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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Here are a couple of hints on how to solve problems involving Newton’s Laws of Motion:
Click here to go to next lesson on Sled Problem.
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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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Click here to go to next lesson on Reference Frames and the Truck Problem .
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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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Click here to go to next lesson on Rubber Tire Problem.
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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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Click here to go to next lesson on Using Newton’s Laws Together.
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This is a good example of Newton’s second and third laws in action and how to use both laws to help you solve a problem…
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Click here to go to next lesson on Chandelier Problem.
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Imagine this one is a chandelier hanging from the ceiling, and you want to find out if your cables are strong enough…
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Click here to go to next lesson on Breaking Loose.
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This is a great example of how to calculate forces for a static (no motion) system, and then what happens if you break loose and allow motion to happen. Note how the coordinate system was oriented to make the math a lot easier.
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Click here to go to next lesson on Pulley Problem.
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Pulley problems are common in physics, and in this example you will learn how to draw FBD with different coordinate systems that work with each drawing individually.
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Click here to go to next lesson on How to Gain and Lose Weight.
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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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Yay! You've completed the section! Now it's time for you to try solving these on your own:
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Yay! You've completed the section! Now it's time for you to try solving these on your own:
Download your Practice Problem set here!
[/am4show]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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2. Let it go.
3. Wheeeee!
4. Tie one end of the string to a chair.
5. Blow up the balloon (don’t tie it).
6. Tape a straw to it so that one end of the straw is at the front of the balloon and the other is at the nozzle of the balloon.
7. Thread the string through the straw and pull the string tight across your room.
8. Let go. With a little bit of work (unless you got it the first time) you should be able to get the balloon to shoot about ten feet along the string.
This is a great demonstration of Newton’s Third Law - the air inside the balloon shoots one direction, and the balloon rockets in the opposite direction. It’s also a good opportunity to bring up some science history. Many folks used to believe that it would be impossible for something to go to the moon because once something got into space there would be no air for the rocket engine to push against and so the rocket could not “push” itself forward.
In other words, those folks would have said that a balloon shoots along the string because the air coming out of the balloon pushes against the air in the room. The balloon gets pushed forward. You now know that that’s silly! What makes the balloon move forward is the mere action of the air moving backward. Every action has an equal and opposite reaction.
Tie a length of string through the room, having at least twenty feet of clear length. Thread two straws onto the string before securing the end. Punch the bottoms out of two foam coffee cups and tape parallel to the threaded straws.
Blow up balloons while they are inside the cups, so they extend out either end. When blowing up the second balloon, sandwich the untied end of the first inflated balloon between the second inflated balloon surface and inside the cup. Hold the second balloon’s end with a clothespin and release!
Download Student Worksheet & Exercises
You now have a great grasp of Newton’s three laws and with it you understand a good deal about the way matter moves about on Earth and in space. Take a look around. Everything that moves or is moved follows Newton’s Laws.
In the next unit, we will get into Newton’s Third Law a little deeper when we discuss momentum and conservation of momentum by whacking things together *HARD*. But more on this later...
Exercises
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
[am4show have='p8;p9;p12;p39;p109;p72;p92;p95;' guest_error='Guest error message' user_error='User error message' ] 1. Blow up the balloon (don’t tie it)
2. Let it go.
3. Wheeeee!
4. Tie one end of the string to a chair.
5. Blow up the balloon (don’t tie it).
6. Tape a straw to it so that one end of the straw is at the front of the balloon and the other is at the nozzle of the balloon.
7. Thread the string through the straw and pull the string tight across your room.
8. Let go. With a little bit of work (unless you got it the first time) you should be able to get the balloon to shoot about ten feet along the string.
This is a great demonstration of Newton’s Third Law - the air inside the balloon shoots one direction, and the balloon rockets in the opposite direction. It’s also a good opportunity to bring up some science history. Many folks used to believe that it would be impossible for something to go to the moon because once something got into space there would be no air for the rocket engine to push against and so the rocket could not “push” itself forward.
In other words, those folks would have said that a balloon shoots along the string because the air coming out of the balloon pushes against the air in the room. The balloon gets pushed forward. You now know that that’s silly! What makes the balloon move forward is the mere action of the air moving backward. Every action has an equal and opposite reaction.
Multi-Stage Balloon Rocket
You can create a multi-stage balloon rocket by adding a second balloon to the first just like you see here in the video:Tie a length of string through the room, having at least twenty feet of clear length. Thread two straws onto the string before securing the end. Punch the bottoms out of two foam coffee cups and tape parallel to the threaded straws.
Blow up balloons while they are inside the cups, so they extend out either end. When blowing up the second balloon, sandwich the untied end of the first inflated balloon between the second inflated balloon surface and inside the cup. Hold the second balloon’s end with a clothespin and release!
Balloon Racecar
Now let's use this information to create a balloon-powered racecar. You'll need the rest of the items outlined above to build your racecar. NOTE: in the video, we're using the popsicle sticks, but you can easily substitute in a sheet of stiff cardboard for the popsicle sticks. (Either one works great!)Download Student Worksheet & Exercises
You now have a great grasp of Newton’s three laws and with it you understand a good deal about the way matter moves about on Earth and in space. Take a look around. Everything that moves or is moved follows Newton’s Laws.
