Chapter 5: Applying Newton's Laws

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You ever just stop and think, like, how does anything even move?

Or not move, for that matter?

Like, why doesn't this table just suddenly decide to float away?

Hmm.

Yeah, that'd be pretty chaotic, wouldn't it?

Total chaos.

But luckily, there are some pretty fundamental principles at work here, and that's exactly what we're going to be exploring today.

So welcome to another deep dive, everybody.

Today we are diving deep into a chapter all about applying Newton's laws.

That's right.

So we've taken this chapter and really tried to break it down and get to the core concepts and the problem -solving techniques.

So you can really get a grasp on how these laws are used in practice and just build a really solid foundation for understanding physics.

Awesome, yeah.

And the chapter is actually laid out really nicely, kind of takes us through things step by step.

We're going to be starting with equilibrium of particles, which is all about, you know, when things are stable, either at rest or moving at a constant speed.

Then we'll get into Newton's second law, dynamics of particles, which that's where we see how forces actually cause things to accelerate.

After that, we'll tackle friction forces, because you can't get away from those.

Then we'll explore dynamics of circular motion, which that's always a fun one.

And finally, we'll kind of zoom out and consider the fundamental forces of nature.

It's a pretty epic journey from the stillness of equilibrium to the very forces that shape the universe.

And we're going to try to make it all make sense, you know, with examples and explanations,

you know, without getting too bogged down in the technical jargon.

Exactly.

We really just want to kind of equip you with a really clear understanding of these core principles.

Cool.

All right.

So let's dive right in, starting with equilibrium of particles.

Now, when we say something's in equilibrium, it means that it's in a state of balance.

In physics terms, this means that either the object is at rest, not moving at all, or it's moving at a constant velocity in what we call an inertial frame of reference.

Right.

Think of it like a train moving smoothly at a constant speed.

No sudden jerks or changes.

Exactly.

Yeah.

And the key here is that there's no acceleration happening, right?

And this all ties back to Newton's first law.

You know, an object will stay in its current state of motion unless a net force acts on it.

So equilibrium, it's basically the result of no net force.

Yeah, exactly.

When the sum of all the forces acting on an object is zero, it's basically a state of no change in motion.

And this concept, I mean, it's everywhere, right?

Like from making sure a bridge stays up to understanding how a car on a flat highway maintains its speed.

Right.

That makes sense.

So the chapter actually provides like a step -by -step strategy for tackling equilibrium problems.

It's problem solving strategy in 5 .1.

And the very first step they emphasize is drawing a free body diagram.

So can you explain what that is exactly?

Oh, yeah, totally.

It's basically like a little sketch of the object you're looking at, completely isolated from everything else around it.

And then you draw arrows to represent every single force acting on it.

So each arrow shows the direction of the force and, you know, roughly its magnitude.

OK, yeah, I think I've seen those before.

And why are they so important?

Well, because it really forces you to account for every single force that's interacting with the object and also their directions, right?

It's kind of like, well, if you're missing a force or you mix up the direction, you're not going to get the right answer.

Kind of like, well, you can't solve a puzzle if you don't have all the pieces.

Right.

Now that makes total sense.

It's like a visual way to make sure you're not overlooking anything.

And then, of course, when you've got multiple objects interacting with each other, we've got to bring in Newton's third law.

You know, for every action, there's an equal and opposite reaction.

Exactly.

Like when you push against a wall, the wall pushes back on you with the same force, but in the opposite direction, of course.

Right.

Yeah, of course.

So how do we incorporate this into our analysis, you know, especially when we're working with equilibrium?

So the thing with Newton's third law, it's about pairs of forces, like object A pushes on object B, then object B pushes back on object A.

So when you're drawing your free body diagram, you've got to be super careful about only including the forces that are acting on that specific object.

Don't get tripped up by the reaction forces because those are acting on the other object.

OK, got it.

So it's all about being super clear about which objects you're focusing on at any given moment.

So you're only looking at the forces that are acting on that object.

Yeah, exactly.

Cool.

OK, so the chapter then introduces this concept of tension, particularly in ropes and cables.

It says that for an ideal weightless rope, the tension is uniform throughout.

So what exactly are we talking about when we say tension?

