All right, class. Today we're going to be looking at linear kinematics, not kinematics, kinetics. So we've covered a little bit of this in the earlier lectures. This is going to be a continuation of the kinematics lecture that we've already previously discussed. So only now we're going to be incorporating force into our linear variables.
So we'll first start with a question. If I could pull it up. So if I stand on a scale while going upwards in an elevator, what will the scale read? So first about, you know, your normal mass, if you stand on a scale, maybe say you're 100 pounds, make it easy, whatever it is. If you're going upwards in an elevator, is that number going to go up or down?
Let's assume that you're, you know, 90 kilograms. individual on earth. We have a gravitational pull that's accelerating us kind of downwards, but we also have an upwards acceleration at a rate of two meters per second. If you kind of read this one right here, and I'll let you think about this for a minute. What do you think would happen if we're going upward, gravity's pulling us downward?
What would our scale, what would the scale look like? What would our weight look like? So whatever you think the answer might be, not from like a numerical standpoint or a specific number, just the concept of this, the number is going to be higher or lower.
What do you think it's going to be? So kinematics is going to kind of talk about this and kind of help us understand what... is exactly happening in this exact answer. So spoiler, the value is actually going to be going up.
So that's why you kind of feel heavier. And then when you're in an elevator, you feel like the force is pulling you down a little bit greater. So before we cover kinematics, which is about describing how an object moves.
But now we're going to move into kinetics, which helps us understand why an object moves by focusing on the forces and moments, which is torques, which we're not going to cover right now, that are applied to an object. So what exactly is kinetics? It is the study of forces and moments that cause motion or change in motion, which lead to the kinematics that we were just talking about earlier.
So in simpler terms, kinetics explains the reason behind the movement that we see, and kinematics describes what the movement is. So to really understand how forces affect movement, we use mechanics. Right here.
We use mechanics in order to understand how this works. And mechanics is a branch of physics that looks at how... bodies interact and respond to different forces.
So in biomechanics, we use this to study how the human body works. And we use Newton's laws in order to kind of help us understand this. And again, we've talked about the first three laws or the three laws of Newton produced already, but now we're going to kind of start applying these a little bit more.
We're also going to consider statics, which is the which basically focus on bodies that are not moving. It's all about balance, not having movement, like forces applying to each other without there being a movement. So imagine someone holding a heavy box and standing perfectly still.
What are the forces acting on them, like gravity pulling the box downward, or your muscles holding the box up, but since they aren't moving, these forces are balanced, so they're going to be equal to each other in one way or the other, which is... opposite of dynamics, which basically deals with bodies that are moving. So we're interested in how forces cause the movement and how things are changing. So it means that, you know, whatever force is being applied to something, it has to be great enough in order to get an object to move.
So say starting to run or throwing a ball, like this is where acceleration, speed, and change in direction come into play. So as we go through today's lecture, we're going to explore some of these principles. of kinetics to help us explain this.
Okay. Newton's laws. These are extremely important. We've covered them a little bit.
as already but let's dive into them a little bit greater detail so newton's first law which is also considered the law of inertia states that an object will remain in a state of constant motion or no motion at all unless acted on by an external force so what does this really mean um we can kind of break this down a bit uh constant motion means an object is either moving at the same speed in a straight line or is completely still. So it's not speeding up, slowing down, or changing direction. What this means is there is no net acceleration. So all the forces acting on the object are balanced.
We're not having an extra force behind something to get it to accelerate. We're not having something more in front of it to get it to decelerate. It's all going to be balanced. So the object won't change its state of motion unless...
an external force will act upon it. So an example of this is pushing a box on a smooth surface with no friction. It'll move unless you stop it or something else like a wall stops it.
Think about like, you know, something sliding on ice where there's very little friction. It's not really going to stop moving until something stops it from moving. So no motion.
simply means that an object is at rest and will stay that way unless a force acts upon it. So this concept is tied to inertia. Inertia is a property of matter, and it's basically an object's resistance to changing its state of motion. So how much will it resist changing its motion? So the more mass something has, the more inertia it has, which means it'll resist change in motion more.
Think about like a semi-truck moving versus maybe a little toy car moving. The force to stop the giant semi-truck from moving has to be really great. You have to apply a lot of force to stop it or change its motion to a different degree. While the little toy truck does not take a whole lot of force in order to change its motion. You can just pick it up to change its motion.
put a finger on it to stop its motion. So again, its inertia is low while the inertia of the truck is large. So again, linear inertia is directly tied to mass in kilograms. So the more mass, the more inertia it's going to have. So we'll talk a little bit more about linear inertia here.