In the next unit, we will get into Newton’s Third Law a little deeper when we discuss momentum and conservation of momentum by whacking things together *HARD*. But more on this later...
Exercises
- What is Newton’s Third Law of Motion?
- Why does the balloon stop along the string?
Click here to go to next lesson on Third Law Explained .
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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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- toy car
- baking soda and vinegar (OR alka-seltzer and water)
- tape
- container with a tight-fitting lid (I don’t recommend glass containers… see if you can find a plastic one like a film canister or a mini-M&M container.)
There are two ways to do this experiment. You can either strap the bottle to the top of a toy car and use baking soda and vinegar, OR use effervescent tablets (like generic brands of alka seltzer) with this modified pop rocket (which you can strap to a toy car, or add wheels to the film canister itself by poking wooden skewers through milk jug lids for wheels and sliding the skewer through a straw to make the axle). Both work great, and you can even do both! This is an excellent demonstration in Newton’s Third Law, inertia, and how stuff works differently here than in outer space. Here’s what you do:
1. Strap the bottle to the top of the toy car or bus with the duct tape. You want the opening of the bottle to be at the back of the vehicle.
2. Put about one inch of vinegar into the bottle.
3. Shove a wad of paper towel as far into the neck of the bottle as you can. Make sure the wad is not too tight. It needs to stick into the neck of the bottle but not too tightly.
4. Pour baking soda into the neck of the bottle. Fill the bottle from the wad of paper all the way to the top of the bottle.
5. Now put the cork into the bottle fairly tightly. (Make sure the corkscrew didn’t go all the way through the cork, or you’ll have leakage issues.)
6. Now tap the whole contraption hard on the ground outside to force the wad of paper and the baking soda into the bottle.
7. Give the bottle a bit of a shake.
8. Set it down and watch. Do not stand behind the bus where the cork will shoot.
9. In 20 seconds or less, the cork should come popping off of the bottle.
What you should see is the cork firing off the bottle and going some 10 or 20 feet. The vehicle should also move forward a foot or two. This is Newton’s Third law in action. One force fired the cork in one direction. Another force, equal and opposite, moved the car in the other direction. Why did the car not go as far as the cork? The main reason is the car is far heavier then the cork. F=ma. The same force could accelerate the light cork a lot more than the heavier car.
Click here to go to next lesson on Inertia and the Second and Third Law.
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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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- film canister or other plastic container with a tight-fitting lid (like a mini-M&M container)
- alka-seltzer or generic effervescent tablets
- water
- outside area for launching
The record for these rockets is 28′ high. What do you think about that? Note – you can use anything that uses a chemical reaction… what about baking soda and vinegar? Baking powder? Lemon juice?
Important question: Does more water, tablets, or air space give you a higher flight?
Variations: Add foam fins and a foam nose (try a hobby or craft shop), hot glued into place. Foam doesn’t mind getting wet, but paper does. Put the fins on at an angle and watch the seltzer rocket spin as it flies skyward. You can also tip the rocket on its side and add wheels for a rocket car, stack rockets, for a multi-staging project, or strap three rockets together with tape and launch them at the same time! You can also try different containers using corks instead of lids.
More Variations: What other chemicals do you have around that also produces a gas during the chemical reaction? Chalk and vinegar, baking soda, baking powder, hydrogen peroxide, isopropyl alcohol, lemon juice, orange juice, and so on.
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Advanced students: Download your Pop Rockets Lab here.
Click here to go to next lesson on Forces Come in Pairs.
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The basic idea I want you to remember about Newton’s Third Law is that forces come in pairs. The wheels on a car spin, and as they do they grip the road and push the road back while at the same time the road pushes forwards on the wheel.
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Review for Forces and Newton’s Three Laws of Motion:
- Newton’s First Law is an object at rest tends to stay at rest and an object in motion tends to stay in motion unless a force acts against it.
- Inertia is a quality of an object that determines how difficult it is to get that object to move, to stop moving or to change directions.
- Force is a push or a pull on something.
- Newton’s Second Law is F=ma or Force equals mass x acceleration. In other words, the more mass something has and/or the faster it’s accelerating, the more force it will put on whatever it hits.
- The more mass something has, the more force that’s needed to get it to accelerate. a=F/m
- Things accelerate because there is a net force acting upon them.
- Things stop accelerating (maintain a constant velocity) because the forces acting on them have equaled out.
- Newton’s Third Law states that every action has an equal and opposite reaction.
Click here to go to next lesson on Applying Newton’s Laws.
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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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Click here to go to next lesson on Newton’s Second Law with Vector Addition.
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Here's another example of how to use Newton's second law along with vector addition of forces to figure out how to model an objects behavior in the real world:
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Newton's laws help us figure out how objects will behave when we apply forces that cause it to move. This is useful in order to be able to to land rockets on the moon, designing race cars that will accelerate faster around a turn on the highway, and so much more. But there's a problem... A lot of people can easily recite Newton's laws, but they either can't use them or understand how to apply them to the real world because they don't really know what they mean. There's evidence all around us about how the world works, but depending on what you focus on, you're going to stack different examples to support your beliefs about how the world works.
