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OK, so let us have a look at the principle of energy conservation, and this is a very powerful concept

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that we can use to solve some kinetics problems.

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So I'm first going to state the principle and then we will break it down.

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And at the end we will look at an example.

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So it says a T1 plus V1 is T2 plus V2.

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So the kinetic energy plus the potential energy will stay constant in a system.

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So you might have heard the statement that energy cannot be created or destroyed.

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This is what this is all about.

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Over here we look at a a isolated system and within that system, the sum of the kinetic and the potential

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energy will stay constant.

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So we have T one and two.

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That's our kinetic energy.

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And we into that is our potential energy.

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So let us look at how you would calculate kinetic energy and potential energy.

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So energy is that Berlanti to do work?

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Kinetic energy is energy.

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That has to do with motion.

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So when something is in motion, it has a certain kinetic energy, a motor vehicle that moves has a

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kinetic energy.

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When you boil water and the water molecules move, those molecules have kinetic energy.

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Potential energy, energy that has to do with the position of a particle relative to date and our date,

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and that is a reference line.

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So if you have a brick that lies on the floor relative to the floor, it has zero potential energy.

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When you pick it up from the floor, you increase its gravitational potential energy, because when

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you drop that brick, it'll fall down to the floor.

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So there's energy stored in the gravitational field as you pick up the brick.

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So and the higher you pick the brick up from the floor, the more you increase its potential energy.

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And that potential energy is measured from a certain reference line.

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In this case, the floor goes.

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So its energy that has to do with the position of a particle relative to its item.

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Now we are going to consider two types of potential energy, firstly, gravitational potential energy

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and then also elastic potential energy, gravitational gravitational potential energy is what I've just

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explained with picking up a brick from a certain height and changing the height and the gravitational

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potential energy is calculated as m g h c take the mass of the object multiplied by gravitational acceleration

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multiplied by the height.

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Now that height can be measured from any reference line.

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And so when you go above the reference line, your gravitational potential energy will be positive.

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If you move your object below the the datum below the reference line, then the gravitational potential

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energy will be negative.

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So gravitational potential energy can be positive or negative.

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To the contrary, elastic potential energy is always positive, and it's calculated as one half case

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squared, OK, is the spring constant?

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Now you can see that AC squared.

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So eight is the distance with which the spring is either compressed or lengthened from its free position.

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And because that length is squared, AC squared is always a squared will always be positive.

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Right.

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So that is why your potential energy is always positive and is calculated by one of case squared.

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And if we add these two, because the system can have gravitational potential energy and also have elastic

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potential energy, if we add these two components, we get the total potential energy.

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And if we add to that our kinetic energy, we get the total energy that we will consider for our system.

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So here's a little example.

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Let's say you have a ball, a tennis ball, and you bounce it on the ground.

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So I've just drawn three positions of the ball.

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Yeah, those little lines between the ball is just to show you that it bounces up and down.

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So in the bottom position, it is next.

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It is on the reference line.

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So there the potential energy is zero and the kinetic energy is a maximum.

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Not moves up as it moves up, the kinetic energy decreases and the potential energy increases, but

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the total amount of energy stays the same.

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So in the middle position, we have a mix between kinetic and potential energy.

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Then the ball moves up even further to the point where it stops and it's now going to move down its

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maximum height there.

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The kinetic energy is zero because the ball stops.

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There's no movement, but it's at its highest from the floor, from our reference line, from our datum.

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So therefore, the potential energy at the top will be a maximum.

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And so as this ball bounces up and down, the ratio between kinetic energy and potential energy constantly

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changes.

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So energy is being converted from potential energy to kinetic energy and from kinetic energy to potential

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energy.

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But the total amount of energy in the system stays the same.

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Of course, the simplification that we make is that we have no friction because the friction of air

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will take energy out of the system.

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So that is why the ball will, after a while, not bounce anymore and lie flat on the ground.

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Also, the impact of the ball on the ground takes energy out, energy dissipates.

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There is a little bit of heat every time the ball squishes, when it hits the when it hits the floor.

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So we just ignore those for illustration purposes here.

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So the total amount of energy in the system remains constant.

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If we have a system of particles, let's say we have three tennis balls that bounce up and down on the

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floor, we just drop them.

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Then if we consider these three tennis balls as a system, then the total amount of energy in the system

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will also remain constant.

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However, the.

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Proportion between kinetic energy and potential energy will constantly change.

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So when a ball is at its maximum height from the ground, it'll have a maximum potential energy.

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And when it's when it stops there, it will have zero kinetic energy.

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Then it moves down back to the ground.

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It accelerates when it hits the ground.

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It has maximum kinetic energy and zero potential energy.

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And anywhere in between, there's a mix of kinetic and potential energy.

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So we can take all the kinetic energies for each one of these balls, all the potential energies, and

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add them together.

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And that will be the same for a different point in the system where we might want to investigate the

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system.

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Different point in time.

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So we look at an example.