Hello everybody, my name is Iman. Welcome back to my YouTube channel. Today we're covering chapter two of MCAT General Physics and Math Review, which is going to introduce us to the fundamental concepts of work and energy. The three main topics we're going to cover here is energy. Within this realm, we'll talk about kinetic and potential energy, as well as total mechanical energy.
We'll also, of course, talk about conservation of mechanical energy. Our second objective will be work. We'll talk about force and displacement.
pressure and volume, as well as power and what the work energy theorem is. And we'll end this chapter with a discussion about mechanical advantage. Here we're going to talk about simple machines, focusing particularly on pulleys. So let's go ahead and begin our discussion with our first objective, which is energy.
Energy refers to a system's ability to do work or more broadly to make something. happen. This definition helps us understand that different forms of energy have the capacity to perform different actions. Einstein once said, everything is energy and that's all there is to it.
Match the frequency of reality, match the frequency of the reality you want, and you cannot help but get that reality. It can be no other way. This is not philosophy. This is physics. Now, even Einstein's famous equation, E equals mc squared, pretty much says that energy and matter are interchangeable.
Energy comes in many different forms and makes up the entirety of the universe in one form or another. With that being said, let's turn our attention to the different forms that energy can take. After that, we'll discuss the two ways that energy can be transferred.
And the majority of this discussion. will actually be covered further in the next chapter, which is all about thermodynamics. Now, one form of energy is kinetic energy. So let's talk about it.
Kinetic energy is the energy of motion. Objects that have mass and that are moving with some speed will have an associated amount of kinetic energy that can be calculated by this equation right here. All right, kinetic energy equals one half Mass times velocity squared. And the SI unit for kinetic energy, as well as all forms of energy, is typically joules. All right?
Objects possess kinetic energy in motion. So a falling object, for example, will have kinetic energy. Now something that is important to understand is the relationship between speed and kinetic energy. So from the equation...
We can see that kinetic energy, all right, we can see that kinetic energy is a function of the square of the speed. So, if the speed doubles, then the kinetic energy will quadruple, assuming that mass is constant. Why?
Because the relationship between kinetic energy and speed or velocity is squared. So, let's say we have a mass of 5 kilograms. All right, and we have a velocity of 2 meters per second. All right, let's calculate kinetic energy. That's going to be 1 half mass times v squared.
So that's going to be 1 half, mass is 5, speed is 2 squared. That's going to give us 1 half 5 times 4. All right, that's 20 over 2, that's equal to 10. That's our kinetic energy. All right, 10 joules. Cool. Now let's keep the mass the same.
Let's double the velocity. Let's say now it's 4 meters per second squared. How does that affect our kinetic energy?
Let's calculate it. Kinetic energy is equal to 1 half mass is 5 times the velocity squared. Now our velocity is no longer 2, it's 4 squared.
What we get is 1 half times 5 times 4 squared, that's 16. All right, 5 times 16, all right, that's 80 over 2, all right, and that's equal to 40, all right? When we doubled our velocity, our kinetic energy quadrupled, all right? So that's a very important relationship that we should understand, all right?
Again. Again, energy is a physical quantity that objects have. We don't know what it is, but we know how it works.
And it exists in many forms. Heat, light, nuclear, kinetic potential. All of it.
It can't be created or destroyed. It can only be transferred between forms. And the first type of kinetic energy we just covered is kinetic energy.
This is the energy due to the object's motion. All energies are scalar, they're not vectors, so kinetic energy is always scalar and it has no direction. That's a very important thing to remember.
With that being said, let's jump into our first practice problem for kinetic energy. This problem says, a 15 kg block initially at rest slides down a frictionless incline, and then it comes to the bottom with a speed of 7 m per second as shown below. What is the kinetic energy of the object at the top and at the bottom of the ramp? Alright, now initially it's at rest. Alright, so its velocity initially is zero.
Alright, and we don't know what the kinetic energy here is. That's what we're trying to figure out. We do know that the mass regardless is 15 kilograms.
Alright, mass initially is 15 kilograms. Mass at the end is 15 kilograms. Alright, now when it...
it comes to the bottom, when it reaches the bottom, it's coming at the bottom with a velocity of 7 meters per second. And again, we want to find the kinetic energy at the end as well. Let's start first with at the top.
