The best way to learn how to solve physics problems is to solve physics problems. You can’t just read about it and think about it in your head… you actually have to do it, just like riding a bike. You can read all about bicycles, how they work and what the individual parts do, but until you sit in the seat and try to ride the thing, it’s really hard to understand. I am going to do a series of different sample physics problems in the videos below and explain everything in detail so you can really see how to apply Newton’s Laws of Motion to problems in the real world.
After you’re done watching the samples, download your practice problem set (at the end of the lessons) and try it yourself!
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Sleds are great to practice physics problems with, because there’s no friction associated with the problem (it’s sitting on ice, not on the ground). This is a good one to start with to get used to how we use the kinematic equations along with Newton’s laws and FBD’s to solve real problems.
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This is a really common thing to see happen in the real world, and one that people have a hard time seeing from the point of view of an outside observer just sitting on the side of the road. If you’ve ever been in a truck where this happened to you, now you know why.
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Here’s a good example of how non-moving objects can be analyzed for missing components by setting the acceleration term in Newton’s second law to zero. (Although I’ve never tried this one, I can only imagine that in the real world, the tire would actually be moving.)
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You can gain and lose weight just by standing on your bathroom scale in an accelerating elevator. In this problem, we'll look at what happens if there's constant velocity, positive and negative acceleration, and also free fall motion (yikes!).
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We're going to experiment with Newton's Third law by blowing up balloons and letting them rocket, race, and zoom all over the place. When you first blow up a balloon, you're pressurizing the inside of the balloon by adding more air (from your lungs) into the balloon. Because the balloon is made of stretchy rubber (like a rubber band), the balloon wants to snap back into the smallest shape possible as soon as it gets the chance (which usually happens when the air escapes through the nozzle area). And you know what happens next - the air inside the balloon flows in one direction while the balloon zips off in the other.
Question: why does the balloon race all over the room? The answer is because of something called 'thrust vectoring', which means you can change the course of the balloon by angling the nozzle around. Think of the kick you'd feel if you tried to angle around a fire hose operating at full blast. That kick is what propels balloons and fighter aircraft into their aerobatic tricks.
We're going to perform several experiments here, each time watching what's happening so you get the feel for the Third Law. You will need to find:
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Question: why does the balloon race all over the room? The answer is because of something called 'thrust vectoring', which means you can change the course of the balloon by angling the nozzle around. Think of the kick you'd feel if you tried to angle around a fire hose operating at full blast. That kick is what propels balloons and fighter aircraft into their aerobatic tricks.
We're going to perform several experiments here, each time watching what's happening so you get the feel for the Third Law. You will need to find:
- balloons
- string
- wood skewer
- two straws
- four caps (like the tops of milk jugs, film canisters, or anything else round and plastic about the size of a quarter)
- wooden clothespin
- a piece of stiff cardboard (or four popsicle sticks)
- hot glue gun
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Let’s take a good look at Newton’s Laws in motion while making something that flies off in both directions. This experiment will pop a cork out of a bottle and make the cork fly go 20 to 30 feet, while the vehicle moves in the other direction!
This is an outdoor experiment. Be careful with this, as the cork comes out with a good amount of force. (Don’t point it at anyone or anything, even yourself!)
Here’s what you need to find:
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Rockets shoot skyward with massive amounts of thrust, produced by chemical reaction or air pressure. Scientists create the thrust force by shoving a lot of gas (either air itself, or the gas left over from the combustion of a propellant) out small exit nozzles.
According to the universal laws of motion, for every action, there is equal and opposite reaction. If flames shoot out of the rocket downwards, the rocket itself will soar upwards. It’s the same thing if you blow up a balloon and let it go—the air inside the balloon goes to the left, and the balloon zips off to the right (at least, initially, until the balloon neck turns into a thrust-vectored nozzle, but don’t be concerned about that just now).
A rocket has a few parts different from an airplane. One of the main differences is the absence of wings. Rockets utilize fins, which help steer the rocket, while airplanes use wings to generate lift. Rocket fins are more like the rudder of an airplane than the wings.
Another difference is the how rockets get their speed. Airplanes generate thrust from a rotating blade, whereas rockets get their movement by squeezing down a high-energy gaseous flow and squeezing it out a tiny exit hole.