So tension is basically the force that's being transmitted through a rope or cable when it's pulled tight.

And since we're assuming an ideal weightless rope here, we can say that the force you apply at one end is transmitted without any loss to the other end and to every point in between.

So think of it like a pulling force that the rope exerts.

OK, so it's like the rope is just a pathway for that force to travel through.

And it's the same amount of force everywhere along that pathway.

Yeah, precisely.

Gotcha.

So the chapter gives some really helpful real world examples to illustrate equilibrium.

One is a hanging object like, you know, a picture frame hanging on a wall.

That one seems pretty intuitive.

Yeah, it's pretty straightforward.

You've got the tension in the string or wire pulling upwards.

And that's got to be equal in magnitude and opposite in direction to the force of gravity pulling the picture downwards.

Otherwise, it wouldn't be hanging there, right?

Exactly.

OK, so then there's this example of a car on a ramp.

This is where things get a little bit more interesting because gravity is still pulling straight down.

But now you've got the ramp at an angle.

So how do we analyze that?

So in this case, it's super helpful to break down the force of gravity into two components, right?

One component is acting parallel to the surface of the ramp and the other is perpendicular to it.

The perpendicular component is balanced by what we call the normal force.

That's the force the ramp exerts on the car, kind of pushing back up against it.

And if the car is in equilibrium, either at rest or moving at a constant speed up or down the ramp, any other forces, like maybe friction if it's not moving, have to balance out the component of gravity that's pulling the car down the ramp.

OK, so it's all about breaking the forces down into components that line up with the ramp.

And then the last example they mentioned is engines being suspended by chains,

kind of similar to the hanging object, but, you know, a bit more going on.

Exactly.

You've got multiple chains involved.

So you have to consider the tension in each chain and how they all work together to balance out the weight of the engine.

And if those chains are at different angles, which they usually are, you've got to resolve the tension in each chain into its horizontal and vertical components.

So the vertical component is going to add up to equal the weight of the engine.

And the horizontal components, well, those got to cancel each other out for the engine to be in equilibrium.

So you end up with a system of equations to solve.

So basically, the key for these more complex equilibrium problems, especially those involving two dimensions, is to break down the forces into their x and y components.

Yeah, exactly.

By doing that, you essentially take this vector equation, you know, the net force equals zero, and you turn it into two much simpler equations, one for the x -direction and one for the a -direction.

And those are way easier to work with algebraically speaking when you're trying to solve for unknowns like the tension in a cable or the angle of a support beam.

OK, that makes a lot of sense, like taking something complex and breaking it down into my more manageable pieces.

All right, so we've covered equilibrium pretty thoroughly, which is, you know, a state of balance, no acceleration.

But now let's get into what happens when things are accelerating.

This brings us to Newton's second law, dynamics of particles.

And at the heart of this is the famous equation, e g of a a g l equals male.

Can you unpack that for us a little?

Absolutely.

So Newton's second law basically tells us how forces affect motion.

It says that the net force acting on an object, that's g dollars, is directly proportional to the object's mass and its acceleration, a dollar, and the direction of the acceleration is always the same as the direction of that net force.

So, you know, a bigger force will create a bigger acceleration for a given mass, and a bigger mass will experience a smaller acceleration under the same force.

So it's all about the relationship between force, mass, and acceleration.

Yeah, exactly.

Now the chapter, again, provides problem solving strategy, problem solving strategy 5 .2 for dynamics problems.

And again, it emphasizes free body diagrams, but there's a really important caveat.

We should never include ma as a force in our free body diagram.

Why is that?

Right, this is super important, because ma, it represents the result of the net force acting on the object.

It's not a separate force itself.

So your free body diagram, it should only show the real physical forces that are acting on the object, things like gravity, tension, friction, normal forces, and any pushes or pulls that are being applied.

The net force is what causes the acceleration, right, as described by that equation, g g equals ma ma, but it's not a force in and of itself.

Okay, so it's like the outcome, not one of the inputs in the equation.

It's the result of all the other forces acting on the object.

Precisely.

Got it.

So the chapter then discusses situations where you have constant forces acting on an object.

So what happens to the motion of an object if it's experiencing a constant net force?

Well, if the net force is constant and the object's mass isn't changing, the Newton second law tells us that the acceleration will also be constant.