All right, what's the kinetic energy at the top? Well, we know what the equation for kinetic energy is. All right, kinetic energy is one half mv squared. All right, so that's going to be one half mass is 15 kilograms.
velocity when it's at the top before it starts moving it's just zero meters per second and that is squared and that's just all going to equal zero joules so the kinetic energy at the top when it's not moving is zero that makes sense right kinetic energy is the energy related to motion and object in motion if it's just sitting at the top there's no motion so obviously the kinetic energy would be zero at the top now what about at the bottom when it's sliding down towards the bottom you All right, what is the kinetic energy there? Well, again, we're going to rely on that same formula, 1 half mv squared. All right, let's plug in 1 half, 15 kilograms. All right, and it's coming to the bottom at a velocity of 7 or speed of 7 meters per second.
All right, and that's squared. All right, so now, all right, if we calculate this, It's going to be about 367.5 joules. All right, so that's the kinetic energy at the bottom. All right, so that's how you want to approach a problem like this. All right, and it's...
It's obvious that if an object is not moving, then its kinetic energy will be zero, just based off of the definition of what kinetic energy is. Now, in addition, we also want to talk about potential energy. All right, potential energy.
refers to the energy that's associated with a given object's position in space, all right, or other intrinsic qualities of the system. Now, potential energy is said to have the potential to do work, and it can take many forms, all right? Energy can be stored as chemical potential energy.
This is the energy we absorb from food, all right? When we eat, when we digest and metabolize it, all right? Another form of potential energy is gravitational potential energy, and this depends on an object's position with respect to some level-identified ground, all right?
And actually, that's something that we're going to focus on here, right? Gravitational potential energy, all right? It depends on an object's position with respect to some level-identified, right? And this is usually called like as the datum, right? The ground or the zero potential.
potential position. Now, this zero potential energy position, it's usually chosen for convenience. For example, you might find it convenient to consider that the potential energy of the pencil in your hand. with respect to the floor, if you're holding the pencil above the floor, all right?
Or with respect to a desktop, if you're holding the pencil over a desk. Now, with that being said, the equation that we can use to calculate gravitational potential energy is this equation right here, all right? Gravitational potential energy is equal to the mass in kilograms times gravity, the acceleration due to gravity, times height.
all right height of the object above your ground potential all right above the datum if you will okay so potential energy is equal to mass times gravity times height now potential energy has a direct relationship with all three of these variables. So changing any one of them by some given factor is going to result in a change in the potential energy by the same factor. So if you triple the height, you'll triple the gravitational potential energy if the other variables stay the same.
If you triple the mass, would the other variables stay the same? Then you're going to triple the potential energy as well. All right, so for example, pretend that you have a mass of 2 kilograms.
All right, your gravity acceleration is 9.8. Let's just say 10 for simplicity in the math. All right, let's say your height is 10 meters.
All right, so then if you're calculating the gravitational potential energy of these variables, that's two times 10 times 10. All right, that's 200. All right, now what if you keep the same mass? All right. kilogram, sorry.
All right, your gravity is 10. All right, what if you double the height to 20? All right, what is your, you've doubled the height. All right, what's going to be your gravitational potential energy now? That's 2 times 10 times 20. All right, so that's going to be 400. You double the height, you doubled the gravitational potential energy.
All right, it's always important to understand the relationship between formulas and the variables that make up that formula. Those are very common kinds of questions on the MCAT, these ratio relationship kind of problems that require you to understand how some variables are related to each other in the equation, all right? So it becomes a little more than just plug and chug, but understanding the ratios between variables and equations.
All right, let's do a practice problem, all right? An 80-kilogram diver leaps from a 10-meter cliff into the sea. like you see in this image. Find the diver's potential energy at the top of the cliff and when he is two meters underwater using sea level as the datum.
So your sea level right here, that's known as like your ground level, all right? So then at the top of the cliff, all right, at the top of the cliff, all right, we're going to use this equation. All right, when he's at the top of the cliff, he's 10 meters away from the sea level.