If you’ve ever used a garden hose, you already know how to make the water stream out faster by placing your thumb over the end of the hose. You’re decreasing the amount of area the water has to exit the hose, but there’s still the same amount of water flowing out, so the water compensates by increasing its velocity. This is the secret to converging rocket nozzles—squeeze the flow down and out a small exit hole to increase velocity.
There comes a point, however, when you can’t get any more speed out of the gas, no matter how much you squeeze it down. This is called “choking” the flow. When you get to this point, the gas is traveling at the speed of sound (around 700 mph, or Mach 1). Scientists found that if they gradually un-squeeze the flow in this choked state, the flow speed actually continues to increase. This is how we get rockets to move at supersonic speeds or above Mach 1.
The image shown here is a real picture of an aircraft as it breaks the sound barrier. This aircraft is passing the speed at which sounds travel. The white cloud you see in the photo is related to the shock waves that are forming around the craft as it moves into supersonic speeds. Because the aircraft is moving through air, which is a gas, the gas can compress and results in a shock wave.
You can think of a shock wave as big pressure front. In this photo, the pressure is condensing water vapor in the air, hence the cloud. There are lots of things on earth that break the sound barrier – bullets and bullwhips, for example. The loud crack from a whip is the tip zipping faster than the speed of sound.
The rockets we’re about to build get their thrust by generating enough pressure and releasing that pressure very quickly. You will generate pressure both by pumping and by chemical reaction, which generates gaseous products. Let’s get started!
For this experiment, you will need:
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To review, Newton’s First Law deals with objects that have balanced forces on it and predicts how they will behave. It’s sometimes called the law of inertia, and it’s the law that is responsible for helping you figure out which egg is raw or hard-boiled without having to crack it open. (If you haven’t done this, you really need to. All you have to do is set the egg spinning on the counter, then gently touch the top with a finger for a second, then release. The egg that stops dead is hard-boiled, and the one that starts spinning again in raw. Don’t know why this works? The raw egg has a liquid center that isn’t connected to the hard shell. When you stopped the shell for a split second, the innards didn’t have time to stop, and they have inertia. When you removed your finger, the liquid exerts a force on the shell and starts it spinning again. The hard-boiled egg is solid all the way through, so when you stopped the shell, the whole thing stops. Newton’s First Law in action.)
Newton’s Second Law of Motion deals with the behavior of objects that have unbalanced forces. The acceleration of an object depends on two things: mass and the net force actin on the object. As the mass of an object increases, like going from a marshmallow to a bowling ball, the acceleration decreases. Or a rocket burning through its fuel loses mass, so it accelerates and goes faster as time progresses. There’s a math equation for the second law, and it’s stated like this: F = ma, where F is the net force, m is the mass, and a is the acceleration. It’s important to note that F is the vector sum of all forces applied to the object. If you miss one or double count one of them, you’re in trouble. Also note that F is the external forces exerted on the object by other objects, not the internal forces because those cancel each other out.
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How do you find the vector sum of all the forces acting on an object? We already looked at how to use a FBD to calculate the net applied force on an object, so now let's put it together with our knowledge about gravity (Fgrav = mg) and friction (Ffriction = μ fnormal) by using our equation: Fnet = ma.
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Remember when we studied Free Fall Motion and we assumed that all objects fall with the same acceleration of g or 9.81 m/s2 ?
Well, that wasn’t the whole truth, because not all objects fall with the same acceleration. But it’s a good place to start out when we’re getting our feet wet with physics. (You’ll find this happens a lot when you get to more advanced concepts… you learn the easier stuff first by ignoring a lot of other things until you can learn how to incorporate more things into your equations.) So why do objects stop accelerating and reach terminal velocity, and how why do more massive objects fall faster than less massive? To answer this, we’ll take a look at air resistance and Newton’s Second Law using the F = ma equation.
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This lesson may give you a sinking sensation but don’t worry about it. It’s only because we’re talking about gravity. You can’t go anywhere without gravity. Even though we deal with gravity on a constant basis, there are several misconceptions about it. Let’s get to an experiment right away and I’ll show you what I mean.
If I drop a ping pong ball and a golf ball from the same height, which one hits the ground first? How about a bowling ball and a marble?
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There are situations where you have two objects interacting with each other, which means that you’ll have two unknown variables you’ll solve for (usually acceleration). You can solve these types of problems in a couple different ways. First, you can look at the entire system and consider both objects as only one object. For example, the Earth and Moon might be combined into one object if we’re looking at objects that orbit the sun, so the mass of the Earth and Moon would be combined into a single mass, m, and would also have the same acceleration, a. This approach is used if you really don’t care about what’s going on between the two objects. Or you could treat each object as it’s own separate body and draw FBD for each one. This second approach is usually used if you need to know the forces acting between the two objects.