And that's really important, because if the acceleration is constant, we can use all those handy kinematic equations that we've learned before to actually describe how the object's motion changes over time, you know, things like its velocity and displacement.

Right, right.

So it makes those calculations a lot more straightforward.

Then we move into systems of connected objects, like they give the example of a glider on a track, and it's connected by a string over a pulley to a hanging weight.

What's the main thing we need to keep in mind when we're analyzing these systems?

Well, the key thing is that the motions of the connected objects are linked, right?

They're constrained.

So if that hanging weight goes down a certain distance, the glider has to move horizontally by the same distance.

This means they're both going to have the same magnitude of acceleration.

So usually what you do is you draw a separate free body diagram for each object.

Then you apply Newton's second law to each object individually.

The tension in that connecting string that acts as an external force on each object, and it's the same throughout the string.

Okay, so it's kind of like analyzing two separate problems, but linked together by that common tension.

And one thing I noticed is that in these accelerating systems, tension and weight, they aren't always equal anymore.

Like they often were in our equilibrium examples.

Why is that?

Right.

That's because in equilibrium, there's no net force, right?

So things like tension and weight, they often perfectly balance each other out.

But in an accelerating system, well, there is a net force.

Like think of the hanging weight.

If it's accelerating downwards, the force of gravity, its weight, has got to be stronger than the tension pulling up on it.

If they were equal, there would be no net force, and the weight wouldn't accelerate.

And same thing for the glider.

The tension in the string is what's pulling it along and causing it to accelerate.

So in dynamics problems, those forces are unbalanced, which is why we see acceleration.

Got it.

So the key difference is whether or not there's a net force causing acceleration.

Okay, so now let's bring in a force that we deal with constantly in the real world.

Friction.

Section 5 .3 dives into this.

So basically, what is friction?

So friction is this force that acts between two surfaces that are in contact.

It always acts in the opposite direction of motion, or the direction that the object would move if friction wasn't there.

It's basically resisting that relative motion between the surfaces.

Okay, so it's like a force that's always trying to slow things down or prevent them from moving in the first place.

Exactly.

And we learned about two main types of friction.

Kinetic friction and static friction.

So let's start with kinetic friction, or $5k.

When does that one come into play?

Kinetic friction happens when two surfaces are already sliding past each other.

And we find, experimentally, that the force of kinetic friction is proportional to what we call the normal force.

That's the force pressing the two surfaces together.

The proportionality constant is called the coefficient of kinetic friction, Tauberi dollar, and that depends on the types of surfaces that are in contact.

Okay, so the rougher the surfaces, the higher the coefficient of friction.

Right, exactly.

And the formula for kinetic friction is $5k equal monk air, where nones in the normal force.

And usually for a given pair of surfaces, that coefficient of kinetic friction is pre -constant over a range of speeds.

Got it.

So what about static friction, Monk?

What's the deal with that one?

So static friction acts between two surfaces that are touching, but they're not actually sliding past each other.

But there might be a force trying to make them move.

Like imagine you're trying to push a really heavy box across the floor, but it's not budging yet.

Yeah, I've been there.

The static friction force is what's preventing it from moving initially.

It's acting equal and opposite to the force you're applying, up to a point.

And unlike kinetic friction,

the force of static friction, it's not constant.

It can be anything from zero up to its maximum value, which we get from the equation 4s max and plus, where water is the coefficient of static friction.

Now if the force you're applying becomes greater than that maximum static friction force, well that's when the box finally starts to move and the friction switches from static to kinetic.

Okay, so static friction is kind of like this adaptable force.

It pushes back just hard enough to keep things from moving until you overcome that maximum limit.

And then it's game over for static friction and kinetic friction takes over.

Yeah, that's a great way to put it.

Cool.

And the chapter also mentions that usually that coefficient of static friction, annolo, is greater than the coefficient of kinetic friction up a close.

So what does that mean in practice?

So that basically means that it usually takes more force to get an object moving from rest than it does to keep it moving at a constant velocity once it's already sliding.

Think back to that heavy box.

It takes a lot of effort to get it started, but then it's a bit easier to keep it going.

Right, that definitely rings true.

I've definitely experienced that.

So the chapter also briefly talks about rolling friction, which has its own coefficient, Mardellers.