All right, this is the zero, the sea level is the zero ground. All right, when he's on top of the cliff, he's 10 meters above the sea level. All right, and so then if we're trying to plug this into our equation MGH.
His mass is 80 kilograms. All right. Gravity is 9.8 meters per second squared. That's gravitational acceleration.
And then he is 10 meters above sea level. Plug this into a calculator. You get 7,840 joules.
That's when he's at the top. Now, what about when he's 2 meters underwater? All right, what's his potential energy then? All right, so U equals mgh.
His mass stays the same, 80 kilograms and 9.8 meters per second squared for g. Now he's 2 meters underground. Now we said that underwater, I'm sorry. We said that the sea level is 0, and if he's 2 meters under the water, then he's minus 2 meters, right? And so we plug that into the calculator.
And what we get is minus 1568 joules. If you're doing this on the MCAT without a calculator, I recommend you rounding this to about 10. And that makes the multiplication a lot easier. And you'll still get something very close to the right answer. Here, you'll get about 8000 joules. Very close to the real answer.
And here, you'll get 800 times 2. You'll get about minus 1600 joules. So very close in regards to number. All right.
Fantastic. That is potential energy, gravitational potential energy specifically. Now, another form of potential energy, we're not going to get too deep into this because it'll be a topic that reappears later, but elastic potential energy is also another type of potential energy. So here, springs and other elastic systems, they can act to store energy.
Every spring has a characteristic length at which it's considered to be relaxed or in equilibrium. Now, when a spring is stretched or compressed past its equilibrium, all right, from its equilibrium length, then that spring possesses elastic potential energy. And that elastic potential energy can be determined from this equation right here. It looks very similar to kinetic potential energy, all right? But it's not.
It just looks it, right? Because the 1 half kx squared, that's very similar. All right, here k is the spring constant.
All right, this is a measure of the stiffness of a spring. And here x is the displacement, is the magnitude of displacement from equilibrium. All right.
So that is elastic potential energy. Now with this understanding of kinetic and potential energy, we can move on to discuss total mechanical energy. The sum of an object's potential and kinetic energy is total mechanical energy. And so this equation is E equals U plus K, where E is the total mechanical energy, U is our potential energy, and K is our kinetic energy.
Now, something that's related that we need to talk about when we discuss this is the first law of thermodynamics and how it accounts for the conservation of mechanical energy, which states that energy is never created or destroyed. It's just merely transformed from one form into another. All right.
Now, this does not mean that the total mechanical energy will necessarily remain constant, though. You'll notice that this total mechanical energy equation here only accounts for potential and kinetic energy. Not all the other forms of energy there are as well, like thermal energy.
All right. Now, if frictional forces are present, obviously some of that mechanical energy will be transformed into... Thermal energy, all right, and it can be what we call lost if you're just looking at total mechanical energy in this form. All right, but note that there is no violation of the first law of thermodynamics if you're fully accounting for all forms of energy. Kinetic, potential, thermal, sound, light, and so on.
Okay, if you accounted for all of them, you'd notice that there is no net gain or loss of total energy. It's merely just transformed from one form into another. All right.
But in this form of our equation, you notice that that isn't necessarily what you'll see because you're not accounting for all forms of energy. All right. But nevertheless, the first law of thermodynamics is true.
All right. Energy cannot be created or destroyed. Instead, it changes from one form.
to another all right and there's so many forms of of of energy there's heat all right there's mechanical there's chemical and there's electromagnetic and in this course we'll learn about all of them in great detail all right so that's really important to say, all right? Note that there's no violation of the first law if we accounted for all forms of energy in our equation. But because we don't, it's not necessarily as evident as it could be, all right?
Now, we can... can say, all right, we can say that in the absence of non-conservative forces, that the sum of the kinetic and potential energies will be constant. Now, conservative forces are those that are path independent, and they do not dissipate energy, all right?
Conservative forces also have potential energies associated with them. All right. So these are examples of forces here that are conservative and non-conservative. So weight, spring, coulomb, these are all conservative types of forces. Friction, air drag, those are non-conservative forces.
Conservative forces abide by the law of conservation of energy. All right. Gravitational force, spring force, et cetera. On the other hand, non-conservative forces are those forces which cause a loss of mechanical energy from the system.
