These types of problems aren’t limited to airplanes, though. Have you ever gone in a boat and drifted off course? Here’s what was happening from a physics point of view:
Please login or register to read the rest of this content.
These types of boat problems usually ask for the following information to be calculated: what is the resultant velocity of the boat, how much time does it take to cross the river, and what distance does the boat drift off course due to the wind? Let’s practice this type of problem again so you really can get the hang of it.
Please login or register to read the rest of this content.
Where else might you encounter this type of problem in the real world? Air balloons! A hot air balloon is pretty much at the mercy of the winds, so it's easy to calculate the component forces and velocities to determine the path of travel. Let's try one...
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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!
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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.)
Please login or register to read the rest of this content.
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!).
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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:
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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:
Please login or register to read the rest of this content.
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:
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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?
Here’s what you need:
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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.
Here’s what you need:
Please login or register to read the rest of this content.
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…
Please login or register to read the rest of this content.
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:
Please login or register to read the rest of this content.
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…
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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:
Please login or register to read the rest of this content.
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.
Please login or register to read the rest of this content.
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!)
Here’s what you need:
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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:
Please login or register to read the rest of this content.
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.
Here’s what you need:
Please login or register to read the rest of this content.
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
Please login or register to read the rest of this content.
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!
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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!
Please login or register to read the rest of this content.
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).
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
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.
Here’s what you need:
Please login or register to read the rest of this content.
Click here to go to next lesson on Forces.
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I’ve included it here so you can participate and learn, too!
Discover how to detect magnetic fields, learn about the Earth’s 8 magnetic poles, and uncover the mysterious link between electricity and magnetism that marks one of the biggest discoveries of all science…ever.
Materials:
- Box of paperclips
- Two magnets (make sure one of them ceramic because we’re going to break it)
- Compass
- Hammer
- Nail
- Sandpaper or nail file
- D cell battery
- Rubber band
- Magnet Wire
Optional Materials if you want to make the Magnetic Rocket Ball Launcher:Four ½” (12mm) neodymium magnets
- Nine ½” (12 mm) ball bearings
- Toilet paper tube or paper towel tube
- Ruler with groove down the middle
- Eight strong rubber bands
- Scissors
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I’ve included it here so you can participate and learn, too!
We’re going to study electrons and static charge. Kids will build simple electrostatic motor to help them understand how like charges repel and opposites attract. After you’ve completed this teleclass, be sure to hop on over the teleclass in Robotics!
Electrons are strange and unusual little fellows. Strange things happen when too many or too few of the little fellows get together. Some things may be attracted to other things or some things may push other things away. Occasionally you may see a spark of light and sound. The light and sound may be quite small or may be as large as a bolt of lightning. When electrons gather, strange things happen. Those strange things are static electricity.
Please login or register to read the rest of this content.
We’re going to learn about kinematics, which is the words scientists use to explain the motion of objects. By learning about scalars, vectors, speed, velocity, acceleration, distance, and more, you’ll be able to not only accurately describe the motion of objects, but be able to predict their behavior. This is very important, whether you’re planning to land a spaceship on a moon, catapult a marshmallow in your mouth from across the room, or win a round of billiards.
Be sure to take out a notebook and copy down each example problem right along with me so you take good notes as you go along. It’s a totally different experience when you are actively involved by writing down and working through each problem rather than passively sitting back and watching.
Click here to start the first lesson in kinematics.
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I've included it here so you can participate and learn, too!
This class is all about Light Waves! Energy can take one of two forms: matter and light (called electromagnetic radiation). Light is energy in the form of either a particle or a wave that can travel through space and some kinds of matter, like glass.
We're going to investigate the wild world of the photon that has baffled scientists for over a century. We'll also do experiments in shattering laser beams, bending and twisting light, and also split light waves into rainbow shadows. Materials:
This class is all about Light Waves! Energy can take one of two forms: matter and light (called electromagnetic radiation). Light is energy in the form of either a particle or a wave that can travel through space and some kinds of matter, like glass.
We're going to investigate the wild world of the photon that has baffled scientists for over a century. We'll also do experiments in shattering laser beams, bending and twisting light, and also split light waves into rainbow shadows. Materials:
- laser pointer
- flashlight
- paper clip
- gummy bear (green and red)
- old CD
- paper clip
- rubber band
- pond water (just a little bit)
If you jump out of an airplane, how fast would you fall? What’s the greatest speed you would reach? In a moment, we’re going to find out, but first let’s take a look at objects that are allowed to fall under the influence of just gravity. There are two important things to keep in mind for free falling objects. First, the object doesn’t experience air resistance. Second, the acceleration of the object is a constant value of 9.8 m/s2 or 32.2 ft/s2.