I can't tell you how many times students ask me how they can make a real light saber from Star Wars. They want to know how to make a light beam into a solid object that's tougher than steel. While I've never seen light do this in the real world, this is one of those unfortunate cases where too much media (like video games and movies) gets mixed in with how we see the world, and warps our understanding of the physical principles of the universe. There are thousands of movies and video games that use "cartoon physics" to get an action to appear on the screen a certain way, and when you watch that, it forms as a model in your mind about how the world works. If you've ever seen characters suspended in mid-air until they realize there's no ground beneath them and then they fall, or people plunging through solid walls at high speeds leaving an exact trace of their outline as they pass through it, or scaring someone which causes them to jump abnormally high in the air, you've seen this in action.
Now don't get me wrong - I love a good movie just as much as the next person, but when you're spending more time watching the world through a box, you're going to make a different model in your mind about how things behave than if you were spending time in the real world. It's not just media, though. One of the most common misconceptions we've already busted in a previous lesson is how an object needs a continuous force on it in order to continue it's motion. This one is totally not true - it's the absence of forces that makes continue its motion. One of the tasks of this physics course is to unravel these misconceptions and help you understand what's really going on by having you think for yourself, figure out what's going on, and evaluate your own thinking to see if it really makes sense.
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Newton's laws help us figure out how objects will behave when we apply forces that cause it to move. This is useful in order to be able to to land rockets on the moon, designing race cars that will accelerate faster around a turn on the highway, and so much more. But there's a problem... A lot of people can easily recite Newton's laws, but they either can't use them or understand how to apply them to the real world because they don't really know what they mean. There's evidence all around us about how the world works, but depending on what you focus on, you're going to stack different examples to support your beliefs about how the world works.
I can't tell you how many times students ask me how they can make a real light saber from Star Wars. They want to know how to make a light beam into a solid object that's tougher than steel. While I've never seen light do this in the real world, this is one of those unfortunate cases where too much media (like video games and movies) gets mixed in with how we see the world, and warps our understanding of the physical principles of the universe. There are thousands of movies and video games that use "cartoon physics" to get an action to appear on the screen a certain way, and when you watch that, it forms as a model in your mind about how the world works. If you've ever seen characters suspended in mid-air until they realize there's no ground beneath them and then they fall, or people plunging through solid walls at high speeds leaving an exact trace of their outline as they pass through it, or scaring someone which causes them to jump abnormally high in the air, you've seen this in action.
Now don't get me wrong - I love a good movie just as much as the next person, but when you're spending more time watching the world through a box, you're going to make a different model in your mind about how things behave than if you were spending time in the real world. It's not just media, though. One of the most common misconceptions we've already busted in a previous lesson is how an object needs a continuous force on it in order to continue it's motion. This one is totally not true - it's the absence of forces that makes continue its motion. One of the tasks of this physics course is to unravel these misconceptions and help you understand what's really going on by having you think for yourself, figure out what's going on, and evaluate your own thinking to see if it really makes sense.
Click here to go to next lesson on Vector Sums.
[/am4show]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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Here's a friction experiment you can do to really see what's going on in the real world with friction:
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Here's a friction experiment you can do to really see what's going on in the real world with friction:
Click here to go to next lesson on Air Resistance.
[/am4show]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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Click here to go to next lesson on Drag Force.
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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?
Here’s what you need:
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- ping pong ball
- golf ball
- you
Download Student Worksheet & Exercises
For this experiment, you’ll need:
Two objects of different weights. A marble and a golf ball, or a tennis ball and a penny for example.
A sharp eye
A partner
1. Take a careful look at both objects and make a prediction about which object will hit the ground first if they are dropped from the same height.
2. Test your prediction. Hold both objects at the same height. Make sure the bottom of both objects are the same distance from the floor.
3. Let them go as close to the same time as possible. Sometimes it’s helpful to roll them off a book.
4. Watch carefully. Which hits the ground first, the heavier one or the lighter one? Try it a couple of times and watch carefully. It will be a little easier for the person who isn’t dropping them to see what happens.
What you should see is that both objects hit the ground at the same time! Gravity accelerates both items equally and they hit the ground at the same time. Any two objects will do this, a brick and a Buick, a flower and a fish, a kumquat and a cow!
“But,” I hear you saying, “if I drop a feather and a flounder, the flounder will hit first every time!” Ok, you got me there. There is one thing that will change the results and that is air resistance.
The bigger, lighter and fluffier something is, the more air resistance can effect it and so it will fall more slowly. Air resistance is a type of friction which we will be talking about later. In fact, if you removed air resistance, a feather and a flounder would hit the ground at the same time!!!
Where can you remove air resistance? The moon!!! One of the Apollo missions actually did this (well, they didn’t use a flounder they used a hammer). An astronaut dropped a feather and a hammer at the same time and indeed, both fell at the same rate of speed and hit the surface of the moon at the same time.
