Think of potential energy as the “could” energy. The battery “could” power the flashlight. The light “could” turn on. I “could” make a sound. That ball “could” fall off the wall. That candy bar “could” give me energy. Potential energy is the energy that something has that can be released. Objects can store energy as a result of their position.
In this experiment, you’re looking for two different things: first you’ll be dropping objects and making craters in a bowl of flour to see how energy is transformed from potential to kinetic, but you’ll also note that no matter how carefully you do the experiment, you’ll never get the same exact impact location twice.
To get started, you’ll need to gather your materials for this experiment. Here’s what you need:
What if you’re wanting to get a motor for a winch on the front of your jeep? What size motor do you need? Here’s how to calculate the minimum power so you don’t spend more cash than you need to for a motor that will still do the job. (Near the end of the video below, I’ll show you how to convert watts to horsepower.)
If you put an ice cube in a glass of lemonade, the ice cube melts. The thermal energy from your lemonade moves to the ice cube. Increasing the temperature of the ice cube and decreasing the temperature of your lemonade. The movement of thermal energy is called heat. The ice cube receives heat from your lemonade. Your lemonade gives heat to the ice cube. Heat can only move from an object of higher temperature to an object of lower temperature.
We’re going to learn about temperature, heat energy, atoms, matter, phase changes, and more in our unit on Thermodynamics as we build steam boats, fire-water balloons, hero engines, thermostats, Stirling engines, and more!
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Does this sound familiar? “I’m too cold. Get me a sweater!” “This soup’s too hot!” “Phew, I’m sweating.” “Yowtch, that pan handle burned me!” If you’ve ever made any of the above comments, then you were talking about thermal energy. Very clever of you, don’t you think? Thermal energy is basically the energy of the molecules moving inside something. The faster the molecules are moving, the more thermal energy that something has. The slower they are moving, the less thermal energy that something has.
I’m sure at some point you’ve said, “Wow, my internal thermal energy is way high! I need a liquid with a low thermal energy.” What… you’ve never said that?! Oh, wait. I bet it sounded like this when you said it, “Wow, I’m hot! I need a cool drink.”
Whenever we talk about the temperature of something we are talking about its thermal energy. Objects whose molecules are moving very quickly are said to have high thermal energy or high temperature. The higher the temperature, the faster the molecules are moving. You may remember that temperature is just a speedometer for molecules.
You may have asked yourself the question, “So, if everything is made of molecules, and these molecules are often speeding up and slowing down…what happens to the stuff these molecules are are made of if they change speed a lot? Will my kitchen table start vibrating across the room if the table somehow gets too hot?” No, it’s pretty unlikely that your table will begin jumping around the room, no matter how hot it gets. However, some interesting things do happen when molecules change speeds.
Temperature is a way of talking about, measuring, and comparing the thermal energy of objects. We use three different kinds of scales to measure temperature. Fahrenheit, Celsius, and Kelvin. (The fourth, Rankine, which is the absolute scale for Fahrenheit, is the one you’ll learn about in college.)
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Absolute zero is the theoretical temperature where molecules and atoms stop moving. They do not vibrate, jiggle or anything at absolute zero. In Celsius, absolute zero is -273 ° C. In Fahrenheit, absolute zero is -459°F (or 0°R). It doesn’t get colder than that!
As you can see, creating the temperature scales was really rather arbitrary: “I think 0° is when water freezes with salt.” “I think it’s just when water freezes.” “Oh, yea, well I think it’s when atoms stop!” Many of our measuring systems started rather arbitrarily and then, due to standardization over time, became the systems we use today. So that’s how temperature is measured, but what is temperature measuring?
Temperature is measuring thermal energy which is how fast the molecules in something are vibrating and moving. The higher the temperature something has, the faster the molecules are moving. Water at 34°F has molecules moving much more slowly than water at 150°F. Temperature is really a molecular speedometer. When something feels hot to you, the molecules in that something are moving very fast. When something feels cool to you, the molecules in that object aren’t moving quite so fast.
Have you ever wondered how an ice-cold glass of water gets waterdrops on the outside of the cup? Where does that water come from? Does it ease it’s way through the glass? Did someone come by and squirt the glass with water? No of course not.
You may have asked yourself the question, “So, if everything is made of molecules, and these molecules are often speeding up and slowing down… what happens to the stuff these molecules are made of if they change speed a lot? Will my kitchen table start vibrating across the room if the table somehow gets too hot?” No, it’s pretty unlikely that your table will begin jumping around the room, no matter how hot it gets. However, some interesting things do happen when molecules change speeds.