Please login or register to read the rest of this content.
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?
Here’s what you need:
Please login or register to read the rest of this content.
Click here to go to next lesson on Velocity.
If acceleration is constant, is velocity also constant? Nope. The image at the top of this page shows that the object is speeding up every second by a certain rate, so velocity is not a constant value. The question is, can we figure out what the speed is at different intervals of time? Of course we can! Here’s how…
Please login or register to read the rest of this content.
Do you expect a curved or a straight line on a p-t graph for free falling objects? A straight line is the slope of the graph, which is also the velocity. A straight line would mean that the velocity is constant, we we already see from the experiment that it isn’t. So we can expect a curve on our p-t graph that looks like a downhill bunny slope… the object starts out slow, then increases speed so the slope will also increase in “steepness” as time goes on. If we indicate the positive direction as upwards, then the slope on the p-t graph will be negative.
Please login or register to read the rest of this content.
For constant acceleration, we can expect a straight line on our v-t graph to have a slope of 9.8 m/s2 in the negative quadrant of the graph, starting at the origin. The object started at rest, then finished with a large negative velocity, meaning that the object is speeding up in the downward direction. The constant negative slope means constant negative acceleration. Remember, that negative sign doesn’t mean it’s slowing down, but rather the minus sign indicates which direction the acceleration is happening in.
Please login or register to read the rest of this content.
If you jump out of an airplane, how fast would you fall? What's the greatest speed you would reach? Let's practice figuring it out without jumping out of a plane.
This experiment will help you get the concept of velocity by allowing you to measure the rate of fall of several objects. It's also a great experiment to record in your science journal.
First, you'll need to find your materials: Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
You have just taken in a nice bunch of information about the wild world of gravity. This next section is for advanced students, who want to go even deeper. There's a lot of great stuff here but there's a lot of math as well. If you're not a math person, feel free to pass this up. You'll still have a nice understanding of the concept. However, I'd recommend giving it a try. There are some fun things to do and if you're not careful, you might just end up enjoying it!
Here's what you need: Please login or register to read the rest of this content.
If I toss a ball horizontally at the exact same instant that I drop another one from my other hand, which one reaches the ground first? For this experiment, you need: Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
This experiment will help you get the concept of velocity by allowing you to measure the rate of fall of several objects. It's also a great experiment to record in your science journal.
First, you'll need to find your materials: Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
You have just taken in a nice bunch of information about the wild world of gravity. This next section is for advanced students, who want to go even deeper. There's a lot of great stuff here but there's a lot of math as well. If you're not a math person, feel free to pass this up. You'll still have a nice understanding of the concept. However, I'd recommend giving it a try. There are some fun things to do and if you're not careful, you might just end up enjoying it!
Here's what you need: Please login or register to read the rest of this content.
If I toss a ball horizontally at the exact same instant that I drop another one from my other hand, which one reaches the ground first? For this experiment, you need: Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
Click here to go to next lesson on Force and Mass.
We're going to learn more about why gravity accelerates all objects equally when we study Newton's Laws in the next section, where you'll discover how force is related to mass. Right now, here's another set of hints on solving physics problems...
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
The motion of objects can be described by words, with images, as well as with the language of math by using graphs, charts, and equations.
We've already learned about the p-t and v-t graphs in our experiments, and now it's time to figure out the kinematic equations that will describe the motion of objects by relating the time, distance, displacement, velocity, speed, and acceleration. They're a really handy set of four equations that you can use to figure out how fast you're moving in a swing, how far your car will skid, the height your rocket will reach, or how far your baseball will go.
Please login or register to read the rest of this content.
We've already learned about the p-t and v-t graphs in our experiments, and now it's time to figure out the kinematic equations that will describe the motion of objects by relating the time, distance, displacement, velocity, speed, and acceleration. They're a really handy set of four equations that you can use to figure out how fast you're moving in a swing, how far your car will skid, the height your rocket will reach, or how far your baseball will go.
Please login or register to read the rest of this content.
