The Science of Everything Podcast - Episode 17: Energy, Work and Momentum

Episode Date: April 2, 2011

An overview of the basic concepts of linear momentum, angular momentum, work and energy. Includes a discussion of the conservation of momentum, why the concept is needed, and some applications of the concept to collisions and rotating objects. The nature of energy is also discussed, along with the different forms of energy, and how the concepts of energy and work are related.

and welcome to the Science of Everything podcast, episode 17, energy, work, and momentum. So, as you would have gathered from the title of this episode, today we're going to talk about momentum, work, and energy. We're going to, I'm going to divide the podcast into three sections. First, I'll talk about linear momentum, and then I'll move on to angular momentum, momentum in terms of rotation, and finally, a section on energy and work. And this podcast continues on from episode 13 on Newtoning and mechanics. So it might be a good idea to listen to that first if you don't have a basic knowledge of Newtonian mechanics. Okay, so start off with linear momentum.

What is linear momentum? Linear momentum is equal to inertial mass times velocity. So inertial mass, as we spoke about in podcast 13, is essentially the amount of stuff that something is made of. It's the mass that contributes to slowing down of the object when a force is applied to it. so the greater the inertial mass, the less it accelerates. So linear momentum is equal to that inertial mass multiplied by velocity. In fact, you can even restate Newton's first law as, in the form of, in the absence of forces, the momentum of an object remains constant.

Remember that the alternative way of stating the Newton's first law is that objects will continue to travel at the same velocity in a straight line until an unbalanced force acts upon them. Well, you can see that if an object is traveling at the same, velocity in a straight line, and obviously its mass is going to be constant, then its momentum also has to be constant. So we have this concept, linear momentum, which is basically mass times velocity. Impulse, by the way, is just the change in momentum, and is equal to the net force that is applied to that object. So you might wonder, why do we have this concept of momentum? Why is it

useful? Why would we multiply mass by velocity? The reason is because of the principle of conservation of momentum. And this principle states that the total linear momentum of a system always remains constant. Always. So, the linear momentum of a particular object stays constant so long as

it's not acted on by a force, but the system as a whole always retains constant linear momentum. So that means that if momentum is removed from one object, it's transferred in equal proportions to another object. So in that sense, momentum is sort of like energy,

it cannot be created or destroyed. There is always a constant amount of it. And so a system is just kind of defined as a collection of objects upon which no external forces are acting. So you might think of the earth and everything on it as a system. Of course, yeah, it's not completely isolated, but for most intensive purposes, forces beyond the earth are not particularly relevant. So for most practical purposes, the earth is an isolated system, at least from our perspective. And so, to give an example of the conservation of momentum, I'll use the classic case of a person on escape, So imagine a person standing on a skateboard and then suppose that they begin to walk forward along the skateboard so that they're walking on the skateboard, if you like, or moving a little bit along the long axis of the skateboard. To do so, they must apply a force to the skateboard with their feet, and as they do that, the skateboard will, of course, apply an equal-on-opposite force on them, on the person towards, so in the direction of their feet, along up their legs. And so these forces are equal in size, and

opposite in direction. And so they will both, but they act on different objects. One force acts on the skateboard, the other force acts on the person. And so both of these forces acting on different objects will cause accelerations of those objects. And so, in fact, what happens is that the skateboard accelerates, say, backwards in the opposite direction to that in which the person is walking, and the person accelerates forwards. And so in absence of any further actions on behalf of the person, they would most likely fall over because their skateboard is moving out from underneath them as they try and move forward. But the basic point is that both of the objects are gaining momentum. They're both accelerating, except in opposite directions. Now, which of the two objects will

gain more velocity? Will they both accelerate to the same speed? The answer is no, because the person weighs a lot more or has a greater inertial mass than the skateboard. But remember, both person and skateboard had the same force applied on them, because the two forces were an equal and opposite force pair, so they had to be the same size. So, given that the force is acting on both objects are the same, but the masses of the objects are different, and also given that momentum equals mass times velocity of the object, and of course we know that linear momentum has to stay constant, the velocity of the skateboard will be much greater than that of the person, because its mass is lower.