Is it warmer upstairs or downstairs? If you’re thinking warm air rises, then it’s got to be upstairs, right? If you’ve ever stood on a ladder inside your house and compared it to the temperature under the table, you’ve probably felt a difference.
So why is it cold on the mountain and warm in the valley? Leave it to a science teacher to throw in a wrench just when you think you’ve got it figured out. Let’s take a look at whether hot air or cold air takes up more space. Here’s what you do:
Making indoor rain clouds demonstrates the idea of temperature, the measure of how hot or cold something is. Here’s how to do it:
Take two clear glasses that fit snugly together when stacked. (Cylindrical glasses with straight sides work well.)
Fill one glass half-full with ice water and the other half-full with very hot water (definitely an adult job – and take care not to shatter the glass with the hot water!). Be sure to leave enough air space for the clouds to form in the hot glass.
This spooky idea takes almost no time, requires a dime and a bottle, and has the potential for creating quite a stir in your next magic show. The idea is basically this: when you place a coin on a bottle, it starts dancing around. But there’s more to this trick than meets the scientist’s eye.
Here’s how you do it:
Clouds are made of hundreds of billions of tiny little droplets of liquid water that have condensed onto particles of some sort of dust. Now let’s turn the heat down a bit more and see what happens. As the temperature drops and the molecules continue to slow, the bonds between the molecules can pull them together tighter and tighter.
At a substance’s boiling, freezing, etc, points, all of the substance must change to the next state. The condition of the bonds cannot remain the same at that temperature. For example, at 100° C water must change from a liquid to a gas. That is the speed limit of liquid water molecules. At 100° C the liquid bonds can no longer hold on and all the molecules convert to gas.
Believe it or not, the concept of heat is really a bit tricky. What we call heat in common language, is really not what heat is as far as physics goes.
Heat, in a way, doesn’t exist. Nothing has heat. Things can have a temperature. They can have a thermal energy but they can’t have heat. Heat is really the transfer of thermal energy. Or, in other words, the movement of thermal energy from one object to another.
If you’ve completed the Soaking Up Rays experiment, you might still be a bit baffled as to why there’s a difference between black and white. Here’s a great way to actually “see” radiation by using liquid crystal thermal sheets.
You’ll need to find a liquid crystal sheet that has a temperature range near body temperature (so it changes color when you warm it with your hands.)
Now let’s take explore how, even though heat can move from one object to another, it doesn’t necessarily mean that the temperature of the objects will change. You may ask, “What? Heat can move from one object to another without temperature changing one little bit?!?!” We’re going to take a look at one of the ways heat can move while the thermometer doesn’t.
When things change phase (change from solid to liquid or liquid to gas or… well, you get the picture) the temperature of those objects don’t change. If you were able to take the temperature of water as it changed from a solid (ice) to a liquid you would notice that the temperature of that piece of ice will stay at about 32° F until that piece of ice was completely melted. The temperature would not increase at all. Even if that ice was in an oven, the temperature would stay the same. Once all the solid ice had disappeared, then you would see the temperature of the puddle of water increase.
By the way, as the ice is melting, from where is heat being transferred? Heat is being transferred, by conduction, from the air.
One key distinction is that objects don’t contain heat, but they contain energy. Heat is the transfer of energy from from one object to another, or from one system to another, like a hot cup of coffee to the cool ambient air. Heat can change the temperature of objects when it transfers the energy. In the example with the coffee cup, it lowered the temperature of the coffee.
Imagine putting a sponge under a slowly running faucet. The sponge would continue to fill with water until it reached a certain point and then water started to drip from it. You could say that the sponge had a water capacity. It could hold so much water before it couldn’t hold any more and the water started dripping out.
Specific heat capacity is how much heat energy a mass of a material must absorb before it increases 1°C. It’s how much heat is needed to raise the temperature of 1 gram of the material. Heat Capacity is how much heat is required to raise the temperature. The units of heat capacity are J per Kelvin, whereas for specific heat capacity, the units are J per (gram-K).
Each material has its own specific heat. The higher a material’s specific heat, the more heat it must absorb before it increases in temperature. Water is unique in that it has a very large specific heat. Liquid water’s specific heat is over 4 which is very high. In comparison, granite is 0.8, aluminum is 0.9, rubbing alcohol is 2.4 and gold is 0.1.