How does rolling friction compare to static and kinetic friction?

So rolling friction is that force that opposes the rolling motion of an object.

And in most cases, it's way smaller than static or kinetic friction for similar surfaces.

That's why things like wheels and ball bearings are so useful, right?

It's way easier to move a heavy object by rolling it than by sliding or dragging it.

Right, absolutely.

OK, so let's apply this knowledge about friction to some examples.

Like say we have a crate that's being pulled across a floor.

What forces do we need to consider now that we've got friction involved?

So you've got the force that's pulling the crate, acting in the direction of the pull.

Then there's the weight of the crate, always acting straight down due to gravity.

And the floor is exerting an upward force on the crate, which we call the normal force.

And finally, we've got friction acting horizontally and opposing the motion.

If the crate's moving, it's kinetic friction.

But if you're pulling on it and it's not moving yet, that's static friction.

And it'll be equal and opposite to your pulling force up to that maximum limit.

OK, so it depends on whether the crate is already moving or not.

What about if we have a toboggan sliding down a snowy slope?

How does the incline change things?

All right, so for this one, the first thing you want to do is break down the toboggan's weight into two components, one that's parallel to the slope and one that's perpendicular.

That perpendicular component is balanced out by the normal force, the force the slope exerts on the toboggan.

And the parallel component, that's what's trying to pull the toboggan downhill.

Kinetic friction acts in the opposite direction, trying to slow it down.

And the difference between that parallel component of the weight and the force of kinetic friction, that determines how fast the toboggan accelerates down the slope.

OK, so the angle of the slope and those components of the weight, they really come into play when figuring out the forces.

All right, so we've covered friction pretty well.

Now let's move on to a completely different type of motion,

circular motion, which is covered in section 5 .4.

So we're talking about objects moving in curved paths going round and round.

What exactly is uniform circular motion?

So uniform circular motion, it means an object is moving in a circle at a constant speed.

And the key word here is speed.

The speed stays the same,

but the velocity, well, that's constantly changing because direction of motion is changing all the time.

And any time velocity changes, that means we have acceleration.

Right, that makes sense.

And this acceleration is called radial acceleration, or sometimes centripetal acceleration.

And it's always directed towards the center of the circle.

The formula is one rod is E2R dual, so it depends on the object's speed and the radius of the circle.

Exactly.

And this acceleration toward the center, that's what keeps the object moving in a circle.

And because we have acceleration, we know from Newton's second law that there has to be a net force causing it.

And in this case, that net force is called the centripetal force, which is given by one to our tour.

But it's super important to understand that centripetal force, it's not a new type of force.

It's just the name we give to whatever force or combination of forces is causing the circular motion.

OK, so it's like a role that a force can play.

And the chapter really emphasizes not using the term centripetal force when we're talking about inertial frames of reference.

So can you explain why that distinction is so important?

Yeah.

So often people think of centrifugal force as a real outward force, like something's pushing the object out from the center of the circle.

But in an inertial frame of reference, that is a frame that's not accelerating,

the only forces acting on the object are those exerted by other objects.

We call the centrifugal force is really just the object's inertia, its tendency to keep moving in a straight line.

It's like when you're in a car turning sharply, you feel pushed outward.

But that's not a real force pushing you.

It's your body trying to keep moving in the direction it was going.

So in physics, we really only talk about the real forces like gravity, tension, friction, and the normal force.

Got it.

So it's like this perceived force, but not an actual force in the way we usually think about them.

OK, so the centripetal force, that's always provided by some real force or combination of forces.

So can you give us some examples of what can provide the centripetal force in circular motion?

Sure.

So let's say you have a ball on a string and you're swinging it around in a circle.

The tension in that string, that's what's providing the centripetal force, pulling the ball inward and keeping it from flying off in a straight line.

OK, so that's a pretty classic example.

What about something like a car going around a curve?

So if it's a flat curve, the centripetal force is usually provided by the static friction between the car's tires and the road.

The tires push outward against the road and the road pushes back on the tires with an equal and opposite force, which is static friction.

And if the car is going too fast or the curve is too sharp, the friction force might not be enough to provide the needed centripetal force and the car might skid.

Yikes.

Yeah, nobody wants that.