So both person and skateboard have gained exactly the same amount of linear momentum, except because of the greater mass of the person, the person is gained less velocity, whereas the skateboard having a lower mass has gained more velocity. Now you might think that this whole scenario is a violation of what I just said that the linear momentum has to always be conserved because before neither skateboard nor the person were moving anywhere so they had a linear momentum of zero, and now they both have linear momentum.

The answer is that the linear momentum of each of these objects is opposite to the other. So linear momentum is a vector, which means it has a direction associated with it. And so if the momentum of the person after they start moving is positive, then the momentum of the skateboard would be negative. And because the two momentum would be exactly equal in magnitude, these positive and negative momentum would cancel each other out, leaving a total linear momentum of zero, which was exactly the same as the linear momentum that prevailed before the person moved along the skateboard. So in this sense, it's kind of like matter and antimatter that they can cancel each other out and then come into existence without violating conservation of charge

because one's positive and one will be negative. Now, I just want to come back to the issue of why we even have this concept of momentum for a minute. I've said before that we have the concept because of the fact of conservation momentum. Basically, we've observed experimentally in many, many different circumstances that momentum is always conserved, and so we define the concept of momentum around that observation. Momentum is actually quite analogous to energy, as I mentioned before, because energy is the stock that is altered by the flow of work. Analogously, momentum is the stock that is altered by the flow of force.

Now, let me just try and explain what I mean there. A stock is, you can think of it as something that's stockpiled. It's something that exists as a certain amount at any given point in time. So, for example, your wealth is a stock. You have a certain amount of it. A flow is different because a flow is an amount that's measured per unit of time. So income is a flow. You can't just have income. You have to have income per some unit of time. And so income is the flow that changes the stock of wealth. Now convert that to momentum and energy. Momentum and energy are both stocks. They're both something, a property that an object can possess at a given time. It can have a certain amount of energy. It can have a certain amount of momentum. Energy can be held in many different forms. Momentum, not so much just linear and angular, but a similar idea. A given object, say a person walking has a given amount of energy, say gravitational potential. elastic potential, kinetic energy, whatever else.

And also they have a certain amount of momentum, their mass times their velocity. Now, their stock of momentum will be altered by a force. So when a force is applied to that person, that directly changes their momentum by the amount of that force. Now, force can change energy, but it's not exactly the same thing. Force changes momentum.

What changes energy is work. And work is defined as the force applied to an object, multiplied by the distance moved by that force. The distance the object is moved by that force. So you can see that they are related, energy, work, force, and momentum. They have sort of the same terms in them. You've got velocity and force and things like that. But they're slightly different.

So energy is changed by work, momentum is changed by force. Just a fact of nature that things happen to work like that, and that's why we need those two separate concepts. Okay, another thing that I want to point out is that the simple classical equation of momentum equals M times V, mass times velocity, is a bit misleading, at least in Einstein, because we know that photons, for example, do not have any mass. They're massless particles, that's why they can travel at the speed of light. However, they still carry momentum.

According to the simple formula, you wouldn't think they would, because although they have a very, they have velocity, a very fast velocity, they don't have any mass, so zero times any V is still going to be zero. However, that simple equation for momentum has to be altered when you start to, get up to very high velocities, relativistic speeds. And that all comes down to special relativity, which is something we haven't covered in this podcast yet, but if you know anything about that,

you know that Newton's equations start to require alterations, additions to them when we get to really fast velocities, such as near the speed of light. And so photons, in fact, do carry momentum, even though you wouldn't think so based on the simple equation. And in fact, we can utilize that fact of photons carrying, momentum in applications such as the solar sail, which is a theoretical method of propulsion that a spacecraft could use, basically, would just have this massive sail made of some kind of material

that would be light, but could absorb sunlight from the sun, and use it to propel itself, basically. It would be just like wind blowing on the sail and pushing the ship forward. This wouldn't be a solar panel. It would literally be using the momentum of the sunlight, in order to accelerate the spacecraft. As far as I know, this hasn't actually been used for anything yet, but it is certainly possible and utilizes the fact that photons indeed do have momentum. Okay, so I want to now talk about collisions and momentum,

