Momentum is a fundamental property of motion, defined as mass multiplied by velocity, and it is conserved in closed systems, meaning the total momentum before an event equals the total momentum after.
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in today's video we're going to look at
momentum which is a property that all
the main thing to know is that momentum
is equal to the mass of an object
multiplied by its velocity
so if we saw a four and a half thousand
kilo dinosaur
charging at 12 meters per second
then its momentum
would be 4 500
times 12.
so 54 000 kilogram meters per second
whereas if we had a 1200 kilo car
traveling at 25 meters per second
then its momentum would be 1200 times 25
an important thing to remember though is
that momentum is a vector quantity
so it has both a magnitude and a direction
direction
so here if we consider the forward
direction to be to the right then the
dinosaur will have a positive momentum
but the car must have a negative momentum
the next thing to know is the
conservation of momentum principle
which is the idea that in a closed system
system
the total momentum before an event like
a collision
is exactly the same as the total
momentum after the
event to see how this works let's
imagine our dinosaur and our car as two
particles which are traveling towards
each other and are going to collide
after which they'll both continue moving
together at the same speed
how would we find their velocity after
the collision
well the first thing we need to do is
find their total momentum before the collision
collision
which we can do by adding together the
dinosaurs and the car's momentums
so 54 000 plus
plus
negative 30 000
which gives us positive 24 000 kilograms
meters per second
then because of our conservation of
momentum principle
we know that once they've collided
their total momentum
must still be positive 24 000
and remember that in this scenario a
positive number means that it's going to
the right
so after our particles collide together
they'll both get carried to the right
because the purple one had more momentum
and because they're both moving together
we can now treat them as a single large particle
particle
so to work out their shared velocity
all we have to do is rearrange our
momentum equation to show that velocity
equals momentum divided by mass
and then plug in the values for this
combined particle
so 24 000
divided by their combined masses from before
before
which would be four thousand five
hundred for the dinosaur
plus twelve hundred for the car
so five thousand seven hundred kilos
which gives us a velocity of four point
so basically after the dinosaur and the
car collide
that both continue moving to the right
now in some circumstances
the momentum before an event might be zero
zero
like it is for stationary objects
which don't have any momentum because
they're not moving
and so in these cases the total momentum
after the event
for example if we imagine a gun before
it's fired
then its initial momentum would be zero
because its velocity is zero
however once the gun fires the bullet
that flies out will have a momentum in
the forward direction
and so to compensate for this
the gun has to recoil backwards with an
equal momentum
so that together the total momentum is
so if we knew that this gun had a mass
of 2 kilos
and that a 5 gram bullet was fired out
at a velocity of 120 meters per second
we should be able to work out the
velocity of the gun's recoil
the key to this is remembering that the
gun's momentum
plus the bullet's momentum
must equal zero
because it started off at zero before
the gun fired
the first thing we want to do is find
the bullet's momentum
using this bottom equation
so we do 0.005
0.005
which is its mass in kilos
times its velocity of 120
which will give us a momentum of 0.6
next we want to try and find the gun's momentum
momentum
so again we just do the mass of two
times the velocity
but because we don't know what the
velocity is yet
we can just write v for velocity
so the momentum will be two v
where two is the mass in kilos
and v stands for the gun's velocity
which we're about to find out
finally we can use these momentum values
for the gun and the bullet to rewrite
our equation
as 2v
plus 0.6
equals 0
and then we can just rearrange this
equation to find out the missing value
of v
so first we subtract 0.6 from both sides
giving us 2v equals negative 0.6
and then we divide both sides by 2
leaving us with v equals negative 0.3
meters per second
which is the gun's recoil velocity
and remember the fact that it's negative
means that it's effectively going backwards
backwards
or in other words it's going in the
the one thing we haven't mentioned yet
is that you need to know that the letter
symbol for momentum is row which looks
like a p
so the momentum equation can also be
written as p
that's everything for this video though
so i hope you enjoyed it if you did then
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