To get the same amount of rubbing alcohol and liquid water to increase the same amount of temperature, you would need to pump about twice the amount of heat into the water. To get the same amount of gold and liquid water to increase the same amount of temperature, you would need to pump 40 times the amount of heat into the water!
If you’ve ever had a shot, you know how cold your arm feels when the nurse swipes it with a pad of alcohol. What happened there? Well, alcohol is a liquid with a fairly low boiling point. In other words, it goes from liquid to gas at a fairly low temperature. The heat from your body is more then enough to make the alcohol evaporate.
As the alcohol went from liquid to gas it sucked heat out of your body. For things to evaporate, they must suck in heat from their surroundings to change state. As the alcohol evaporated you felt cold where the alcohol was. This is because the alcohol was sucking the heat energy out of that part of your body (heat was being transferred by conduction) and causing that part of your body to decrease in temperature.
As things condense (go from gas to liquid state) the opposite happens. Things release heat as they change to a liquid state. The water gas that condenses on your mirror actually increases the temperature of that mirror. This is why steam can be quite dangerous. Not only is it hot to begin with, but if it condenses on your skin it releases even more heat which can give you severe burns. Objects absorb heat when they melt and evaporate/boil. Objects release heat when they freeze and condense.
Do you remember when I said that heat and temperature are two different things? Heat is energy – it is thermal energy. It can be transferred from one object to another by conduction, convection, and radiation. We’re now going to explore heat capacity and specific heat. Here’s what you do:
Heat can also change the state of matter. When an ice cube melts into a liquid puddle, it remains at the same temperature until the phase change is complete, and only then does the temperature begin to rise, even though heat was added throughout the entire process. The thermometer reading will stay on the same temperature reading until the ice is completely melted.
This experiment is for advanced students. Did you know that eating a single peanut will power your brain for 30 minutes? The energy in a peanut also produces a large amount of energy when burned in a flame, which can be used to boil water and measure energy.
Peanuts are part of the bean family, and actually grows underground (not from trees like almonds or walnuts). In addition to your lunchtime sandwich, peanuts are also used in woman’s cosmetics, certain plastics, paint dyes, and also when making nitroglycerin.
What makes up a peanut? Inside you’ll find a lot of fats (most of them unsaturated) and antioxidants (as much as found in berries). And more than half of all the peanuts Americans eat are produced in Alabama. We’re going to learn how to release the energy inside a peanut and how to measure it.
If you can remember thermostats before they went ‘digital’, then you may know about bi-metallic strips – a piece of material made from of two strips of different metals which expand at different rates as they are heated (usually steel and copper). The result is that the flat strip bends one way if heated, and in the opposite direction if cooled.
Normally, it takes serious skill and a red-hot torch to stick two different metals together, but here’s a homemade version of this concept that your kids can make using your freezer. Here what you do:
The triple point is where a molecule can be in all three states of matter at the exact same time, all in equilibrium. Imagine having a glass of liquid water happily together with both ice cubes and steam bubbles inside, forever! The ice would never melt, the liquid water would remain the same temperature, and the steam would bubble up. In order to do this, you have to get the pressure and temperature just right, and it’s different for every molecule.
The triple point of mercury happens at -38oF and 0.000000029 psi. For carbon dioxide, it’s 75psi and -70oF. So this isn’t something you can do with a modified bike pump and a refrigerator.
However, the triple point of water is 32oF and 0.089psi. The only place we’ve found this happening naturally (without any lab equipment) is on the surface of Mars.
Because of these numbers, we can get water to boil here on Earth while it stays at room temperature by changing the pressure using everyday materials. (If you have a vacuum pump, you can have the water boil at the freezing point of 32oF.)
Here’s what you need to do:
In our example of the ice and the lemonade, it would work like this. The lemonade has a higher temperature than the ice. (The molecules are moving faster than the ice molecules.)
The faster moving molecules of the lemonade would transfer heat to the ice causing the ice molecules to move faster (increase temperature) and eventually change from solid to liquid.
In turn, since the faster moving molecules of the lemonade moves energy (transfers heat) to the ice, they slow down. This causes the temperature of your drink to decrease and that is what makes your lemonade nice and cold. Heat can be transferred in three different ways: conduction, convection and radiation.