and how this all works. In order to help understand how momentum works in collisions, I'm just going to outline this scenario of a car, hitting a brick wall. So suppose we have a car that's moving at a constant velocity, and it hits a brick wall and it stops. Now both objects after the collision are now at rest. And so they still have mass, but they don't have any velocity,

and so their momentum of both the car and the brick wall is zero. Now, that would seem to contradict the conservation of linear momentum because before the car hit the wall, it clearly had momentum because it was moving. So where did the momentum go if it can't be destroyed, if it always has to be conserved? The answer is the momentum actually goes into the planet that the wall is anchored into. or more precisely it, the momentum goes into the system of the wall, the planet and the car wreckage

altogether, so, you know, the planet and everything that's on the planet. And the momentum is carried into all of these other objects, you know, throughout the planet and so on by vibrations from the impact. So essentially when the car hits the wall, the momentum from that collision is carried by force, which remember is the flow that mediates transfers of momentum, the momentum is carried by force essentially throughout the whole planet, almost like a mini-earthquake. it would be far too small to actually detect that. The entire planet, of course, doesn't react instantly to this collision,

because the vibrations can only travel at finite speed throughout the planet, but it still does travel through. Now, it might sound a bit strange that when we crash into a wall, the planet moves and takes on the momentum because the planet doesn't seem to be knocked out of its orbit or anything. The answer to that is that the planet is so much larger than the car that there is no noticeable change in anything. Remember, momentum is mass times velocity.

Now, compare the mass of the car to the mass. of the earth, and even if the car was traveling at 100 miles per hour when it hit the wall, the total linear momentum of the car would be minuscule compared to the linear momentum of the earth. And then, so when you, compared to the huge mass of the earth, the amount of velocity that would have to be added to the earth to come to that total change in linear momentum, would just be so minuscule that wouldn't even notice it. You probably wouldn't even be out to measure it, even with the most accurate instruments, I would say. One thing you might be thinking of is that even if a single car crashing into a wall doesn't do very much,

maybe if we kept doing this, you know, crashing thousands of cars into thousands of walls for a long time, we could actually somehow alter the orbit of the planet or something like that. And I believe that would be theoretically possible in some ways, like many nuclear explosions on one side of the planet or something like that. But it wouldn't happen with just cars, because the thing is that the moment, the car did not begin traveling to constant velocity. it began at rest and then it accelerated to get to a constant velocity. Well, how did it accelerate? The answer is that its wheels apply to force to the earth, or the road, and the road applied a force back to it, which allowed the car to move.

So essentially, in doing that, and using traction against the planet in the first place, the car has sort of borrowed or taken linear momentum from the planet, and then by smashing into the wall, it just returns the exact same amount of linear momentum that it borrowed when it accelerated. So, there's no loss of momentum anywhere in this process. Linear momentum is always conserved. Okay, so having covered linear momentum, I now want to move on and talk about angular momentum. Angular momentum is just the rotational analog of linear momentum. So, angular momentum is a property of spinning or rotating objects, and like linear momentum,

it too is always conserved. So I just want to highlight the point that there's sort of two subtypes of angular momentum, that of spinning versus that of rotating objects. Now, a rotating object is like the Earth rotating about its axis. It spins around so that a point on the outer surface will move around the center of the object and then come back to the same relative point and it's spinning around like that, like a spinning top.

It's rotating about its central axis. Compare that to a spinning object which is actually moving in a circular orbit about another object. And that's like the Earth orbit, about the Sun. That's spinning angular momentum. They're both sort of the same thing, because if you think about it, like, what we define as an object is kind of arbitrary, so you can think of an atom in the spinning top, near the edge of the spinning top,

as kind of being in a free orbit about another atom in the middle of the spinning top. But for conceptual ease, we usually separate the two out. So angular momentum is similar to linear momentum, because it's also equal to mass times velocity, but there's also an extra term added in there, which is R for radius. The radius refers to the distance between the central point about which the object is rotating or spinning and the object itself. So, for example, the Earth and the Sun are one AU apart, one astronomical unit. And the astronomical unit is defined such that it is equal to the distance between the Earth and Sun. So Earth and the Sun are one AU apart. And so the Earth's angular momentum, as it orbits

the Sun would be equal to the mass of the Earth, multiplied by the velocity of the Earth, the speed is going around at all, but multiplied by that distance of one AU, and that will give you the total angular momentum. So that means that not only can you increase angular momentum by speeding up the rate at which you travel about the object, but also by moving further away. And this is sort of intuitive if you think about how much effort it takes to rotate a ball on a string around you when it's on a short string. versus a long string, it's much harder when the string is longer, even though the mass of the ball doesn't change and you're still trying to spin it at the same speed.