Ask someone this question: Which will hit the ground first, if dropped from the same height, a bowling ball or a tennis ball? Most will say the bowling ball. In fact, if you asked yourself that question 5 minutes ago, would you have gotten it right? It’s conventional wisdom to think that the heavier object falls faster. Unfortunately, conventional wisdom isn’t always right. Gravity accelerates all things equally. In other words, gravity makes all things speed up or slow down at the same rate. We will be discussing acceleration more in a later lesson. If you would like more details on the math of this, it will be at the end of this lesson in the Deeper Lesson section.
This is a great example of why the scientific method is such a cool thing. Many, many years ago, there was a man of great knowledge and wisdom named Aristotle. Whatever he said, most people believed to be true. The trouble was he didn’t test everything that he said. One of his statements was that objects with greater weight fall faster than objects with less weight. Everyone believed that this was true.
Hundreds of years later Galileo came along and said “Ya know…that doesn’t seem to work that way. I’m going to test it” The story goes that Galileo grabbed a melon and an orange and went to the top of the Leaning Tower of Pisa. He said, “Look out below!” and dropped them! By doing that, he showed that objects fall at the same rate of speed no matter what their size.
It is true that it was Galileo who “proved” that gravity accelerates all things equally no matter what their weight, but there is no real evidence that he actually used the Leaning Tower of Pisa to do it.
Advanced Students: Download your Gravity Lab here.
Exercises
- What did you notice from your data? Did heavier or lighter objects fall faster? Did more massive objects or smaller objects fall faster? What characteristic seemed to matter the most?
- Is gravity a two-way force, like the attractive-repulsive forces of a magnet?
- If I were to drop a bowling ball and a balloon filled with a gas six times heavier than air (sulfur hexafluoride SF6) and inflated to the exact size of the bowling ball from my roof, which will strike the ground first?
Click here to go to next lesson on Two-body problems.
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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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Click here to go to next lesson on Newton’s Third Law of Motion.
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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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Click here to go to next lesson on Four Fundamental Forces.
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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.
Here’s what you need:
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- 2 Business card magnets (those thin flat magnets that are the size of business cards)
- Fingers
Download Student Worksheet & Exercises
1. Take two business card magnets and stick them together black side to black side. They should be together so that the pictures (or whatever’s on the magnets) are on the outside like two pieces of bread on a sandwich.
2. Now grab the sides of the magnets and drag one to the right and the other to the left so that they still are magnetically stuck together as they slide over one another.
Did you notice what happened as they slid across one another? They stuck and slipped didn’t they? This is a bit like friction. As two surfaces slide across one another, they chemically bond and then break apart. Bond and break, bond and break as they slide. The magnets magnetically “bonded” together and then broke apart as you slide them across on another. (The chemical bonds don’t work quite like the magnetic “bonds” but it gives a decent model of what’s happening.) There are many mysteries and discoveries to be uncovered with this concept. Go out and make some!
Exercises
- What is the difference between static and kinetic friction? Which one is always greater?
- Design an experiment where you can observe and/or measure the difference between static and kinetic friction.
Click here to go to next lesson on Types of Forces.
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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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Click here to go to next lesson on Resultant Force.
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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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Click here to go to next lesson on Practicing Resultant Forces.
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Now let’s take it a step further and look at how you’d analyze a ball being yanked on by two kids in different directions:
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Click here to go to next lesson on Vector Notation & Trigonometry.
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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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Click here to go to next lesson on Using Vectors and Trig in Physics Problems.
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Now let’s put the coordinate systems together with vector addition into this more realistic problem we’re going to run into with our study in physics:
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Click here to go to next lesson on Force fields.
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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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Click here to go to next lesson on Gravitational Fields & Weightlessness.
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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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Think about it for a second. If a space ship is orbiting the Earth what is it doing? It’s constantly falling! If it wasn’t moving forward at 10’s of thousands of miles an hour it would hit the Earth. It’s moving fast enough to fall around the curvature of the Earth as it falls but, indeed, it’s falling as the Earth’s gravity is pulling it to us.
Otherwise the ship would float out to space. So what is the astronaut doing? She’s falling too! The astronaut and the space ship are both falling to the Earth at the same rate of speed and so the astronaut feels weightless in space. If you were in an elevator and the cable snapped, you and the elevator would fall to the Earth at the same rate of speed. You’d feel weightless! (Don’t try this at home!)
Click here to go to next lesson on Weight & Mass.
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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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Click here to go to next lesson on Gravity on Other Planets.
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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
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Download Student Worksheet & Exercises
- We need to talk about the difference between weight and mass. In everyday language, weight and mass are used interchangeably, but scientists know better.
- Mass is how much stuff something is made out of. If you’re holding a bowling ball, you’ll notice that it’s hard to get started, and once it gets moving, it needs another push to get it to stop. If you leave the bowling ball on the floor, it stays put. Once you push it, it wants to stay moving. This “sluggishness” is called inertia. Mass is how much inertia an object has.
- Every object with mass also has a gravitational field, and is attracted to everything else that has mass. The amount of gravity something has depends on how far apart the objects are. When you step on a bathroom scale, you are reading your weight, or how much attraction is between you and the Earth.
- If you stepped on a scale in a spaceship that is parked from any planets, moons, black holes, or other objects, it would read zero. But is your mass zero? No way. You’re still made of the same stuff you were on Earth, so your mass is the same. But you’d have no weight.