All right. So for example, friction is a non-conservative force. Now, one method is to consider, one method to approach this kind of thing, all right, is to consider the change in energy of a system moving from one setup to another. So in mechanical terms, this means an object undergoes a particular.
particular displacement. If the energy change is equal regardless of the path taken, then the force acting on the object are again all conservative. All right, so what that means is, consider the change in energy of the system, all right, where the system is brought back to its original step.
If the change in energy around any round-trip path is zero, or if the change in energy is equal despite any path taken between two points then that force is conservative all right that's how we know that uh forces like weight spring coulomb right those are conservative all right if if you If you consider change of energy in the system as it's brought back to its original position, if the change in energy round trip is zero, then the force is conservative. The other method is to consider the change in energy of a system moving from one setup to another. In mechanical terms, this means objects undergo a particular displacement, and if the energy change is equal regardless of the path taken, then the force is... acting on an object are again all conservative.
When the work done by non-conservative forces is zero, or when there are no non-conservative forces acting on the system, then the mechanical energy of the system will remain. constant. And what we can do is we can write the following expression, that the change in total mechanical energy is equal to the total change in potential energy plus the total change in kinetic energy, and that will equal to zero.
All right? The work done by non-conservative forces will be exactly equal to the amount of energy lost from the system. All right?
In reality, I'm sorry, when there are no non-conservative forces acting on the system, the total mechanical energy of the system will remain constant. That's where we get this expression from. But when non-conservative forces are present, then total mechanical energy is...
not conserved. All right. And so you have this original expression, delta E equals delta U plus delta K.
Okay. All this to say, all right, all this to say that when we're talking about conservation of mechanical energy, energy. All right. You can talk about conservative forces and you can talk about non-conservative forces.
All right. If the change in energy around any round trip path is zero, all right, then the force is conservative. All right.
Work done by non-conservative forces is zero or when there are no non-conservative forces acting on the system, then the total mechanical energy of the system is going to remain constant. And so if you're doing change in total mechanical energy for a for a conservative force, it's going to be zero. But when non-conservative forces are present, all right, then the total mechanical energy is not conserved, all right? And you can figure that out using this expression, all right?
With that being said, let's do a practice problem. A baseball of mass 0.25 kilograms is thrown in the air with an initial speed of 30 meters per second. But because of air resistance, the ball ball returns to this ground with a speed of 27 meters per second. Find the work done by air resistance. Air resistance is a non-conservative force.
And so, to solve this problem, the energy equation for a non-conservative system is needed. All right, so that's going to be total change in energy is equal to total change of potential plus total change in kinetic. Now, in this case, All right, delta U here is equal to zero because the initial and final heights are the same. All right, so our total potential energy goes to zero.
All right, and so now what we have is our... Delta E, all right, our total work for non-conservative forces is equal to delta E, which is equal to zero plus delta K. All right, delta K is change in kinetic energy.
So this is going to be one half mass times velocity final squared. minus one half mv initial squared. All right, so let's plug that in.
What we can do to rewrite this is one half mv final squared minus v initial squared. And that's going to be one half times 0.25 kilograms, all right, times 27 meters per second squared. Minus 30 meters per second squared. All right.
And what that gives us, all right, if we plug it into a calculator, is minus 21.4 joules. This negative sign in the answer indicates that the energy is being dissipated from the system. Had we been talking about this with no air resistance, all right, then the initial speed and the final speed would be the same.
And the total change in energy, total mechanical energy, would just be zero because there are no non-conservative forces acting on the system. And in that case, when there are no non-conservative forces acting on the system, then the total mechanical energy of the system is going to remain constant. And it would be just zero.
But since we have non-conservative forces like air resistance present... then the total mechanical energy is not conserved. And then we have to use this work non-conservative energy equation that says total mechanical energy change in total mechanical energy is equal to total change in potential plus total change in kinetic.
All right, and that's exactly what we did to solve this problem here. Fantastic. We're going to stop here for now.
In the next video, we'll continue this lecture on work and energy, and then we'll do some practice problems. Let me know if you have any questions, comments, concerns down below. Other than that, good luck, happy studying, and have a beautiful, beautiful day, future doctors.