When something feels hot to you, the molecules in that something are moving very fast. When something feels cool to you, the molecules in that object aren’t moving quite so fast. Believe it or not, your body perceives how fast molecules are moving by how hot or cold something feels. Your body has a variety of antennae to detect energy. Your eyes perceive certain frequencies of electromagnetic waves as light. Your ears perceive certain frequencies of longitudinal waves as sound. Your skin, mouth and tongue can perceive thermal energy as hot or cold. What a magnificent energy sensing instrument you are!
Let’s find out how to watch the hot and cold currents in water. Here’s what you need to do:
Every time I’m served a hot bowl of soup or a cup of coffee with cream I love to sit and watch the convection currents. You may look a little silly staring at your soup but give it a try sometime!
Convection is a little more difficult to understand than conduction. Heat is transferred by convection by moving currents of a gas or a liquid. Hot air rises and cold air sinks. It turns out, that hot liquid rises and cold liquid sinks as well.
Room heaters generally work by convection. The heater heats up the air next to it which makes the air rise. As the air rises it pulls more air in to take its place which then heats up that air and makes it rise as well. As the air get close to the ceiling it may cool. The cooler air sinks to the ground and gets pulled back near the heat source. There it heats up again and rises back up.
This movement of heating and cooling air is convection and it can eventually heat an entire room or a pot of soup. This experiment should allow you to see convection currents.
Heat is transferred by radiation through electromagnetic waves. Remember, when we talked about waves and energy? Well, heat can be transferred by electromagnetic waves. Energy is vibrating particles that can move by waves over distances right? Well, if those vibrating particles hit something and cause those particles to vibrate (causing them to move faster/increasing their temperature) then heat is being transferred by waves. The type of electromagnetic waves that transfer heat are infra-red waves. The Sun transfers heat to the Earth through radiation.
If you hold your hand near (not touching) an incandescent light bulb until you can feel heat on your hand, you’ll be able to understand how light can travel like a wave. This type of heat transfer is called radiation.
Now don’t panic. This is not a bad kind of radiation like you get from x-rays. It’s infra-red radiation. Heat was transferred from the light bulb to your hand. The energy from the light bulb resonated the molecules in your hand. (Remember resonance?) Since the molecules in your hand are now moving faster, they have increased in temperature. Heat has been transferred! In fact, an incandescent light bulb gives off more energy in heat then it does in light. They are not very energy efficient.
Now, if it’s a hot sunny day outside, are you better off wearing a black or white shirt if you want to stay cool? This experiment will help you figure this out:
You can’t get through a science or engineering degree without having performed a calorimetry lab. A calorimetry experiment is made of of inexpensive equipment (it only uses a coffee cup and a thermometer) and the calculations needed to do the experiment are pretty easy, so you can already tell that teachers are going to like them. They are useful in figuring out the specific heat capacity and the heat of fucion or dissolution of an unknown substance (usually a lump of metal). Here’s how to make a coffee cup calorimeter and do the calculations:
The Drinking Bird is a classic science toy that dips its head up and down into a glass of water. It’s filled with a liquid called methylene chloride, and the head is covered with red felt that gets wet when it drinks. But how does it work? Is it perpetual motion?
Let’s take a look at what’s going on with the bird, why it works, and how we’re going to modify it so it can run on its own without using any water at all!
There are lots of different kids of heat engines, from stirling engines to big jet turbines to the engine in your car. They all use clever ways to convert a temperature difference into motion.
Remember that the molecules in steam move around a lot faster than in an ice cube. So when we stick hot steam in a container, we can blow off the lid (used with pistons in a steam engine). or we can put a fan blade in hot steam, and since the molecules move around a lot, they start bouncing off the blade and cause it to rotate (as in a turbine). Or we can seal up hot steam in a container and punch a tiny hole out one end (to get a rocket).
One of the first heat engines was dreamed up by Hero of Alexandria called the aeolipile. The steam is enclosed in a vessel and allowed to jet out two (or more) pipes. Although we’re not sure if his invention ever made it off the drawing board, we do know how to make one for pure educational (and entertainment) purposes. Are you ready to have fun?
Here’s what you do:
This project is for advanced students.This Stirling Engine project is a very advanced project that requires skill, patience, and troubleshooting persistence in order to work right. Find yourself a seasoned Do-It-Yourself type of adult (someone who loves to fix things or tinker in the garage) before you start working on this project, or you’ll go crazy with nit-picky things that will keep the engine from operating correctly. This makes an excellent project for a weekend.