- What is your weight on Earth? Let’s find out now.
- Step on the scale and read the number. Write it down.
- Now, what is your weight on the Moon? The correction factor is 0.17. So multiply your weight by 0.17 to find what the scale would read on the Moon.
- For example, if I weigh 100 pounds on Earth, then I’d weight only 17 pounds on the Moon. If the scale reads 10 kg on Earth, then it would read 1.7 kg on the Moon.
What’s Going On?
Weight is nothing more than a measure of how much gravity is pulling on you. This is why you can be “weightless” in space. You are still made of stuff, but there’s no gravity to pull on you so you have no weight. The larger a body is, the more gravitational pull (or in other words 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, the dog and I both have gravitational fields! Since we are both bodies of mass, we have a gravitational field which will pull things toward us. All bodies have a gravitational field. However, my mass is so 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.
Think about it for a second. If a space ship is orbiting the Earth, what is it doing? It’s constantly falling! If it wasn’t moving forward at tens of thousands of miles an hour it would hit the Earth. It’s moving fast enough to fall around the curvature of the Earth as it falls but, indeed, it’s falling as the Earth’s gravity is pulling it to us.
Otherwise the ship would float out to space. So what is the astronaut doing? She’s falling, too! The astronaut and the space ship are both falling to the Earth at the same rate of speed and so the astronaut feels weightless in space. If you were in an elevator and the cable snapped, you and the elevator would fall to the Earth at the same rate of speed. You’d feel weightless! (Don’t try this at home!)
Either now, or at some point in the future you may ask yourself this question, “How can gravity pull harder (put more force on some things, like bowling balls) and yet accelerate all things equally?” When we get into Newton’s laws in a few lessons, you’ll realize that doesn’t make any sense at all. More force equals more acceleration is basically Newton’s Second law.
Well, I don’t want to take too much time here since this is a little deeper then we need to go but I do feel some explanation is in order to avoid future confusion. The explanation for this is inertia. When we get to Newton’s First law we will discuss inertia. Inertia is basically how much force is needed to get something to move or stop moving.
Now, let’s get back to gravity and acceleration. Let’s take a look at a bowling ball and a golf ball. Gravity puts more force on the bowling ball than on the golf ball. So the bowling ball should accelerate faster since there’s more force on it. However, the bowling ball is heavier so it is harder to get it moving. Vice versa, the golf ball has less force pulling on it but it’s easier to get moving. Do you see it? The force and inertia thing equal out so that all things accelerate due to gravity at the same rate of speed!
Gravity had to be one of the first scientific discoveries. Whoever the first guy was to drop a rock on his foot, probably realized that things fall down! However, even though we have known about gravity for many years, it still remains one of the most elusive mysteries of science. At this point, nobody knows what makes things move toward a body of mass.
Why did the rock drop toward the Earth and on that guy’s foot? We still don’t know. We know that it does, but we don’t know what causes a gravitational attraction between objects. Gravity is also a very weak force. Compared to magnetic forces and electrostatic forces, the gravitational force is extremely weak. How come? No one knows. A large amount of amazing brain power is being used to discover these mysteries of gravity. Maybe it will be you who figures this out!
Exercises
- Of the following objects, which ones are attracted to one another by gravity?
a) Apple and Banana b) Beagle and Chihuahua c) Earth and You d) All of the above - True or False: Gravity accelerates all things differently
- True or False: Gravity pulls on all things differently
- If I drop a golf ball and a golf cart at the same time from the same height, which hits the ground first?
- There is a monkey hanging on the branch of a tree. A wildlife biologist wants to shoot a tranquilizer dart at the monkey to mark and study him. The biologist very carefully aims directly at the shoulder of the monkey and fires. However, the gun makes a loud enough noise that the monkey gets scared, lets go of the branch and falls directly downward. Does the dart hit where the biologist was aiming, or does it go higher or lower then he aimed? (This, by the way, is an old thought problem.)
Click here to go to next lesson on Force and Mass Units.
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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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Click here to go to next lesson on Friction.
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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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Click here to go to next lesson on Types of Friction.
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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!)
Here’s what you need:
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- 7-9″ balloon
- water bottle with a sport-top (see video for a visual – you can also use the top from liquid dish soap)
- old CD
- paper cup (or index card)
- thumbtack
- hot glue gun
- razor with adult help
There’s air surrounding us everywhere, all at the same pressure of 14.7 pounds per square inch (psi). You feel the same force on your skin whether you’re on the ceiling or the floor, under the bed or in the shower. An interesting thing happens when you change a pocket of air pressure – things start to move.
This difference in pressure causes movement that creates winds, tornadoes, airplanes to fly, and the air to rush out of a full balloon. An important thing to remember is that higher pressure always pushes stuff around. While lower pressure does not “pull,” we think of higher pressure as a “push”.
The stretchy balloon has a higher pressure inside than the surrounding air, and the air is allowed to escape out the nozzle which is attached to the water bottle cap through tiny holes (so the whole balloon doesn’t empty out all at once and flip over your hovercraft!) The steady stream of air flows under the CD and creates a cushion of air, raising the whole hovercraft up slightly… which makes the hovercraft easy to slide across a flat table.