Inertia as well, as we discussed, is the resistance to change in motion. And specifically here, it's the resistance to linear motion. So we're looking at linear inertia. So in a line going straight across.
In simple terms, how hard is it to stop or start something from moving in a straight line? That truck example, that little toy car example. A body with more inertia, which means it has more mass, more kilograms, higher kilograms, will be... harder to move or stop than a body with less inertia so uh think of it this way it's much easier to push a box filled with pillows than to push a box filled i don't know with rocks or books something heavy um the mass of the books create uh more resistance to being moved which means like the books or the rocks whatever it is has more inertia so inertia is also impacted by, you know, gravitational acceleration.
Sorry, I should have clicked that slide. So the more mass an object has, the more it's affected by gravity, making it even harder to move. So this is why pushing heavy objects on Earth feels much harder than moving lighter objects.
The heavier objects has more resistance due to its mass and the pull of gravity. So you think of something on the moon, which if the gravity is less, we would actually see less inertia. Like if you're pushing a box of, you know, the box of books versus pillows, the box of books is actually going to have less inertia on the moon than it would on Earth. So essentially, inertia is the force fighting against any attempt to change an object's motion.
So again, the more mass, the stronger the gravity, the less likely it will be. to move, the more resistant it will be to movement. So we can talk a little bit about some examples here of linear mode inertia.
So We have a few different things here. Let's just send them out. If we're looking at the football example here on the right, the linemen are typically much larger than any other player. That's why you have to be really big to be a lineman. This larger mass means they're less likely to be moved over.
You know, you want to have a... high inertia for a football player like a lineman or else they're just going to get walked right over and that would be bad for the quarterback's sake. Another example is like a shot putter. The shot itself is relatively small mass compared to like a lineman or something but it's much easier to accelerate to a high speed when thrown.
This demonstrates the object with a smaller mass and therefore smaller inertia is much easier to move. It's easier to move that ball, the shot put than it is a football player. And we go to the tennis ball example. It's less inertia out of all of them.
It doesn't take much mass or much force in order to get the tennis ball moving. You can chuck a tennis ball fairly easily, not without much force being applied to it when compared to a, you know, shot put or, you know, a football player. Okay. Let's see if you kind of grasp these concepts so far. I know they're a little bit complex to some with kind of this quick question in order to jump off the ground, what must you overcome?
So go ahead and think about that for a second. All right. The answer is gravitational acceleration.
So gravity is constantly pulling us towards the earth, which is why we stay. grounded. When you jump, you have to generate enough force to overcome gravity's pull. So the heavier you are, the more mass you need to generate or the more force you need to generate to jump. And, you know, gravity is pulling very hard on someone with a lot more mass.
So that's why jumping takes a lot more effort than just lifting your foot. You know, you have to overcome both your bodies. inertia and gravity's inertia in order to get yourself up off the ground um this is going to move us into newton's second law uh which explains the relationship between force mass and acceleration so these two are newton's first and second law are fairly similar just newton's second law is a little bit more of the um kind of the application of the concepts in the first law so um you The law states that a body's acceleration is proportional to the net force applied to it and inversely proportional to its mass.
So in other words, proportional to the net force basically means that if you apply more force to an object, it will accelerate more. So the harder you push something, the faster it moves. Inversely proportionate to mass means that the heavier an object is or an object with.
more mass uh harder it's going to be harder to accelerate so uh for the same amount of force a heavier object will accelerate much slower than a lighter object so if i push a you know truck or i don't know truck's gonna be too hard i guess maybe a uh if i kick a bowling ball versus kicking a soccer ball they're both going to move but the you know bowling ball you it's going to move a lot less, you know, far because I'm putting the same amount of force into it, but the mass is going to be greater. So it's going to accelerate as much as a soccer ball. It's also going to hurt a lot more, but that is why we can kind of generate this equation here, which is acceleration equals net force times mass. And, you know, the F equals MA is the other way we look at this.
And you can kind of inner work this equation, mass equals force. Net forces times acceleration, just based on this. So this relationship we use for all of these different problems and are these different scenarios. So if we're looking to try and isolate acceleration, force is our mass, we just use this equation. So a quick algebra in order to figure out our answer.
Oh, and this negative one just means it's going to be forces divided by mass. So acceleration equals forces divided by mass. Force equals mass times acceleration.
Mass equals net force divided by acceleration. That's why that negative one is there. I just couldn't, didn't want to draw the division sign. Okay, so we kind of covered the basics of Newton's second law, so we're going to expand on this by looking at the relationship between force, mass, and acceleration in a little bit more detail.
So the equation used to describe this relationship is F equals ma. We've known this already. net force is represented by the F, which is a combination of all the forces acting on an object.