Developed in 1810s, this engine was widely used because it was quiet and could use almost anything as a heat source. This kind of heat engine squishes and expands air to do mechanical work. There’s a heat source (the candle) that adds energy to your system, and the result is your shaft spins (CD).
This engine converts the expansion and compression of gases into something that moves (the piston) and rotates (the crankshaft). Your car engine uses internal combustion to generate the expansion and compression cycles, whereas this heat engine has an external heat source.
This experiment is great for chemistry students learning about Charles’s Law, which is also known as the Law of Volumes, which describes how gases tend to expand when they are heated and can be mathematically written like this:
where V = volume, and T = temperature. So as temperature increases, volume also increases. In the experiment you’re about to do, you will see how heating the air causes the diaphragm to expand which turns the crank.
Momentum can be defined as inertia in motion. Something must be moving to have momentum. Momentum is how hard it is to get something to stop or to change directions. A moving train has a whole lot of momentum. A moving ping pong ball does not. You can easily stop a ping pong ball, even at high speeds. It is difficult, however, to stop a train even at low speeds.
Mathematically, momentum is mass times velocity, or p = mv.
Momentum is a vector quantity, because it’s based on velocity, so you’ll expect to have a number and a direction in your answer for momentum questions. The heavier something is and/or the faster it’s moving the more momentum it has. The more momentum something has, the more force it takes to get it to change velocity and the more force it can apply if it hits something.
Think about baseball. When you hit a baseball, do you just smack it with the bat or do you follow through with the swing? You follow through right? Do you see how impulse relates to your baseball swing? If you follow through with your swing, the bat stays in contact with the ball for a longer period of time. This causes the ball to go farther. Follow through is important in golf, bowling, tennis and many sports for the same reason. The longer the force is imparted, the farther and faster your ball will go.
Ok, let’s add impulse and momentum together and see what we get. Impulse changes momentum. If an object puts an impulse on another object, the momentum of both objects will change. If you continue to push on your stalled car, you will change the momentum of the car right? If you are riding your bike while not paying any attention and crash into the back of a parked car, you will put an impulse on the car and you and the car’s momentum will change. (As a kid, I did this pretty often. That’s what you get when you ride and wonder at the same time. Believe me when I tell you that my momentum changed a lot more than the car’s did!!)
In fact, there is a mathematical formula about this impulse and momentum thing. Impulse = change in momentum or Ft = change in mv. Force x time = mass x velocity. Does that sound familiar to anyone? It’s awfully similar to Newton’s second law (F=ma) isn’t it? In fact it’s the same thing: F t = m v
Now if we divide both sides by “t” we get F = mv / t.
Another way to say v is d/t (distance over time). So now we have F = m (d/t) / t. Those two “t’s” together are the same as t2 and d/t2 is “a” (acceleration). So what we have now is F = ma!
Here is a quick experiment… first, find a wall. Then hit it with your bare fist. (Take it easy, just hit it with enough force that you feel the impact.) Now put a pillow in front of the wall and hit it with about the same force as you hit it before. With the pillow in front of the wall, you can hit it a little harder if you like but again, don’t go nuts!
What did the pillow do? It slowed the time of impact. Remember our formula Ft = mv. When the momentum of your moving fist struck the wall directly, the momentum was cut to zero instantly and so you felt enough force to hurt a bit. When the pillow was in the way it took longer for your momentum to come to zero. So you could hit the pillow fairly hard without feeling much force. Basically a bike helmet is like a pillow for you head. It slows the time of impact, so when you fall off your bike, there is much less force on your head. Just be glad your mom doesn’t make you wear a pillow on your head!
So let’s go back to momentum for a minute. Momentum is inertia in motion. It is how much force it takes to get something to slow down or change direction. One more concept I’d like to give you this month, is conservation of momentum. This is basically momentum equals momentum or mathematically mv = mv. (Momentum is mass times velocity.) When objects collide, the momentum that both objects have after the collision, is equal to the amount of momentum the objects had before the collision. Let’s take a look at this with this experiment.
Second Law of Motion: Momentum is conserved. Momentum can be defined as mass in motion. Something must be moving to have momentum. Momentum is how hard it is to get something to stop or to change directions. A moving train has a whole lot of momentum. A moving ping pong ball does not. You can easily stop a ping pong ball, even at high speeds. It is difficult, however, to stop a train even at low speeds.
Materials: garden hose connected to a water faucet
A rebound is a special kind of collision where objects bounce off each other instead of sticking to each other. There’s a change in the direction and a speed change.