Once you get the hang of how to solve the four kinematic equations, you can put this together with your understanding of the v-t and p-t diagrams to make a more complete picture of the motion in your system. Remember how we learned that the slope of the line on a v-t graph is the acceleration of the object, and that you could use the area bounded by the axis and the slope to find the displacement? Now you’ve got two ways of figuring out the displacement, velocity, acceleration, and time in any problem. How can you use the two methods together to make you more efficient and effective at solving physics programs? Here’s how…
Please login or register to read the rest of this content.
Physics is your big chance to show off your inner artist by drawing what you see through a scientists eyes in a special way so others can understand your big ideas. We're going to practice making models in our mind of what's going on in the real world, and learning how to write it down on paper using the language of mathematics so you can communicate with others and work together designing your inventions and predicting what might happen next. All scientists, engineers, technicians, including folks like Feynman and Einstein, learned how to represent the real world on paper in a visual way using diagrams. (Although Nobel prize winner Dr. Richard Feynman got frustrated and invented his own diagrams, which we still use today in quantum mechanics.)
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
Graphs are used all over the field of physics, and the p-t and v-t graphs are the ones used most for moving objects, especially when describing the projectile motion of objects. With one peek at the graph, you can tell a lot about what's going on, which is one reason they are so useful. You don't have to pour over pages of equations to get a sense of what's going on with the experiment.
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
The position-time “p-t” graph is one that gets used a lot, and since it's axes are position and time, the slope of the line will give average velocity to describe the motion of an object. If the velocity is constant, then the slope is constant and you'll see a straight line (either uphill or downhill). If velocity is changing, you'll see a curved rather than straight line for the slope. A steeper line indicates larger velocity. An uphill slope means positive velocity, downhill indicates negative velocity. If the slope is downhill and curved, but it starts out like a skier on a bunny hill, then the negative velocity starts slow and moves fast as time goes on, which is a sign of negative acceleration (starting slow and speeding up). If the slope looks instead like starting at the top of a black diamond run, then the object starts with a high negative velocity but ends with a slower velocity, a indication of positive acceleration.
Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
The velocity-time “v-t” graphs are another common type of graph you'll run across that describe motion of an object. The shape and slope of the lines on the graph will tell you a lot about what's going on with the motion of the object, and here's how you decipher it: If the line is a straight, horizontal line, then the velocity stayed constant and there's no acceleration, like when you're driving on the freeway. Your car is moving at a steady 65 mph in a straight line.
However, if you're at a stoplight that just turned green, you're going to start changing your velocity by increasing your speed, giving you a positive acceleration. The graph will be a straight line starting at the origin and moving uphill. The slope of the line is positive, indicating your positive acceleration.
So can you tell if an object is moving in a positive or negative direction? Yes! A positive velocity means an object is moving in a positive direction, so if the line is in the positive region of the graph, you know it's traveling in a positive direction. By the same logic, if the slope is in the negative regions of the graph, the object is traveling in a negative direction. For slopes crossing the axis, the object is changing directions.
Can you figure out if an object is speeding up or slowing down? Yes again! Speeding up means that the magnitude of the velocity is increasing in value (the number only, ignoring the plus or minus sign), so if the line is moving away from the x-axis, it's speeding up. And if it's approaching the x-axis, it's slowing down.
Please login or register to read the rest of this content.
However, if you're at a stoplight that just turned green, you're going to start changing your velocity by increasing your speed, giving you a positive acceleration. The graph will be a straight line starting at the origin and moving uphill. The slope of the line is positive, indicating your positive acceleration.
So can you tell if an object is moving in a positive or negative direction? Yes! A positive velocity means an object is moving in a positive direction, so if the line is in the positive region of the graph, you know it's traveling in a positive direction. By the same logic, if the slope is in the negative regions of the graph, the object is traveling in a negative direction. For slopes crossing the axis, the object is changing directions.
Can you figure out if an object is speeding up or slowing down? Yes again! Speeding up means that the magnitude of the velocity is increasing in value (the number only, ignoring the plus or minus sign), so if the line is moving away from the x-axis, it's speeding up. And if it's approaching the x-axis, it's slowing down.
Please login or register to read the rest of this content.
This experiment is one of my favorites in this acceleration series, because it clearly shows you what acceleration looks like.
The materials you need is are:
- a hard, smooth ball (a golf ball, racket ball, pool ball, soccer ball, etc.)