The reason for that is because the angular momentum of the ball is much greater, and you have to apply a force to the string of the ball in order to accelerate it to that angular momentum. And so that requires more effort. So like linear momentum, angular momentum is a vector, and it's defined in a sort of a complicated way, which I won't talk about, because you have to kind of visualize it, because there's the direction. that the object is spinning in, and then there's the direction of the axis and round, which it's spinning is said to point to, the right-hand rule, if you've ever heard of that, if you've ever done some physics, you'll know what I mean. But the point is that it's still a vector, even though the definition of the direction is a bit more complicated in this case.

Another point that I want to make is that linear and angular momentum are separate concepts, although they are clearly related, because they both relate to math and velocity, they are separate. So, for example, the Earth's rotation about its axis or around the sun does not add anything to its linear momentum. They are separate from each other. And also, like linear momentum, the conservation of angular momentum has been verified many or many times by different experiments. And so it's sort of like conservation of energy, conservation of linear momentum, and conservation of angular momentum are sort of some of the three most fundamental conservation laws of physics. Even though two of them sort of have a similar name, they're actually defined quite separately.

So linear and angular momentum, related, but distinct also. Now, I also want to talk about the concept of the axis of rotation, the center of the object that's doing the spinning or the rotating. The point that we define as the axis is largely arbitrary. It doesn't matter. The point is that the calculation of angular momentum will be accurate, as long as you consistently use the same axis, and then adjust the distance of the object from that axis. So there's nothing intrinsic about that concept of the axis of rotation. It just depends on how you define it the calculations will still work out. Okay, so moving on to the concept of torque.

Now, torque is analogous to, it's basically a force, but it's a special type of force. It's a force that causes rotation. Or more specifically, a force that alters angular momentum. So remember, a force, just a normal force, alters, is the flow that alters the stock of linear momentum. Torque is the flow that alters the stock of angular momentum. and when there is no net torque acting on a system, the total angular momentum of that system is always conserved. And so this concept of the conservation of angular momentum

is useful to understand the rotation of objects and how that rotation can change as the object changed. For example, when the solar system was forming, it was believed to form it out of a very large, initially sparse cloud of gas, and as that gas collapsed under its own gravitational forces, the rate, so that cloud of gas was originally spinning just very slightly, so it had some very, well, had some initial amount of angular momentum.

But as the cloud collapsed, it's the distance from the edge of the cloud to the center of the cloud, or the axis of rotation diminished, obviously, because it's getting smaller. And as that occurred, the clouds began to spin faster, because with the same mass, obviously, the mat hasn't gone anywhere, And a smaller distance, the only way to balance out angular momentum is to spin more rapidly. And the classic example of this that you hear all the time is when the dancer, the spinning dancer pulls in their arms, their radius goes down, and so they spin faster to maintain angular momentum.

So moving back to the concept of torque, talk is defined such that only the portion of a force that acts perpendicular to the direction, which it is turning as a parallel to the axis of rotation. you kind of have to see a diagram to make sense of this, actually causes, actually changes angular momentum. So, torque is a force that changes angular momentum, but in order to act as a torque, forces need to be aligned in a particular direction. Okay, so now moving on to the final part of this podcast, which will be about energy and work. Now, I spoke about energy a bit earlier, because I described that it was, I described it as being sort of like momentum in that it's something that's always conserved. But we hear about energy a lot more than we hear about momentum, probably because it appears in, I guess, more different contexts

and more different ways than momentum does. Momentum only appears when objects are in motion, whereas energy does not have to involve motion, at least not at the macroscopic scale. So what is energy? What is it really? Energy is an abstract quantity whose identity is unknown, but it always remains constant in the closed system, like linear and angular momentum, always a constant amount of it.

