OK, so let us have a look at the principle of energy conservation, and this is a very powerful concept
that we can use to solve some kinetics problems.
So I'm first going to state the principle and then we will break it down.
And at the end we will look at an example.
So it says a T1 plus V1 is T2 plus V2.
So the kinetic energy plus the potential energy will stay constant in a system.
So you might have heard the statement that energy cannot be created or destroyed.
This is what this is all about.
Over here we look at a a isolated system and within that system, the sum of the kinetic and the potential
energy will stay constant.
So we have T one and two.
That's our kinetic energy.
And we into that is our potential energy.
So let us look at how you would calculate kinetic energy and potential energy.
So energy is that Berlanti to do work?
Kinetic energy is energy.
That has to do with motion.
So when something is in motion, it has a certain kinetic energy, a motor vehicle that moves has a
kinetic energy.
When you boil water and the water molecules move, those molecules have kinetic energy.
Potential energy, energy that has to do with the position of a particle relative to date and our date,
and that is a reference line.
So if you have a brick that lies on the floor relative to the floor, it has zero potential energy.
When you pick it up from the floor, you increase its gravitational potential energy, because when
you drop that brick, it'll fall down to the floor.
So there's energy stored in the gravitational field as you pick up the brick.
So and the higher you pick the brick up from the floor, the more you increase its potential energy.
And that potential energy is measured from a certain reference line.
In this case, the floor goes.
So its energy that has to do with the position of a particle relative to its item.
Now we are going to consider two types of potential energy, firstly, gravitational potential energy
and then also elastic potential energy, gravitational gravitational potential energy is what I've just
explained with picking up a brick from a certain height and changing the height and the gravitational
potential energy is calculated as m g h c take the mass of the object multiplied by gravitational acceleration
multiplied by the height.
Now that height can be measured from any reference line.
And so when you go above the reference line, your gravitational potential energy will be positive.
If you move your object below the the datum below the reference line, then the gravitational potential
energy will be negative.
So gravitational potential energy can be positive or negative.
To the contrary, elastic potential energy is always positive, and it's calculated as one half case
squared, OK, is the spring constant?
Now you can see that AC squared.
So eight is the distance with which the spring is either compressed or lengthened from its free position.
And because that length is squared, AC squared is always a squared will always be positive.
Right.
So that is why your potential energy is always positive and is calculated by one of case squared.
And if we add these two, because the system can have gravitational potential energy and also have elastic
potential energy, if we add these two components, we get the total potential energy.
And if we add to that our kinetic energy, we get the total energy that we will consider for our system.
So here's a little example.
Let's say you have a ball, a tennis ball, and you bounce it on the ground.
So I've just drawn three positions of the ball.
Yeah, those little lines between the ball is just to show you that it bounces up and down.
So in the bottom position, it is next.
It is on the reference line.
So there the potential energy is zero and the kinetic energy is a maximum.
Not moves up as it moves up, the kinetic energy decreases and the potential energy increases, but
the total amount of energy stays the same.
So in the middle position, we have a mix between kinetic and potential energy.
Then the ball moves up even further to the point where it stops and it's now going to move down its
maximum height there.
The kinetic energy is zero because the ball stops.
There's no movement, but it's at its highest from the floor, from our reference line, from our datum.
So therefore, the potential energy at the top will be a maximum.
And so as this ball bounces up and down, the ratio between kinetic energy and potential energy constantly
changes.
So energy is being converted from potential energy to kinetic energy and from kinetic energy to potential
energy.
But the total amount of energy in the system stays the same.
Of course, the simplification that we make is that we have no friction because the friction of air
will take energy out of the system.
So that is why the ball will, after a while, not bounce anymore and lie flat on the ground.
Also, the impact of the ball on the ground takes energy out, energy dissipates.
There is a little bit of heat every time the ball squishes, when it hits the when it hits the floor.
So we just ignore those for illustration purposes here.
So the total amount of energy in the system remains constant.
If we have a system of particles, let's say we have three tennis balls that bounce up and down on the
floor, we just drop them.
Then if we consider these three tennis balls as a system, then the total amount of energy in the system
will also remain constant.
However, the.
Proportion between kinetic energy and potential energy will constantly change.
So when a ball is at its maximum height from the ground, it'll have a maximum potential energy.
And when it's when it stops there, it will have zero kinetic energy.
Then it moves down back to the ground.
It accelerates when it hits the ground.
It has maximum kinetic energy and zero potential energy.
And anywhere in between, there's a mix of kinetic and potential energy.
So we can take all the kinetic energies for each one of these balls, all the potential energies, and
add them together.
And that will be the same for a different point in the system where we might want to investigate the
system.
Different point in time.
So we look at an example.