- tape or chalk
- a slightly sloping driveway (you can also use a board for a ramp that's propped up on one end)
Grab a friend to help you out with this experiment - it's a lot easier with two people.
Are you ready to get started really discovering what acceleration is all about?
Here's what you do: Please login or register to read the rest of this content.
Please login or register to read the rest of this content.
Click here to go to next lesson on Describing Motion with Equations
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I’ve included it here so you can participate and learn, too!
We’re ready to deal with the topic you’ve all been waiting for! Join me as we find out what happens to stars that wander too close, how black holes collide, how we can detect super-massive black holes in the centers of galaxies, and wrestle with question: what’s down there, inside a black hole?
Materials:
- marble
- metal ball (like a ball bearing) or a magnetic marble
- strong magnet
- small bouncy ball
- tennis ball and/or basketball
- two balloons
- bowl
- 10 pennies
- saran wrap (or cup open a plastic shopping bag so it lays flat)
- aluminum foil (you’ll need to wrap inflated balloons with the foil, so make sure you have plenty of foil)
- scissors
Mechanics is the study of the motion of objects. This is a great place to start your studies in physics since it’s such a BIG idea. We’ll be learning the language, laws, concepts, and principles that explain the motion of objects. We’re going to learn about kinematics, which is the words scientists use to explain the motion of objects. By learning about scalars, vectors, speed, velocity, acceleration, distance, and more, you’ll be able to not only accurately describe the motion of objects, but be able to predict their behavior. This is very important, whether you’re planning to land a spaceship on a moon, catapult a marshmallow in your mouth from across the room, or win a round of billiards.
Please login or register to read the rest of this content.
We can describe how something moves with words, numbers, graphs, charts, or equations. To do that, we need to measure things with rulers and stopwatches. If I asked you how fast your car goes on the freeway, you could say fast or you could also say 55 mph. That 55 mph is a quantitative number that describes the motion of your car. The car travels 55 miles every hour. It’s also a scalar quantity, since you only mentioned the magnitude (how fast the car is going) and not it’s direction. A vector quantity is when you’d say 55 mph southeast. Vectors include a number and a direction. Scalars deal only with numbers.
Please login or register to read the rest of this content.
Distance and displacement sound the same, don’t they? But they’re just a little different from each other, and here’s how: distance is a scalar quantity, like 5 miles. Displacement is a vector quantity that describes how far out of place an object is, like going up and down the same flight of 8 steps. Your distance is 16 steps, but your displacement is zero, since you physically traveled 8 steps up and 8 steps down, but your total is zero since we also take into account the direction of travel, and everything cancels out.
Please login or register to read the rest of this content.
Have you noticed that scalar quantities ignore direction, and vector quantities take direction into account? Speed and velocity also sound the same, don’t they? But again, one is a vector and one is a scalar. Speed is the scalar quantity that describes how fast something is moving, like 100 mph. It’s the rate that something covers over a distance.
Rockets are fast, so they have high speeds, which means they cover large distances in a short amount of time. Compared to the speed of light, however, rockets are quite slow. (You always have to keep in mind what you are comparing to.) Velocity is a vector quantity that has a magnitude and a direction, like 100 mph north. It doesn’t matter if your speeding up or slowing down (we take that into account when we look at acceleration of an object). Velocity is the change in distance over a given time, or v = d / t. If a jet travels 600 miles in an hour, then it’s moving at 600 mph. A car going 25 miles in a half hour is moving at 50 mph. A snail crawling an inch every four minutes is moving at 0.25 inches per minute. You can mix up the units of distance and time to be whatever is most useful to you, whether it’s miles per hour, feet per minute, or meters per second. Most objects don’t just travel at one speed, however.
When you travel in a car, sometimes it’s on the freeway (65 mph), sometimes you’re at a stoplight (zero mph), sometimes you’re driving through the neighborhood (25 mph), and so forth. Your car has a lot of speed changes, so it’s useful to be able to calculate the average speed and average velocity of your car. It’s also useful to know the speed or velocity at a given instant in time, called your instantaneous speed or instantaneous velocity.
Please login or register to read the rest of this content.
Acceleration is defined as a change in velocity. In other words, it is a change in speed or a change in direction. It is how much time it takes something to go from one velocity to another. Remember that velocity is speed and direction. If you go straight ahead on your bike at a constant speed of 5 mph, you are not accelerating because neither your speed nor your direction is changing. Now, if you are stopped at a stop light and it turns green, you are accelerating as your speed increases from zero to 10 mph.