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If I asked you to define the word force, what would you say? You probably have a feeling for what force means, but you may have trouble putting it into words. It’s kind of like asking someone to define the word “and” or “the”. Well, this lesson is all about giving you a better feeling for what the word force means. We’ll be talking a lot about forces in many lessons to come. The simplest way to define force is to say that it means a push or a pull like pulling a wagon or pushing a car. That’s a correct definition, but there’s a lot more to what a force is than just that.
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Friction is everywhere! Imagine what the world would be like without friction! Everything you do, from catching baseballs to eating hamburgers, to putting on shoes, friction is a part of it. If you take a quick look at friction, it is quite a simple concept of two things rubbing together.
However, when you take a closer look at it, it’s really quite complex. What kind of surfaces are rubbing together? How much of the surfaces are touching? And what’s the deal with this stick and slip thing anyway? Friction is a concept that’s many scientists are spending a lot of time on. Understanding friction is very important in making engines and machines run more efficiently and safely.
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There are two big categories that forces fall into: contact forces, and forces resulting from something called action-at-a-distance, like gravitational, magnetic, and electrical forces. Contact forces come into play when objects are physically touching each other, like friction, air resistance, tension, and applied forces (like when your hand pushes on something, or you kick a ball with your foot).
Action-at-a-distance forces show up when the sun and planets pull on each other gravitationally. The sun isn’t in contact with the Earth, but they still exert a force on each other. Two magnets repel each other even though they don’t touch… that’s another example of action-at-a-distance force. Inside an atom, the protons and the electrons pull on each other via the electrical force.
The units of force are in “Newtons”, or N like this: “my suitcase weighs 20N”. 1 N = 1 kg * m/s2. A force is also a vector, meaning that is has magnitude and direction. The force my suitcase exerts on the ground is 20N in the downward direction. Scientists and engineers use arrows to indicate the direction of force.
We’ll learn how to do this by drawing “Free Body Diagrams”, or FBDs. These are really useful for inventors and engineers, because with one look at a structure or machine, they can see all the forces acting on it and quickly be able to tell if the object is experiencing unbalanced forces, and if so what would happen. Unbalanced forces can cause rockets to crash, aircraft to somersault, bridges to collapse, trains to roll off the track, skyscrapers to topple, machines to explode or worse!
We’re going to learn how to see forces by making a model of the real world down on paper, drawing in all the forces acting on the object and use a little math to figure out important information like acceleration, force and velocity. Most engineers and scientists spend a year or more studying just this one concept about FBDs (and also MADs: “Mass-Acceleration Diagrams”) in college, so let’s get started…
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In order to figure out what’s going on with an object, you have to take a look at the forces being applied to it. Forces are a vector, meaning that they have a direction and a magnitude. Your weight is not just a number, but it’s also in the downward direction. When we look at the forces that act on an object (or system of objects), we need to know how to combine all the forces into a single, resultant force which makes our math a lot easier. Here’s a set of videos that will show you how to do this:
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There’s a different type of notation for x and y axes called “i-hat” and “j-hat”. This next video will show you exactly what you need to know to understand how to use them together so you don’t get confused! If you haven’t learned about “sines” or “cosines” yet, or it’s been awhile since you’ve studied triangles, this video will show you exactly what you need to know in order to solve physics problems. We’re not going to spend time deriving where these came from (if you’re interested in that, just open up a trigonometry textbook), but rather we’re going to learn how to use them in a way that real scientists and engineers do.
Take out your notebook and take notes on the law of sines, law of cosines, and write down definitions for sine, cosine, and tangent based on what you learn in the video, especially if you’re new to all this. Take it slow and you’ll catch on soon enough, because math isn’t just a shiny box of tools you just learn about, but you need to take the tools out of the box and learn how to crank with them. And sometimes, you learn how to use a impact driver when you need it, not ahead of time for someday when you might need it. Don’t get stuck if you haven’t seen some of these math principles yet or if they don’t make sense where they came from – just start using them and your brain will pick it up on the way as you learn how to apply them. Again, don’t feel like you have to complete a comprehensive course in trig to be able to figure out how to add vectors together! Just follow these simple steps…
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Force fields aren’t just something for science fiction writers. They are actually a very real and very mysterious part of the world in which you live. So, what is a force field? Well, I can’t tell you. To be honest, nobody can. There’s quite a bit that is still unknown about how they work. A force field is a strange area that surrounds an object. That field can push or pull other objects that wander into its area. Force fields can be extremely tiny or larger than our solar system.
