mr.p: Good morning.
Today we are going to review linear momentum,
impulse, and collisions.
Topics that are covered on the AP Physics 1 Exam.
Bo: Hey guys.
Billy: Hey Bo. Bobby: Hi Bo.
♫ flipping physics ♫
mr.p: Momentum is the product of mass and velocity,
and it has dimensions of kilograms times meters per second,
which has no special name.
Because velocity is a vector, momentum is also a vector.
The symbol for momentum is a lower-case p,
not to be confused with an upper-case P,
which stands for Power,
or the curly-looking p,
which is the lower-case Greek letter rho,
which can stand for volumetric mass density.
One common usage for momentum is that it is
conserved during all collisions and explosions.
Which means the sum of the initial momentums is
equal to the sum of the final momentums.
And, unlike conservation of energy,
you do not need to identify the initial and final points,
because the initial point is always right before
and the final point is always right after
the collision or explosion.
Remember, momentum is a vector.
And if the objects are moving in two dimensions,
that means you need to have two different
conservation of momentum equations.
One for the x-direction, and one for the y-direction.
Bobby, what are the types of collisions?
Bobby: Uh, there is an elastic collision,
where the objects bounce off of one another,
and both momentum and kinetic energy are conserved.
Then there is the perfectly inelastic collision,
where the objects stick together
and then move as one after the collision.
In perfectly inelastic collisions,
momentum is conserved and kinetic energy is not conserved.
mr.p: Many collisions are somewhere in between
elastic collisions and perfectly inelastic collisions.
They are called inelastic collisions.
During inelastic collisions, momentum is conserved,
however, kinetic energy is not conserved.
The elastic and perfectly inelastic collisions
are basically the two ideal extremes.
Ok, let's go back to Newton's Second Law.
Net force equals mass times acceleration, where both
force and acceleration are vectors, and now
we can substitute in the equation for acceleration...
to get mass times change in velocity over change in time,
and change in velocity is velocity final
minus velocity initial.
Multiply through by mass to get mass times velocity final
minus mass times velocity initial,
divided by the change in time,
which is equal to the momentum final minus
the momentum initial divided by the change in time,
which is the change in momentum over the change in time.
In other words,
a restatement of Newton's Second Law in terms of momentum
is that the sum of the forces
equals the change in momentum over change in time,
where both force and momentum are vectors.
And, if we rearrange the equation,
we get the equation for impulse.
Impulse equals the change in momentum,
which equals the net force times the change in time.
Typically the symbol for impulse is an upper-case J.
Now, this doesn't quite match the equation
on your equation sheet for impulse.
That's because generally during collisions,
we use something called the impulse approximation.
Which says that,
during the short time interval of the collision,
that force of impact is so much larger
than the other forces,
that the net force can be approximated
as the force of impact.
Therefore, impulse is equal to the change in momentum,
which is equal to the force of impact
times the change in time.
All during the collision.
And the cool thing about impulse
is this is how all of our safety equipment works.
Safety belts, airbags, helmets, packaging foam,
they're all based on the concept of impulse.
During a collision, an airbag doesn't change
how fast your body was moving before the collision,
how fast you were moving after the collision,
or the mass of your body,
so regardless of whether you have an airbag or not,
the impulse, the change in momentum of your body
during that collision will be the same.
What an airbag does is it increases the change in time
of your body during that collision
to then decrease the force of impact on your body
during the collision.
I actually rode my bike off of a dock
into a lake several times
to show this basic concept for a flipping physics video.
Now, there will be times when
the impact force is not constant.
In that case, you can either use the average impact force,
or you could use a graph.
And the area between the curve and the time axis
is the impulse.
And, Billy, what are the dimensions for impulse?
Billy: Impulse is impact force times change in time,
so it is in Newtons times seconds.
Bo: Impulse is also equal to change in momentum,
so impulse has the same dimensions as momentum.
Kilograms times meters per second.
mr.p: Yes, impulse is in Newtons times seconds,
which is the same thing as
kilograms times meters per second.
We have reached the end of my review
of linear momentum and impulse for AP Physics 1.
My next review video is about rotational kinematics.
You are more than welcome to enjoy that video.
And, you can go to my website, flippingphysics.com,
which has all of my AP Physics 1 review videos
organized with lecture notes.
Thank you very much for learning with me today.
I enjoyed learning with you.