The word ‘acceleration’ is a little confusing, since sometimes people say someone is ‘accelerating’ when they really mean that they are ‘moving really fast’. Acceleration simply means changing speed or direction, not if they are going fast or not. Also, in physics we don’t use the word deceleration. We use positive and negative acceleration. So if you went from 10 mph to zero, you’d say that you have a negative acceleration, not deceleration.
Now what happens if you are in a car and it turns a corner at a constant speed of 15 mph? Is it accelerating or not? Well, the speed is not changing but its direction is, so it is indeed accelerating.Remember back when we talked about gravity? We learned that gravity accelerates things at 32 feet per second². Now this may make a little more sense. Gravity made something continue to increase in speed so that after one second of having the force of gravity pull on something, that something has reached a speed of 32 feet per second. When that thing started falling it was at 0 velocity, after a second it’s at 32 feet per second after 2 seconds it’s at 64 feet per second and so on.It’s the old formula v = gt or velocity equals the gravitational constant (32 ft/s²) times time.
Please login or register to read the rest of this content.
If something has an acceleration of 5 ft/s² how fast will it be going after 1 second…2 second…3 seconds? After one second it will be going 5 ft/s; after two seconds 10 ft/s; and after three seconds 15 ft/s. Again, it’s just like v = gt (v is velocity, g is the gravitational constant, t is time) but put the rate of acceleration of the object in place of g to get the formula v = at or velocity equals acceleration times time.
Once in a while, an object will change its velocity by the same amount at the same rate, and when this happens, it's called constant acceleration, since the velocity is changing by the same amount each time. Note that constant acceleration is not the same as constant velocity. If an object is changing speed, no matter how consistently it does it, it's still accelerating since it doesn't have a constant velocity. Objects in free fall motion, like a sky diver, experiences constant acceleration and may also eventually reach a constant velocity, but this is a very special case (we'll talk more about that later).
Average acceleration is found by dividing the average velocity (the difference between the initial and final velocity points) by the time lapsed between the two points. Acceleration is measured in a variety of units, but the most common are "meters per second squared" (m/s2) or "feet per second squared" (ft/s2).
Please login or register to read the rest of this content.
Download Student Worksheet & Exercises
Take a look at your marks. See how they get farther and farther apart as the ball continues to accelerate? Your ball was constantly increasing speed and as such, it was constantly accelerating. By the way, would it have mattered what the mass of the ball was that you used? No. Gravity accelerates all things equally. This fact is what Galileo was proving when he did this experiment. The the weight of the ball doesn’t matter but the size of the ball might. If you used a small ball and a large ball you would probably see differences due to friction and rotational inertia. The bigger the ball, the more slowly it begins rolling. The mass of the ball, however, does not matter.
Exercises
Is acceleration a scalar or a vector quantity? You could argue that it's both actually, but in physics it's usually a vector. This means that acceleration has a magnitude and a direction. The direction is either "+" or "-", depending on if an object is increasing or decreasing speed. Usually, objects that speed up have their acceleration vector in the same direction as the object is moving in. If it's slowing down, then the arrow flips to be in the opposite direction.
Once in a while, an object will change its velocity by the same amount at the same rate, and when this happens, it's called constant acceleration, since the velocity is changing by the same amount each time. Note that constant acceleration is not the same as constant velocity. If an object is changing speed, no matter how consistently it does it, it's still accelerating since it doesn't have a constant velocity. Objects in free fall motion, like a sky diver, experiences constant acceleration and may also eventually reach a constant velocity, but this is a very special case (we'll talk more about that later).
Average acceleration is found by dividing the average velocity (the difference between the initial and final velocity points) by the time lapsed between the two points. Acceleration is measured in a variety of units, but the most common are "meters per second squared" (m/s2) or "feet per second squared" (ft/s2).
Please login or register to read the rest of this content.
Download Student Worksheet & Exercises
Take a look at your marks. See how they get farther and farther apart as the ball continues to accelerate? Your ball was constantly increasing speed and as such, it was constantly accelerating. By the way, would it have mattered what the mass of the ball was that you used? No. Gravity accelerates all things equally. This fact is what Galileo was proving when he did this experiment. The the weight of the ball doesn’t matter but the size of the ball might. If you used a small ball and a large ball you would probably see differences due to friction and rotational inertia. The bigger the ball, the more slowly it begins rolling. The mass of the ball, however, does not matter.
