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Hey I'm Kiarashi
And I'm Himal, it's like the Himalaya without aya.
And today, we're going to talk about
ELASTIC COLLISIONS!
So first, we are going to explain what a collision is,
a collision is an isolated event between two moving objects
that exerts force on each other
There are two types of collisions
But today we will be talking about elastic collisions.
We are going ot define what elastic collision is and what it isn't
To make things as simple as possible,
we are now two objects in one dimensional space.
And elastic collision is a collision in which both kinetic energy and momentum are conserved.
And this means that the two objects say separate was before and after the collision
This happens by the objects bouncing off each other, or one taking place after hitting the other
This inelastic collision which momentum is conserved, but not kinetic energy.
In this case two objects stick to each other.
Hey Himal do you mind if I use the freeze real quick?
I have to break down some collisions.
Yes sure man here you go.
Wonderful...
So the main two concepts to know for elastic and inelastic collision are
Conservation of momentum
and Conservation of Kinetic energy
Remember that collision for momentum is P equal MV
, where M is the mass of the object, and V is the velocity of the object.
For elastic collisions in one dimension, conservation of momentum applies.
That means if the sum of the momentum of the objects before the collision
is the same as the sum of the momentums of the object after the collision
We can write down as m1v1, the momentum of this first object,
before the collision plus m2v2, the momentum of the second object before the collision
is equal to m1v1', which is the momentum of the first object after the collision
plus m2v2', which is the momentum of the second object after the collision
As we can see, the sum of the momentum before the collision is
equal to sum of the momentum after the collision.
Let's take a look at the conservation of energy for elastic collisions.
So, remember that the equation for kinetic energy is 'one half mv squared,'
where m is the mass of the object and v is the velocity of the object.
So for elastic collisions, we can write this down as 'one half m1v1 squared,'
which is the kinetic energy of the first object before the collision,
plus 'one half m2v2 squared,' which is the kinetic energy of the second object before the collision
is equal to one half m1v1' squared plus one half m2v2' squared.
where this is the kinetic energy of the first object after the collision
and this is the kinetic energy of the second object after the collision
So as we can see here, the sum of the kinetic energy before the collision
is equal to the sum of the kinetic energy after the collision,
meaning that the kinetic energy for the total system is considered.
Hey let's do some more examples in real life
Here, we have two steel disks.
This would be our object 1
and this would be our object 2.
As we can see here, object 1 has stayed roughly in the same location as object 2 before the collision,
and object 2 moved at roughly the same velocity as object 1 before the collision
Let's do it again
Okay, let's look at some more examples here.
Here we have two marbles colliding into each other.
The marbles bounced off each other at roughly equal and opposite velocities,
signifying an elastic collision.
Let's take a look at one more example.
This time these two identical cars bouncing into each other.
As you can see here, the velocities of the cars after the collision is significantly lower
than the velocity before the collision.
Let's look at that one more time.
So this collision is something we're more likely to see in the real life
because no collision is truly elastic.
This is because the kinetic energy of object 1
is never fully transferred as kinetic energy to the second object as a lot of the energy
is dissipated as heat, sound into the object.
Elastic collisions are so important as they provide very good models of what collisions should be
under ideal conditions.
My name is Himal, and this is Kiarashi
And this has been elastic collisions.