 2 dashed is equal
to P 1 plus P 2 that is the total final
momentum is defining the total initial
momentum of the system thank you
visit exam viacom to watch free
educational videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and much more thanks once again
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Nov 08, 2024 Last updated |
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