If we increase the force applied to an object, we'll increase acceleration. Assuming its mass stays the same, we increase the mass of an object, keeping the acceleration the same, we're going to need more force. So yeah, they're all very much interconnected.
I think the only thing else I want to talk about this is the unit of force which is newtons. So the unit of force is derived from this equation. A newton is defined by the force required to accelerate a mass of an object that's one kilogram at a rate of one meter per second.
So one newton equals one kilogram per meter per second squared. So if you apply one net force of newton to an object that is one kilogram uh it will accelerate one meter per second squared so that's what this little one newton equals down here uh above here is signifying so um but we can easily apply newton's second law to different things like running or jumping um so like i don't think Quick example would be, you know, when you start running, you apply force to the ground with your legs so that the forces propel you forward. The harder you push, the faster you accelerate. So this is just basically Newton's law, second law in action.
Okay. Oh, here's a conversion here. One kilogram is 240. covered before.
Okay. I think I'm going to move on to Newton's third law. This one is a little bit different than the other ones. It's all about the concept of action and reaction. So this law states that when a body exerts a force on another body, so body A exerts a force on body B, right here, there is an equal opposite force by body B.
on body A. In other words, for every action, there's an equal and opposite reaction. We've covered this with ground reaction forces a lot already. So this is true in all interactions between two objects or bodies. So the forces exerted on each other are equal in magnitude, but in the opposite direction.
So if I push against the wall, it's going to push the equal and opposite direction against my hand. So yeah, you're exerting, imagine you're exerting a force on the wall, we'll call that, let's see, here we go. Kind of this example I wanted to talk about a little bit. So imagine you're pushing against the wall, you're exerting a force on the wall, let's call that force A going to B. So this first part of the equation, but the wall is also pushing back on you, which is going to be the other side of it, this negative force.
be going to a so the forces are going to be equal but it's going to be a negative force because if we're pushing on it's going to be a positive force and it's going to be in the opposite direction that vector force is going to be directly going against you um and we can think about this in like these free body diagrams here which are essential tools i know we did this in lab one i know some people maybe struggle with us a little bit so all used to doing these free body diagrams are really important um but these tools are essential for kind of understanding what forces are acting on a system. So a free body diagram is a simple stick figure or sketch of the system where we draw all the external forces acting on the system. So here's a little bit of the process here. We sketch the system out.
We had to identify the system or object we're analyzing. In this case, it is the foot of this sprinter. We're looking at the left foot of Usain. bolt. So we'll draw a simple stick figure sketch, which is kind of shown right here.
Whoa, that did not look like I want. Okay, that's fine. So there was a lag, I think.
So the simpler we draw it, the better. It doesn't need to be detailed. It just could be a box, it could be a circle, it could be a dot even, just as long as you're able to draw all the force vectors onto it.
These forces can include things like gravity, ground reaction force, muscular forces applying to it, and any other applied forces. So you sketch the system, acceleration is drawn on it. And then our process, yeah, I just talked about this, identify the system, draw the external forces acting on the system, and then you can also draw the internal forces and where they're being applied to the system.
So in some cases, we will also need to draw moment arms and torques. One sec. Sorry, my screen was freezing there. So where was I? I don't know.
By using these free body diagrams, we can break down complex movements and pinpoint how different forces are contributing to those motions by breaking down, you know, how much is the friction force applying versus this acceleration force right here being applied. And then also the ground reaction force, the resultant force versus the, you know, weight of gravity. Yeah, yeah. So they're really important to get a good visual of things. Here's a little bit of some examples.
We can take a look at these two free body diagrams. One is with a soccer player and the other one is with a gymnast on rings. So soccer player, when the soccer player is kicking the ball, we can draw a free body diagram of just the leg.
I prefer instead of like looking at like this and just draw. Oh man, man, I cannot draw with this pad, but we'll just draw the ball itself. And the external forces that include the force of the foot acting on the ball.
So at which angle is the force acting on the ball? Then we can also, so let's say we're kicking the ball upward this direction. We have a force, maybe a force going up and to the right. We also have like, you know, maybe air resistance going against wherever this force is going.
Maybe there's some friction force moving against the movement of the ball. There's also the force of gravity acting down on it. Sorry, this is not a great visual for you guys, but kind of an idea of like how these forces can be drawn on this.
And you want to draw them in the correct direction that they're going in. Okay. So another example is this gymnast on the rings.
These vectors are already drawn, so we have the forces acting on the gymnast, including gravitational, pulling him down. And then the reaction force of the rings pulling him back up. And because they're in equilibrium, let's just say there's equal distribution between the right and left ring here. So these two forces, because he's not moving, are going to be equal to this downward force.