A way to picture a force field is to imagine an invisible bubble that surrounds a gizmo. If some other object enters that bubble, that object will be pushed or pulled by an invisible force that is caused by the gizmo. That’s pretty bizarre to think about isn’t it? However, it happens all the time. As you sit there right now, you are engulfed in at least two huge force fields, the Earth’s magnetic field and the Earth’s gravitational field.
Gravity doesn’t care what size something is or whether or not it is moving, Gravity treats all things equally and accelerates them the same. Notice, that I say gravity accelerates all things equally, not gravity pulls on all things equally. Gravity does pull harder on some things than on other things. This is why I weigh more than a dog. I am made of more stuff (I have more atoms) than the average dog, so gravity pulls on me more.
Weight is nothing more than a measure of how much gravity is pulling on you. This is why you can be “weightless” on a scale in space. You are still made of stuff, but there’s a balance of the gravity that is pulling on you and the outward force due to the acceleration since you’re moving in a circle (which you do in order to remain in orbit), so it feels like you have no weight.
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The larger a body is, the more gravitational pull or the larger a gravitational field it will have. The Moon has a fairly small gravitational field (if you weighed 100 pounds on Earth, you’d only be 17 pounds on the Moon), the Earth’s field is fairly large and the Sun has a HUGE gravitational field (if you weighed 100 pounds on Earth, you’d weigh 2,500 pounds on the sun!).
As a matter of fact, both the dog and I both have gravitational fields! Since we are both bodies of mass we have a gravitational field which will pull things towards us. All bodies have a gravitational field. However, my mass is sooooo small that the gravitational field I have is miniscule. Something has to be very massive before it has a gravitational field that noticeably attracts another body.
So what’s the measurement for how much stuff you’re made of? Mass. Mass is basically a weightless measure of how much matter makes you, you. A hamster is made of a fairly small amount of stuff so she has a small mass. I am made of more stuff, so my mass is greater than the hamster’s. Your house is made of even more stuff so its mass is greater still.
So, here’s a question. If you are “weightless” in space, do you still have mass? Yes, the amount of stuff you’re made of is the same on Earth as it is in your space ship. Mass does not change but since weight is a measure for how much gravity is pulling on you, weight will change.
Did you notice that I put weightless in quotation marks? Wonder why?
Weightlessness is a myth! Believe it or not, one is never weightless. A person can be pretty close to weightless in very deep space but the astronauts in a space ship actually do have a bit of weight.
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The difference between weight and mass often trips up college students, so let’s straighten this out. The mass of an object is how much stuff something is made out of, and the weight is the force of gravity acting on it. Mass deals with how much stuff there is, and weight deals with the pull of the Earth. Mass will never change no matter where you put the object, unless you take a bite out of it or pile more stuff on top of it. The weight can change depending on where you place it, like on another planet.
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If you could stand on the Sun without being roasted, how much would you weigh? The gravitational pull is different for different objects. Let’s find out which celestial object you’d crack the pavement on, and which your lightweight toes would have to be careful about jumping on in case you leapt off the planet.
Weight is nothing more than a measure of how much gravity is pulling on you. Mass is a measure of how much stuff you’re made out of. Weight can change depending on the gravitational field you are standing in. Mass can only change if you lose an arm.
Materials
- Scale to weigh yourself
- Calculator
- Pencil
Units In the US system of units, both mass and weight are measured in “pounds” or “lb”. That’s a BIG problem, because mass isn’t the same as weight, so how could their units be the same? The answer is, the units are not the same, but they look very similar. The units for mass are kg (kilograms) or lbm (pronounced “pounds mass”) and the units for force are N (Newtons) or lbf (pronounced “pounds force”). The trouble comes in when we drop that third character and “lbf” or “lbm” becomes just plain “lb”. That’s the problem, and it’s a major headache for students to understand. Here’s the main thing I want you to remember: 1 lbm is NOT equal to 1 lbf. Here’s a video that will explain how you use both of these in a real world:
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Friction is the force between two objects in contact with one another when one object moves (or tries to move) across another on the surface. Friction is dependent on the types materials that are in contact with one another (rubber versus leather, for example), and how much pressure is put on the materials, and whether the surfaces are wet, dry, hot, cold… it’s really complicated. Friction happens due to the electromagnetic forces between two objects. Friction is not necessarily due to the roughness of the objects but rather to chemical bonds “sticking and slipping” over one another.