Exercises
- Was the line a straight line?
- It should be close now, and the slope represents the acceleration it experienced going down the ramp. Calculate the slope of this line.
- What do you think would happen if you increased the height of the ramp?
- Knowing what you do about gravity, what is the highest acceleration it can reach?
For Advanced Students...
Please login or register to read the rest of this content.Is acceleration a scalar or a vector quantity? You could argue that it's both actually, but in physics it's usually a vector. This means that acceleration has a magnitude and a direction. The direction is either "+" or "-", depending on if an object is increasing or decreasing speed. Usually, objects that speed up have their acceleration vector in the same direction as the object is moving in. If it's slowing down, then the arrow flips to be in the opposite direction.
Click here to go to next lesson on Vector Diagrams
Chemistry is all about studying chemical reactions and the combinations of elements and molecules that combine to give new stuff. Chemical reactions can be written down as a balanced equation that shows how much of each molecule and compound are needed for that particular reaction. Here’s how you do it:
Please login or register to read the rest of this content.
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I've included it here so you can participate and learn, too
Our solar system includes rocky terrestrial planets (Mercury, Venus, Earth, and Mars), gas giants (Jupiter and Saturn), ice giants (Uranus and Neptune), and assorted chunks of ice and dust that make up various comets and asteroids.
Did you know you can take an intergalactic star tour without leaving your seat? To get you started on your astronomy adventure, I have a front-row seat for you in a planetarium-style star show. I usually give this presentation at sunset during my live workshops, so I inserted slides along with my talk so you could see the pictures better. This video below is long, so I highly recommend doing this with friends and a big bowl of popcorn. Ready?
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I’ve included it here so you can participate and learn, too!
Sound is a form of energy, and is caused by something vibrating. So what is moving to make sound energy?
Molecules. Molecules are vibrating back and forth at fairly high rates of speed, creating waves. Energy moves from place to place by waves. Sound energy moves by longitudinal waves (the waves that are like a slinky). The molecules vibrate back and forth, crashing into the molecules next to them, causing them to vibrate, and so on and so forth. All sounds come from vibrations.
Materials:
- 1 tongue-depressor size popsicle stick
- Three 3″ x 1/4″ rubber bands
- 2 index cards
- 3 feet of string (or yarn)
- scissors
- tape or hot glue
If you’re into magic shows, this is a good one to perform for an audience, because the solution goes from purple to pink to green to blue and back again!
Le Chatelier’s principle states that when the temperature is raised, an equilibrium will shift away from the side that contains energy. When temperature is lowered, the reaction shifts toward the side that contains the energy. That’s a little hard to understand, so that’s why there’s a really cool experiment that will show you exactly what we see happening with this principle.
Remember that exothermic reactions are chemical reactions that give off energy. In this experiment, this reaction is exothermic, which is going to be an important key in predicting which way the system will balance itself as it gets subjected to temperature changes.
Please login or register to read the rest of this content.
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I’ve included it here so you can participate and learn, too!
Soar, zoom, fly, twirl, and gyrate with these amazing hands-on classes which investigate the world of flight. Students created flying contraptions from paper airplanes and hangliders to kites! Topics we will cover include: air pressure, flight dynamics, and Bernoulli’s principle.
Materials:
- 5 sheets of 8.5×11” paper
- 2 index cards
- 2 straws
- 2 small paper clips
- Scissors, tape
- Optional: ping pong ball and a small funnel
We’re going to do an experiment where it will look like we can boil soda on command… but the truth is, it’s not really boiling in the first place! If you drink soda, save one for doing this experiment. Otherwise, get one that’s “diet” (without the sugar, it’s a lot easier to clean up).
Please login or register to read the rest of this content.
Molecules are the building blocks of matter.
You’ve probably heard that before, right? But that does it mean? What does a molecule look like? How big are they?
While you technically can measure the size of a molecule, despite the fact it’s usually too small to do even with a regular microscope, what you can’t do is see an image of the molecule itself. The reason has to do with the limits of nature and wavelengths of light, not because our technology isn’t there yet, or we’re not smart enough to figure it out. Scientists have to get creative about the ways they do about measuring something that isn’t possible to see with the eyes.
Here’s a cool experiment you can do that will approximate the size of a molecule. Here’s what you need:
Please login or register to read the rest of this content.