Want to make an advanced model Hovercraft using wires, motors, and leftovers from lunch? Then click here.
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Advanced students: Download your Hovercraft Lab here.
Click here to go to next lesson on Static and Kinetic Friction.
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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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Click here to go to next lesson on Everyday Friction.
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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.
Here’s what you need:
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- About 5 different shoes
- A board, or a tray, or a large book at least 15 inches long and no more then 2 feet long.
- A ruler
- Paper
- Pencil
- A partner
Download Student Worksheet & Exercises
1. Put the board (or whatever you’re using) on the table.
2. Put the shoe on the board with the back of the shoe touching the back of the board.
3. Have a partner hold the ruler upright (so that the12 inches end is up and the 1 inch end is on the table) at the back of the board.
4. Slowly lift the back of the board leaving the front of the board on the table. (You’re making a ramp with the board). Eventually the shoe will begin to slide.
5. Stop moving the board when the shoe slides and measure the height that the back of the board was lifted to.
6. Look at the 5 shoes you chose and test them. Before you do, make a hypothesis for which shoe will have the most friction. Make a hypothesis. On a scale from 1 to 5 (or however many shoes you’re using) rate the shoes you picked. 1 is low friction and 5 would be high friction. Write the hypothesis next to a description of the shoes on a piece of paper. The greater the friction the higher the ramp has to be lifted. Test all of the shoes.
7. Analyze the shoes. Do the shoes with the most friction show any similarities? Are the bottoms made out of the same type of material? What about the shoes with very little friction?
Any surprises with which shoe had the most or least friction? Compare the shoe with the most friction and the shoe with the least friction. Do you notice anything? Usually, the shoe that has the most friction has more shoe surface touching the board then most of the other shoes.
Also, often the shoe with the least friction, has the least amount of shoe touching the board. Since friction is all about two things rubbing together, the more surface that’s rubbing, the more friction you get. A tire on you car should have treads but a race car tire will be absolutely flat with no treads at all. Why?
The race car doesn’t have to worry about rain or wetness so it wants every single bit of the tire to be touching the surface of the track. That way, there is as much friction as possible between the tire and the track. The tire on your car has treads to cut through mud and water to get to the nice firm road underneath. The treads actually give you less friction on a flat dry road!
Some of you might have used a skateboard shoe for your experiment. Notice, that the skateboard shoe has quite a flat bottom compared to most other shoes. This is because a skateboarder wants as much of his or her shoe to touch the board at all times.
Exercises
- What is friction?
- What is static friction?
- What is kinetic friction?
Click here to go to next lesson on Newton’s Second Law of Motion.
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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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What happens when you kick a soccer ball? The ‘kick’ is your external force. The ball will continue in a straight line as long as it can, until air drag, rolling resistance, and gravity cause it to stop.
Find out more about this key principle in Unit 1 and Unit 2.
Download Student Worksheet & Exercises
Exercises
- What is inertia?
- What is Newton’s First Law?
- Will a lighter or heavier race car with the same engine win a short-distance race (like the quarter-mile)?
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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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Here’s what you need:
- you
- the Earth (or any planet that’s convenient)
- a ball
Download Student Worksheet & Exercises
Here’s what you do:
1. Jump!
2. Carefully observe whether or not you come back down.
3. Take the ball and throw it up.
4. Again, watch carefully. Does it come down?
Gravity is probably the force field you are most familiar with. If you’ve ever dropped something on your foot you are painfully aware of this field! Even though we have known about this field for a looooong time, it still remains the most mysterious field of the four.
What we do know is that all bodies, from small atoms and molecules to gigantic stars, have a gravitational field. The more massive the body, the larger its gravitational field. As we said earlier, gravity is a very weak force, so a body really has to be quite massive (like moon or planet size) before it has much of a gravitational field. We also know that gravity fields are not choosy. They will attract anything to them.
All types of bodies, from poodles to Pluto, will will attract and be attracted to any other type of body. One of the strangest things about gravity is that it is only an attractive force. Gravity, as far as we can tell, only pulls things towards it. It does not push things away. All the other forces are both attractive (pull things towards them) and repulsive (push things away). (Gravity will be covered more deeply in a later lesson.)
Exercises
- What did you determine about gravity and how it affects the rate of falling?
- Did changing the object affect the rate of falling? Why or why not?
- Did changing the variable affect the rate of falling? Why or why not?
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Advanced students: Download your Gravitational Force Lab here.
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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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For this incredibly easy, super-amazing experiment, you’ll need to find:
- a plastic cup
- hard covered book
- toilet paper tube
- a ball that’s a bit smaller then the opening of the cup but larger than the opening of the toilet paper tube (you can also use an egg when you really get good at this trick!)
1. Put the cup on a table.
2. Put the book on top of the cup.
3. This is the tricky part. Put the toilet paper tube upright on the book, exactly over the cup.
4. Now put the ball on top of the toilet paper tube.
5. Check again to make sure the tube and the ball are exactly over the top of the cup.
6. Now, hit the book on the side so that it moves parallel to the table. You want the book to slide quickly between the cup and the tube.
7. If it works right, the book and the tube fly in the direction you hit the book. The ball however falls straight down and into the cup.