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Hovercraft transport people and their stuff across ice, grass, swamp, water, and land. Also known as the Air Cushioned Vehicle (ACV), these machines use air to greatly reduce the sliding friction between the bottom of the vehicle (the skirt) and the ground. This is a great example of how lubrication works – most people think of oil as the only way to reduce sliding friction, but gases work well if done right.
In this case, the readily-available air is shoved downward by the pressure inside of balloon. This air flows down through the nozzle and out the bottom, under the CD, lifting it slightly as it goes and creating a thin layer for the CD to float on.
Although this particular hovercraft only has a ‘hovering’ option, I’m sure you can quickly figure out how to add a ‘thruster’ to make it zoom down the table! (Hint – you will need to add a second balloon!)
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What if there’s a lot of friction? Have you ever felt that you need to give something a shove before it starts moving? You have to overcome static friction in order to experience kinetic friction. (Static friction is higher in magnitude than kinetic friction, generally speaking.)
The equation for determining the friction is: f = μ Fnormal, where μ = the coefficient of friction.
For kinetic friction: fkinetic = μk Fnormal, where μk = the coefficient of kinetic friction
For static friction: fstatic = μs Fnormal, where μs = the coefficient of kinetic friction
Scientists have to figure out μs and μk by doing experiments, and they compile that data in tables for others to look up when they need it. Here’s how you can do that very same experiment to determine the coefficient of friction between two surfaces:
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Now let’s talk about the other ever present force on this Earth, and that’s friction. Friction is the force between one object rubbing against another object. Friction is what makes things slow down.
Without friction things would just keep moving unless they hit something else. Without friction, you would not be able to walk. Your feet would have nothing to push against and they would just slide backward all the time like you’re doing the moon walk.
Friction is a very complicated interaction between pressure and the type of materials that are touching one another. Let’s do a couple of experiments to get the hang of what friction is.
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First Law of Motion: Objects in motion tend to stay in motion unless acted upon by an external force. Force is a push or a pull, like pulling a wagon or pushing a car. Gravity is a force that attracts things to one another. Gravity accelerates all things equally. Which means all things speed up the same amount as they fall.
Materials: ball
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Click here to go to next lesson on Newton’s Law of Motion in Detail.
Ok, sort of a silly experiment I admit. But here’s what we’re going for – there is an invisible force acting on you and the ball. As you will see in later lessons, things don’t change the way they are moving unless a force acts on them. When you jump, the force that we call gravity pulled you back to Earth. When you throw a ball, something invisible acted on the ball forcing it to slow down, turn around, and come back down. Without that force field, you and your ball would be heading out to space right now!
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Click here to go to next lesson on Inertia.
Ever wonder how magicians work their magic? This experiment is worthy of the stage with a little bit of practice on your end.
Here’s how this activity is laid out: First, watch the video below. Next, try it on your own. Make sure to send us your photos of your inventions here!
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Next time you watch a drag race, notice the wheels. Are they solid metal discs, or do they have holes drilled through the rims? I came up with this somewhat silly, but incredibly powerful quick science demonstration to show my 2nd year university students how one set of rims could really make a difference on the racetrack (with all other things being equal).
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Click here to go to next lesson on Introducing the Idea of Net Forces.
It is very rare, especially on Earth, to have an object that is experiencing force from only one direction. A bicycle rider has the force of air friction pushing against him. He has to fight against the friction between the gears and the wheels. He has gravity pulling down on him. His muscles are pushing and pulling inside him and so on and so on.
Even as you sit there, you have at least two forces pushing and pulling on you. The force of gravity is pulling you to the center of the Earth. The chair is pushing up on you so you don’t go to the center of the Earth. So with all these forces pushing and pulling, how do you keep track of them all? That’s where net force comes in.
The net force is when you add up all of the forces on something and see what direction the overall force pushes in. The word “net”, in this case, is like net worth or net income. It’s a mathematical concept of what is left after everything that applies is added and subtracted. The next activity will make this clearer.
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