Now, energy can, of course, be transformed from one form to another, but it cannot be created or destroyed. Einstein has told us in the equation equals MC squared that mass is in fact a form of energy, a highly congealed form of energy, in fact. So this is what happens in a nuclear power station or a nuclear bomb. A very small amount of matter is converted into a large amount of energy. And the inverse is also possible,

although that only happens to a very limited degree in particle accelerators where they can use a lot of energy to make a small amount of matter. So in some sense, everything in the universe is energy. It's either literally energy like photons or gravitation, potential energy or heat or whatever, or it's matter, which is a congealed form of energy. However, just remember that energy is an abstract concept. It doesn't describe any particular object or any particular mechanism

or anything really very concrete at all. It can be thought of as a construct, a bookkeeping device that we use to help us balance all the equations and keep track of things. And, of course, it's a very useful predictive device, but it doesn't really mean anything just by itself. I mean, they're just numbers in equations, which we know, you know, stay constant and balance and can be converted from one form to another in certain ratios, but what it is fundamentally we don't really know.

Okay, so I just want to talk about a couple of the different kinds of force that you may have heard of. One, sorry, not force, the kinds of energy that you may have heard of. A very common one is, of course, kinetic energy, which is defined as one-half of the mass of the object in motion, multiplied by the square of the velocity of that object. Now I bring this up because that sounds an awful lot like linear momentum. In fact, during the difference is that instead of just M times V, mass times velocity, it's half M times v squared. So just moving around the exponents and other terms a little bit, but it's very similar. You might think why we need both of these quantities, kinetic energy and momentum, and they sound very similar to each other.

The answer is that kinetic energy is not always conserved. in more restrictive conditions, whereas linear momentum is conserved in all conditions, in all types of collisions, in all types of interactions. Kinetic energy is only conserved in elastic collisions. Like, for example, the classic case of elastic collisions is billiard balls on a billiard table. One ball rolls, hits another one,

the first ball will stop, and the second ball will continue to roll at the same speed as the first ball, more or less. Elastic collisions occur when there's no energy that's lost due to, that's converted to heat or friction or compression of the balls or anything else. It's just pure kinetic energy of one ball converted to kinetic energy of another ball. Another example of a system that's often said to exhibit perfectly elastic collisions are gas particles in a gas. However, in reality, there's no such thing as a truly perfectly elastic collision.

It's an abstraction. Remember, the characterizing feature of a perfectly elastic collision is that none of the energy is converted to heat, sound, friction, or anything else. All of it goes from kinetic energy of one object to kinetic energy of the other object. And it turns out that when you do the equations for these, that the only way a perfectly elastic collision can work out to conserve both kinetic energy and momentum is for one object to take on the full velocity of another.

So, for example, think of the billiard balls again. When you hit around billiard balls, you see that when one ball hits another, if it hits it head-on, you know, sufficiently, then that second ball takes on the entire velocity of the first ball, and the first ball stops. That is, if they hit sort of head-on, if they hit side-on, then that's a different matter. But if they hit head-on, that will occur. Wouldn't it be possible for both balls to continue moving, but say at half the speed or something like that, half the velocity? Indeed, that would be consistent with linear momentum, because, with the conservation of linear momentum,

because that's just m-times v. But it would not be consistent with the conservation of kinetic energy, which is half mv squared. If you do the equations there, you find that the only way to balance both kinetic and energy, and momentum is for the second ball to take on the entire momentum, or excuse me, entire velocity of the first ball. However, if you're playing pool with balls made of some sticky material or a bouncing material, then rubber, for example, then the collisions would be far from perfectly elastic, and so this linear momentum would not be, excuse me, kinetic energy would not be conserved, but linear momentum would still be conserved, because that is always conserved.