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I've included it here so you can participate and learn, too!
Blast your imagination with this super-popular class on rocketry! Kids learn about fin design, hybrid and solid-state rocketry, and how rockets make it into space without falling out of orbit. This class is taught by a real live rocket scientist (me!). We'll launch rockets during the class, too!
Please login or register to read the rest of this content.
This is a recording of a recent live teleclass I did with thousands of kids from all over the world. I've included it here so you can participate and learn, too!
We're going to cover energy and motion by building roller coasters and catapults! Kids build a working catapult while they learn about the physics of projectile motion and storing elastic potential energy. Let's discover the mysterious forces at work behind the thrill ride of the world’s most monstrous roller coasters, as we twist, turn, loop and corkscrew our way through g-forces, velocity, acceleration, and believe it or not, move through orbital mechanics, like satellites. We’ll also learn how to throw objects across the room in the name of science… called projectile motion. Are you ready for a fast and furious physics class?
This is a really neat game invented in 1967 by two mathematicians that was soon after published in Scientific American, where it caught fire with people all over the world. It’s a very simple game with a lot of interesting mathematics in it, and all you need are two people, a pencil, and paper.
Having trouble with your 6, 7, 8, and 9 multiplication tables? Sneak a peek at this nifty trick for multiplying single digits together. All you need is a set of hands and about ten minutes, and you'll be a whiz and multiplying with your hands.
Please login or register to read the rest of this content.
Cryptarithms are a puzzle where the digits are replaced by letters or symbols. When the numbers are replaced by letters of the alphabet and it spells something readable, it’s called Alphametics.
One day, my kid asked me how a calculator comes up with its answers. That's a great question, I thought. How does a calculator do math?
After thinking about it, I realized this was a great way to teach him about binary numbers. I am going to show you how to not only count in binary, but also help you understand the basis of all electronic devices by knowing this key element.
An electromagnet is a magnet you can turn on and off using electricity. By hooking up a coil of wire up to a battery, you will create an electromagnet. When you disconnect it, it turns back into a coil of wire. Since moving electrons cause a magnetic field, when connecting the two ends of your wire up to the battery, you caused the electrons in the wire to move through the wire in one direction. Since many electrons are moving in one direction, you get a magnetic field!
Please login or register to read the rest of this content.
Have you ever wondered why you just can’t just shine a flashlight through a lens and call it a laser? It’s because of the way a laser generates light in the first place.
The word LASER is an acronym for Light Amplification by Stimulated Emission of Radiation.
That’s a mouthful. Let's break it down.
Let's do an experiment that shows you how a laser is different from light from a flashlight by looking at the wavelengths that make up the light.
Laser light is collimated, meaning that it travels in parallel rays. Here’s a really cool experiment that will show you the difference between a non-collimated light, like from a flashlight and collimated light from a laser.
Ordinary light from a light bulb diverges as it travels. It spreads out and covers a larger and larger area the further out you go. A laser has little to no divergence, so we way that laser light is collimated.
Please login or register to read the rest of this content.
Lasers light is different from light from a flashlight in a couple of different ways. Laser light is monochromatic, meaning that it’s only one color.
Laser light is also coherent, which means that the light is all in synch with each other, like soldiers marching in step together. Since laser light is coherent, which means that all the light waves peaks and valleys line up. The dark areas are destructive interference, where the waves cancel each other out. The areas of brightness are constructive interference, where the light adds, or amplifies together. LED light is not coherent because the light waves are not in phase.
Please login or register to read the rest of this content.
Diffraction is how light bends as it passes through very narrow slits or around very thin objects like a hair. When light travels around a hair, two wave patterns form, and those waves interfere with each other constructively (they add together to form a bright region) or destructively (the cancel each other out and leave a dark spot).
This experiment looks at the light and dark areas of interference to determine the wavelength of a laser. You can do this for lasers that don’t have labels on them, so you really don’t know what wavelength they are!
Please login or register to read the rest of this content.
Gummy bears are a great way to bust one of the common misconceptions about light reflection. The misconception is this: most students think that color is a property of matter, for example if I place shiny red apple of a sheet of paper in the sun, you’ll see a red glow on the paper around the apple.
Where did the red light come from? Did the apple add color to the otherwise clear sunlight? No. That’s the problem. Well, actually that’s the idea that leads to big problems later on down the road. So let’s get this idea straightened out.
Please login or register to read the rest of this content.