And think about it, he's pushing. you know, himself up onto it, he's actually going to have to generate more forces against the rings, which are in turn going to generate more forces against him in the opposite direction. So in both these cases, we're using these free body diagrams to break down a little bit more complex problems.
Now, let's talk a little bit more about force data. We've already done this to collect data in our first lab. But.
These are really important tools in biomechanics in general. So again, it's basically measuring how much force the body is exerting on the ground, like when you're walking, jumping, or sprinting. So the force plate will collect continuous data on the forces being applied to it.
So these readings include ground reaction forces, which can tell us how much force is being exerted on the ground. And then these will send through, you know, electrical cables to a computer where it will actually write down the magnitude values and process by the computer. And we can get, you know, multiple different readings.
We can get the vertical aspect and good force data play, not the ones we have in our lab, which only gives us vertical, how much, you know, forces are being applied vertically to it. We can actually get, you know... how much is going horizontal anterior posterior you know in like an x, y, and z coordinate, as you can kind of see here.
So like, it can measure almost that vector angle, and like how much of that is going to be in the y axis, how much of that is going to be in the x axis, and how much is that going to be in the z axis, as you can kind of see here. So we can go a little bit more into ground reaction forces. We've covered this a bit already in your labs, or if you haven't, you should have, which is, you know, an important concept.
in biomechanics because it directly ties into Newton's third law. So whenever we make contact with the ground, whether we're walking, running, or jumping, the ground is going to push back against us with an equal and opposite force. This is known as ground reaction forces. And it's a perfect example of Newton's third law for every action there is an equal and opposite reaction.
So when we push down on the ground with your foot, the ground's going to push back. Same, you know, opposite, equal direction. But the ground reaction forces are crucial to understand how we move and how we generate forces in order to get around our environments with gates or running or jumping or whatever it is.
All the forces that we push into the ground are going to allow us to move, and those ground reaction forces are helping us do that. So we measure ground reaction forces using force plates. The force plate. detects the amount of force applied and its direction as we were talking about the x y or z coordinates and it's going to give us a graph that looks at vertical ground reaction forces horizontal or medial lateral or i mean uh anterior posterior and then also medial lateral so kind of the x y and z coordinates um so by analyzing these ground reaction forces we can effectively understand how someone's moving and if there's maybe an issue with it their movement patterns. So this is a good example of a squat.
We're looking at this, this is someone standing there on the force plate before they start going into squat. This is maybe them, I don't know, prepping for the squat, and then they go down into the squat, then we come right back up. This is them at the bottom of the squat, kind of in line with, well, probably a in line with their body weight and then they push up up up up up and then this right here is showing them almost they're basically off the plate so this is a jump actually and then this giant force we see is the impact of them jumping back down onto the plate after the jump is done okay and this is going to be uh big in your lab in kinetics we're going to be looking at a jump so understanding where On this graph, the bottom of the squat is versus the part of the squat that we're actually pushing into the plate, which is this, this area right here. I know I'm kind of making a mess of this graph, but we'll cover this more in lab and more detail in lab and understanding, you know, impulse.
And also, I think later in this lecture, we'll cover a little bit more on that as well. So we've talked about this already. So I'm going to briefly go over it.
So external forces are the forces that act on the body outside of a system. So examples of this would be the ground reaction forces, air resistance, you're pushing against someone that is a external force. And the internal forces are the things happening within the system or body. This is the forces generated by your muscles, your ligaments, your tendons, your bones, as they interact with each other. So when you're running, you're contracting your muscles.
to move your legs and that those are all internal forces that cause that movement. Yeah, pretty, pretty simple. Now we can look at a little bit more of a free body diagram for maybe an exercise like a dumbbell exercise.
As we've kind of discussed before, we have internal and external forces involved in the movement. So here is kind of what we'll first draw. the arm here.
So first we have some external forces acting on this arm. This is your gravity of the dumbbell pushing down on it. This is also the gravity of the arm. Hey, cat, sorry. Out of here.
Sorry about that. The cat is... Acting up.
Where was I? Oh, so we're drawing vector forces of gravity in the arm. So we have the weight of the arm is pulling the arm down.
And we also have the weight of this weight pulling the arm down. These are going to pull this way. And the only way, say it's in equilibrium, we're holding it like an isometric contraction, the force generated by this muscle right here, probably your biceps, bicep brachii, is keeping the arm stable. If these forces, the force of the arm and the force of the weight are greater than this force right here of the bicep. then the arm is going to move downward.
But if it's greater, it's going to move upward. You're going to see dynamic moving in the opposite direction. So kind of how we should draw out these forces. Okay, I'm going to stop here. I need a break.
I'll be posting the next lecture in a little bit, and this is going to continue on.