Okay, so kinetic energy, basically just the energy that an object has because of its motion. As I said before, defined as half mass times velocity squared. But there are many other forms of energy as well, apart from just kinetic energy. One that I've already mentioned is gravitational potential energy, which is the energy that an object possesses as a result of its location in a gravitational field. So if you walk up to the top of a hill, or even better example, a cliff, you can jump off and you'll fall down. And as you fall down, you will gain kinetic energy.

accelerating downwards. And that tells you that you must have had some form of energy that's now being converted into that kinetic energy because the kinetic energy can't just come from nowhere. The answer is that that energy came from the location that you had in the gravitational field of the earth. As you move further away from the earth, you gain gravitational potential energy because you have the potential now to sort of fall down and therefore gain kinetic energy as you move back towards the center of the earth, back down into that gravitational well. Elastic potential energy is a sort of a similar concept, potential energy, but in the form of an elastic object, like, for example, a slinky, if you stretch a slinky really far out and then let it go, it snaps inwards rapidly.

In other words, both ends of the slinky accelerate inwards towards each other. That kinetic energy is telling you that that acceleration, kinetic energy must have come from somewhere, and the answer is it came from the elastic potential energy embodied in the stretched slinky before you let it go. So heat or internal thermal energy is another example of energy. And this is the kind that you can detect if you touch a frying pan when it's hot or something like that. You feel your finger burning, and the reason for that is because of the higher thermal energy of the object. It's got energy in there. And there are many other different types of energy as well.

I've only mentioned a few. Another one is electromagnetic energy, of course, or electromagnetic potential energy, caused by the location of an object in an electromagnetic field. So, for example, if you hold a fridge magnet just above the fridge and then let it go, it will pull itself to the fridge and stick to it. That motion, that sideways motion, assuming your fridge is upstanding, is not caused by gravity because it's moving sideways. If gravity doesn't pull sideways, it pulls it down.

That force is actually generated by the magnetic attraction between fridge and fridge magnet. And so once again, you've got it holding that magnet there, you've got a case of potential energy. because of the position of that magnet in the magnetic field of the fridge. There are many different types of energy. But the most important thing to remember is that energy is always held constant. It's always conserved. It can be converted from one formy to another, but it can never be destroyed completely.

It can be converted into matter and back, but never destroyed. If you listen to my podcast about the origin of the universe, there's some debate as to whether that involved a device. violation of the conservation of energy or not, or whether the energy came from some sort of quantum field fluctuation that happened before the beginning of the universe, or coincident with it or something. But check out that podcast for more information on that. And finally, I want to talk a little bit about work. Now, work is the flow that alters the stock, which is called energy, the stock of energy. So work is analogous to force and analogous to talk. It's a flow that

also is the stock of energy. Now work is defined as I mentioned before as force applied multiplied by distance moved, the distance that you move an object. And this is a bit of an interesting definition because that tells you that you can apply a force without doing any work. For example, if you stand, if you just stand holding a heavy object, say a couple of bricks, that's going to be difficult to do. You're going to have to strain against that to prevent the bricks from falling to the ground. However, if you're just standing there, the velocity of the distance traveled, moved by the bricks, the distance that you've moved the bricks is zero. And so, no matter what force you're applying, you're applying a force to the bricks,

of course, because you're holding them up against gravity, you're applying a vertical force to them, but you haven't moved them anywhere. So force times distance is some F times zero, zero distance, which gives zero. So even though you're applying a force to the bricks, you're not doing any work on the bricks. that may sound a bit odd until you remember the fact that work is the flow that alters the stock of energy. And think about it, the bricks are just staying there. They're staying in the same position. They're not accelerating. They're not getting hot or anything like that. They're just there. That means that their energy is not changing. And so if their energy isn't changing, then there shouldn't be any work being done on them because if work is being done, that means energy is changing.

Interestingly, just to expand on this case of the bricks, the momentum of the bricks isn't changing either, which is obvious because of the fact that they're... Well, they're not moving, but even if they were moving, they wouldn't be accelerating, so their velocity would be constant. So where is that force going if you're not changing the momentum

or angular momentum or energy of the bricks? The answer is that you are still applying a force to them, but that force is being offset, exactly balanced out by the force of gravity. So net force acting on the bricks is zero, and net force not only does it not do any work,

but it's also not going to change the linear momentum or angular momentum of the object or the system. Another point to note is that only the convector component of the force that is applied in the direction that an object is moving actually contributes to the change in energy of that object. So for example, if you're pushing a large heavy object along a floor, say, I don't know, you're pushing it along a heavy chair along the carpet, so there's a fair bit of friction, and you're sort of pushing a bit down and a bit forwards, as you move the furniture around, you can divide that force, that diagonally downward force, into two vector components, one horizontal along the ground

and one vertical towards the ground, and only the component of that force that acts parallel to the ground, forwards, in other words, actually will convert into doing work on the chair, because the component of the force that acts downwards is not moving the chair at all. I mean, it would be moving if you could move through the floor, but obviously you can't. So the ground just pushes back and that force doesn't do anything, except increases the frictional force, actually, between the chair and the ground. So only the force acting along the direction of travel that you're moving the chair contributes to work.