8. If it works say TAAA DAAA!
Download Student Worksheet & Exercises
This experiment is all about inertia. The force of your hand got the book moving. The friction between the book and the tube (since the tube is light it has little inertia and moves easily) causes the tube to move. The ball, which has a decent amount of weight, and as such a decent amount of inertia, is not effected much by the moving tube. The ball, thanks to gravity, falls straight down and, hopefully, into the cup. Remember the old magician’s trick of pulling the table cloth and leaving everything on the table? Now you know how it’s done. “Abra Inertia”!
So inertia is how hard it is to get an object to change its motion, and Newton’s First Law basically states that things don’t want to change their motion. Get the connection?
Exercises
- What are two different pairs of forces in this experiment?
- Explain where Newton’s Three Laws of motion are observed in this experiment.
Click here to go to next lesson on Inertia in Real Life.
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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).
[am4show have='p8;p9;p12;p39;p92;' guest_error='Guest error message' user_error='User error message' ] Here's what you need: two unopened cans of soup.
One should be clam chowder, the other chicken broth. Prop up a long table up on one end about 6-12" (you can experiment with the height later). You're going to roll them both down the table at the same time. Which do you expect to reach to bottom first - the chicken or the clam?
Not only do my college students need to figure out which one will win, they also have to tell me why. The secret is in how you calculate the inertia of each. Take a guess, then watch the video, do the activity, then read the explanation at the bottom (in that order) to get the most out of this experiment.
Download Student Worksheet & Exercises
Inertia is a quality of an object that determines how difficult it is to get that object to move, to stop moving, or to change directions. Generally, the heavier an object is, the more inertia it has. An elephant has more inertia than a mushroom. A sumo wrestler has more inertia than a baby. Inertia is made from the Latin word "inert," which means "lacking the ability to move". Inertia isn't something people have a grasp of, though, as it's something you must mathematically calculate from an object's mass and size.
When riding in a wagon that suddenly stops, you go flying out. Why? Because an object in motion tends to stay in motion unless acted upon by an outside force (Newton's First Law). When you hit the pavement, your motion is stopped by the sidewalk (external force). Seatbelts in a car are designed to keep you in place and counteract inertia if the car suddenly stops.
Did you know that Newton had help figuring out this First Law? Galileo rolled bronze balls down an wood ramp and recorded how far each rolled during a one-second interval to discover gravitational acceleration. And René Descartes (the great French philosopher) proposed three laws of nature, all of which Newton studied and use in his published work.
All of these thinkers (and many more) had to overcome the long-standing publicly-accepted theories that stemmed from the Greek philosopher Aristotle, which was no small feat in those days. Aristotle had completely rejected the idea of inertia (he also thought that weight affected falling objects, which we now know to be false). But remember that back then, people argued and talked about ideas rather than performing actual experiments to discover the truth about nature. They used words and reason to navigate through their world more than scientific experimentation.
Exercises
Inertia of a solid cylinder = 1/2 * (mr²) Inertia of a cylindrical shell = 1/12 * (mr²)
If the radius of the soup is 6.5 cm and the mass for both is the same (345 grams, or 0.345kg), and the mass of an empty can is 45 grams, then:
(CLAM) Inertia of a solid cylinder = 1/2 * (mr²) = 1/2 * (0.345kg)*(6.5cm)² = 7.29 kg cm² (CHICKEN) Inertia of a cylindrical shell = 1/12 * (mr²) = 1/12 * (0.045kg) *(6.5cm)² = 0.158 kg cm²
The numerical value for the solid cylinder is larger than the shell, which tells us that it has a greater resistance to rolling and will start to rotate much slower than the shell. This makes logical sense, as it's easier to get the shell alone to rotate than move a solid cylinder. Remember, you must use the mass of the cylinder shell (empty can) when calculating the chicken's inertia, as the broth itself does not rotate and this does not have a 'rolling resistance'!
Advanced students: Download your Chicken and Clam Lab here. [/am4show]
[am4show have='p8;p9;p12;p39;p92;' guest_error='Guest error message' user_error='User error message' ] Here's what you need: two unopened cans of soup.
One should be clam chowder, the other chicken broth. Prop up a long table up on one end about 6-12" (you can experiment with the height later). You're going to roll them both down the table at the same time. Which do you expect to reach to bottom first - the chicken or the clam?
Not only do my college students need to figure out which one will win, they also have to tell me why. The secret is in how you calculate the inertia of each. Take a guess, then watch the video, do the activity, then read the explanation at the bottom (in that order) to get the most out of this experiment.
Download Student Worksheet & Exercises
Inertia & History
Inertia is a quality of an object that determines how difficult it is to get that object to move, to stop moving, or to change directions. Generally, the heavier an object is, the more inertia it has. An elephant has more inertia than a mushroom. A sumo wrestler has more inertia than a baby. Inertia is made from the Latin word "inert," which means "lacking the ability to move". Inertia isn't something people have a grasp of, though, as it's something you must mathematically calculate from an object's mass and size.