So what about those banked curves that you see on highways?

How do those work?

So when a curve is banked, the normal force from the road actually has a horizontal component that points towards the center of the circle.

So that component of the normal force can help provide the centripetal force.

And the car doesn't have to rely as much on friction.

In fact, if the curve is banked at just the right angle for a specific speed, the horizontal component of the normal force can provide all the centripetal force that's needed.

And theoretically, no friction is even required.

Wow, that's really interesting.

So it's kind of like the banking helps the car turn.

What about those situations where you have circular motion but in a vertical plane, like a roller coaster going around a loop?

Ah, yeah.

So in those cases, gravity starts playing a much bigger role, right?

So at the bottom of the loop, the normal force from the track has to be greater than the weight of the roller coaster to provide the centripetal force because gravity is acting in the opposite direction.

And at the top of the loop, both the weight and the normal force are acting downwards and they both contribute to the centripetal force.

So the forces, they kind of shift and change throughout the loop.

Okay, yeah.

So it's a lot more dynamic than just a horizontal circle.

And lastly, there's a brief mention of non -uniform circular motion.

What's the key difference between that and uniform circular motion?

So the main difference is that in non -uniform circular motion, not only is the direction changing but the speed is also changing.

So now you've got both a radial component of acceleration towards the center of the circle and a tangential component, which is tangent to the circle and responsible for the change in speed.

So this means you also have a tangential component of the net force in addition to the radial component.

Okay, so it's a little more complex because you're dealing with changes in both speed and direction.

All right, so we've covered quite a bit of ground with circular motion.

Now let's wrap things up by zooming out to the biggest picture,

the fundamental forces of nature.

So this is section 5 .5.

What are we talking about here?

So we're talking about the most basic forces in the universe, the ones that underlie all the other forces that we've been discussing,

and there are four of them.

The gravitational force, the electromagnetic force, the strong nuclear force and the weak nuclear force.

Wow.

Okay, can you give us like a brief overview of each of those?

So gravity, that's the force of attraction between any two objects that have mass.

It's what holds the planets in orbit around the sun, what makes things fall to the earth.

It's a long range force, but it's also the weakest of the four.

Then there's the electromagnetic force, which acts between electrically charged particles.

It's responsible for a ton of stuff, like light, electricity, magnetism and chemical reactions.

It's also a long range force,

and it's much stronger than gravity.

The strong nuclear force that one acts between the protons and neutrons within the nucleus of an atom, and it's incredibly strong, hence the name.

It's what holds the nucleus together, despite the protons all having the same charge and wanting to repel each other, but it's also a very short range force and only acts over tiny distances.

And finally, there's the weak nuclear force, which is responsible for certain types of radioactive decay.

It's also a short range force, and it's weaker than the strong and electromagnetic forces.

Okay, so those are the four fundamental forces.

And how do they connect to the forces that we've been talking about in this chapter?

Like weight, tension, normal force, and friction.

So all of those everyday forces that we experience, they're basically manifestations of these fundamental forces.

Like weight, that's just the gravitational force exerted by the earth on an object.

The normal force, tension, and friction,

those are all ultimately due to electromagnetic interactions between atoms and molecules.

Okay, so it's like these fundamental forces are working behind the scenes, creating all the forces that we see and experience in our everyday lives.

Yeah, exactly.

And the chapter actually mentions that physicists are trying to unify all four of these forces into one grand theory,

which is pretty mind blowing when you think about it.

It really is.

It makes you realize how interconnected everything is.

So wow, we've really covered a lot in this deep dive into applying Newton's laws.

We started with equilibrium, then explored dynamics, tackled friction, got a handle on circular motion, and finally zoomed out to those fundamental forces.

And hopefully, you now have a much better grasp on these core physics concepts and how they relate to each other.

It really is amazing how Newton's laws can explain so much about how the world works.

It really is.

So as you go about your day, you know, maybe take a moment to notice these principles at work around you.

Like think about the forces involved when you see a bird flying or when you toss a ball, or even just when you're walking down the street.

Yeah, or think about how engineers have to consider these laws when they design things like buildings and cars and planes.

Exactly.

It's everywhere.

Well, thanks for joining us for this deep dive into the world of Newton's laws.

Until next time, see you then.