So that's why it's a good idea if you're trying to push something along the floor to not push down. In fact, to squat or get down as low as you can and push only, horizontally. In fact, if you can push a little bit upwards, that in fact will help a little bit, because the frictional force, particularly the static frictional force between the floor and an object increases as those two objects are pushed together. So if you push down on an object, it will be harder to move along the floor, and that's, I think, sort of intuitive. Okay, and so I want to talk just briefly a bit more about this concept of the force is doing no work,

because it does seem a bit nonsensical that you can be standing there, straining, and not doing any work. So that actually means that, you know, Olympic weightlifters, when they're struggling to lift that 300 kilos or whatever it is that they lift, holding it over their head, they're not doing any work on the weight. And that sounds a bit odd because it certainly looks like they're doing work. They're certainly straining there. So what's going on? Now, we know that they're not moving the weight anywhere,

at least when they've already picked it up, they're not moving anywhere, so there's no velocity, so there's no distance traveled and therefore no work. But why is it they're still, like, sweating and grunting and stuff like that? That seems to indicate they're doing work. what's going on there? The answer is that actually you are doing work, but you're not doing work on, so for example, the weightlifter, the weightlifter is not doing work on the weight. They're actually doing work on themselves in a sense. Now, what do I mean by that? Think of it this way, if the weightlifter, you know, lift a lot of weights and did a lot of working out, they would clearly get hungry,

they would clearly become tired, they've clearly used up energy. And if they've used up energy, Remember that work is the flow that alters the stock of energy. So if the stock of energy is changed, that must have mean that there's been some kind of work to change that stock. In fact, there has been work, but not work on the weight. In fact, the work all occurs inside the body of the weightlifter, or the person doing the holding. Specifically inside the muscles of that person, because in order to hold up a weight, muscle cells need to periodically or sort of continuously, in a sense, contract, and then relax and then contract. again. And that involves movement of molecules around about inside your arms or, well, anywhere in your body where there are

muscles, inside your muscle cells. And that movement of molecules requires energy. And so in order to get that energy, your body has to metabolize sugars and things that you've eaten and stuff like that. So energy is being converted from one form to another by changes, by movement of substances and changing chemical bombs and stuff like that inside your body. So there is work being done. Now remember, the muscle cells themselves are actually moving. So there is a force, because the muscles all sort of pull on each other, or pushing each other, that's force, and there is distance travel because they're actually moving. The muscle cells physically get bigger and smaller, and they move about, and stuff like that. So you've got distance, and you've got force, those multiply together, you get work.

And so your muscles or muscle cells, individual muscle cells, are doing work on each other. and that work then can go into applying a force on the weight that you're holding. It will also go into generating some excess heat and sweating and things like that. But that total work that's being done within the body does not actually do any work on the weight itself. So there's a key idea here is that there's a distinction between work being done on one object versus work being done on another object. you can be doing work on one object without doing work on another object. In the case of the person, the person's muscle cells are doing work on each other, but the person as a whole, even though they're using energy and their straining,

are not actually doing any work on the weight that they're holding up. Okay, that's about all I had for this podcast on momentum, energy and work. If you enjoyed this podcast, please leave a review on iTunes. I think I only have one review, and it would be nice to get a couple more. You can also write to me, if you have any suggestions or feedback or anything. Or just to let me know you're listening, it'd be nice to know that someone's actually hearing these podcasts, and I'm not just talking to myself. You can write to me at FODs12 at gmail.com.

That's F-O-D-S-1-2 at gmail.com. Thanks for listening again, and I'll speak to you next time.