When riding in a wagon that suddenly stops, you go flying out. Why? Because an object in motion tends to stay in motion unless acted upon by an outside force (Newton's First Law). When you hit the pavement, your motion is stopped by the sidewalk (external force). Seatbelts in a car are designed to keep you in place and counteract inertia if the car suddenly stops.
Did you know that Newton had help figuring out this First Law? Galileo rolled bronze balls down an wood ramp and recorded how far each rolled during a one-second interval to discover gravitational acceleration. And René Descartes (the great French philosopher) proposed three laws of nature, all of which Newton studied and use in his published work.
All of these thinkers (and many more) had to overcome the long-standing publicly-accepted theories that stemmed from the Greek philosopher Aristotle, which was no small feat in those days. Aristotle had completely rejected the idea of inertia (he also thought that weight affected falling objects, which we now know to be false). But remember that back then, people argued and talked about ideas rather than performing actual experiments to discover the truth about nature. They used words and reason to navigate through their world more than scientific experimentation.
Who wins, and why?
The chicken soup wins, for a very simple reason. Imagine that the cans are transparent, so you can see what does on inside the cans as they roll down the ramp. Which one has just the can rolling down the ramp, and which has the entire contents locked together as it rolls? The can of the chicken soup will rotate around the soup itself, while the clam chowder acts as a solid cylinder and rotates together. So the inertial mass of the clam is much greater than the inertial mass of the soup, even though the cans weigh the same.Exercises
- What is inertia (in your own words)?
- Why does one soup can always win?
For Advanced Students...
[/am4show][am4show have='p9;p39;' guest_error='Guest error message' user_error='User error message' ] So, how do you calculate the inertia of the chicken soup and the clam? Here's the mathematical formulas from the back of a Dynamics textbook (a typical course that all Engineers take during their 2nd year of college).Inertia of a solid cylinder = 1/2 * (mr²) Inertia of a cylindrical shell = 1/12 * (mr²)
If the radius of the soup is 6.5 cm and the mass for both is the same (345 grams, or 0.345kg), and the mass of an empty can is 45 grams, then:
(CLAM) Inertia of a solid cylinder = 1/2 * (mr²) = 1/2 * (0.345kg)*(6.5cm)² = 7.29 kg cm² (CHICKEN) Inertia of a cylindrical shell = 1/12 * (mr²) = 1/12 * (0.045kg) *(6.5cm)² = 0.158 kg cm²
The numerical value for the solid cylinder is larger than the shell, which tells us that it has a greater resistance to rolling and will start to rotate much slower than the shell. This makes logical sense, as it's easier to get the shell alone to rotate than move a solid cylinder. Remember, you must use the mass of the cylinder shell (empty can) when calculating the chicken's inertia, as the broth itself does not rotate and this does not have a 'rolling resistance'!
Advanced students: Download your Chicken and Clam Lab here. [/am4show]
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:
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- a rope (at least 3 feet long is good)
- a friend
- a sense of caution
(Be careful with this. Don’t pull too hard and please don’t let go of the rope. This is fun but you can get hurt if you get silly.)
Download Student Worksheet Exercises
1. You and your friend each grab an opposite end of the rope.
2. Both of you pull just a bit on the rope.
3. Have your friend pull a bit harder than you. Notice the direction that you both move.
4. Now you pull harder than your friend. Now which way do you go?
5. Lastly, both of you pull with the same strength on the rope. Even though you are both pulling, neither one of you should move.
In this experiment, there were always at least three forces pulling on the rope. Can you think of the three? They are you, your friend and gravity. You were pulling in one direction. Your friend was pulling in another direction and gravity was pulling down.
When one of you pulled harder (put more force on the rope) than the other person, there was a net force in the direction of the stronger pull. The rope and you guys went in that direction.
When both of you were pulling the same amount, there was an equal force pulling the rope one way and another equal force pulling the rope the other way. Since there were two equal forces acting in two opposite directions, the net force equaled zero, so there was no movement in either direction. No net force in this case means no movement.
As you’ll see when you learn about Newton’s second law, no net force means no acceleration.
Let’s take another look at the bicycle rider we talked about earlier. To make things easier, we’ll call him Billy. For Billy to speed up, he needs to win the tug of war between all of the forces involved in riding a bicycle. In other words, his muscles need to put more force on the forward motion of the bike than all of the forces of friction that are pushing against him.
If he wants to slow down, he needs to allow the forces of friction to win the tug of war so that they will cancel out his forward motion and slow down the bike. If he wants to ride at a steady speed, he wants the tug of war to be tied. His muscles need to exert the same amount of force pushing forward as the friction forces pulling in other directions.
Advanced Students: Download your Net Forces Lab here.
Exercises:
- For scenario 1, in which direction did you both move? Draw the free body diagram below
- For scenario 2, in which direction did you both move? Draw the free body diagram below
- For scenario 3, in which direction did you both move? Draw the free body diagram below
- For scenario 4, in which direction did the rope move? Draw the free body diagram below
- What was the same about question 1 and question 4? What was different?
- Even though the forces were less in question 1 than question 4, what was the net force for both?
- There were always at least 3 forces acting on the rope, what were they? Did you include the third force in your free body diagram?
- If the rope wasn’t moving, but you had only one force moving down, what does that tell you about the force you and your friend exerted?
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