Imagine a tennis ball striking a brick wall. The ball initially has a sped of 10 m/s, and after it hits the wall, it bounces back in the opposite direction at half the speed. What is the velocity change? It’s 10+5 m.s or 15 m/s.
Would the acceleration be greater or less than a ball that rebounds with a speed of 8 m/s? (Greater, since acceleration depends on velocity change, and the change in velocity for the second throw is 12 m.s). Which has the greatest momentum change? (The first case, since momentum change depends on velocity change.)
Sometimes an object will have the same (or nearly the same) speed as it had before impact, and these are called elastic collisions. These kinds of collisions also have the same kinetic energy and same momentum before and after the collision.
The Third Law of Motion shows up in collisions between objects. When two objects hit each other, they experience forces of the same magnitude but in opposite directions at impact. Those forces cause one object to speed up and the other to slow down. Even though the forces between the two objects are equal in magnitude, their accelerations are not.
Newton’s Second Law of Motion states that acceleration depends on force and mass, which means if you smack a ping pong ball with a bowling ball, one is going to have a higher acceleration than the other after the collision.
Golfers and baseball players use this principle to drive the ball far from their collision point by swinging the club or bat at high speeds, and even though the ball and bat experience the same force (in magnitude) at impact, the acceleration of the ball is much higher than the bat because the ball has a much lower mass. If you’re playing pool, then you can expect the billiard balls to experience the same accelerations after impact since the balls are all the same mass.
The Conservation of Momentum tells us that the total momentum of a system (a set of objects) is a constant value that doesn’t change. The total momentum of two objects before the collision is equal to the total mo momentum of the two after the collision. The momentum lost by one object is gained by the other. You can think about momentum as money being exchanged between two people. If each person has $20, and one person gives the other $5, the money transfers from one person to the other. The money lost by the first person is gained by the other, but the total amount of money is the same before and after the transaction ($40).
Particles that move close to the speed of light have a different equation for momentum in order for momentum to be conserved using Einstein’s relativistic equations. The speeds of large objects like baseballs, bullets, and satellites are so much less than the speed of light so we can use Newton’s equations for it. If you’re studying electrons and other subatomic particles, you must use equations from special relativity.
Sometimes it’s easiest to solve the problem by shrinking all the objects down to tiny particles. But in order to do that, you have to account for how lumpy and heavy (or light) your object. A baseball bat doesn’t balance in the exact middle of the bat. You have to account for the fact that the grip is skinnier than the end you hit with. But how would you figure that out? Here’s how…
If a particle moves in only one dimension, like a train on as straight track, it’s easy to answer the question about where it is because there’s only one component to it: “13m North” or “-3.6 feet.” It’s a single number with units and a positive or negative sign… that’s it. Pretty simple, right?
Well, the truth is that most objects move in two or three dimensions, and so we need more information to tell us where that object is, so we use vectors. We’re going to focus on objects moving in a two dimensional plane.
We’re going to study particles (or projectiles) that move in two dimensions. This can be a cannon ball after being fired, a baseball after being thrown, a golf ball after being hit, a soccer ball after being kicked, or any other situation you can think of where an object is under the influence of only gravity after the initial force applied to move the object. (Usually we ignore wind resistance when we do these types of problems.)
The FBD of projectiles is simply a downward pointing arrow to indicate the weight. If it looks strange to have a force not in the direction of the object’s travel path, just remember that a force isn’t needed to sustain motion… it’s actually the opposite! Objects stop moving because of the forces applied to it. The FBD are always a snapshot of the forces acting on the object in that moment. The object can be moving in one direction and the force acting in another.
A projectile is a particle that is only experiencing gravity, and in most cases, gravity is only acting in one direction. Gravity doesn’t influence the horizontal motion (if we accounted for air resistance, then there would be a force in this direction as well), only the vertical motion. That’s why the ball falls to the ground when you throw it.
This means that a bullet fired horizontally from a gun experiences a constant horizontal velocity and a downward vertical acceleration. A bullet fired from a gun pointed up at a 45 degree angle also experiences a constant horizontal velocity and a downward vertical acceleration. A bullet fired from a gun in outer space away from any gravitational influences would travel up at a 45 degree path away from the gun and experience constant horizontal and vertical velocity.
Now let’s do a set of physics problems so you can really see how to solve these. The first one shows you how to not only calculate an angle buried in a trig function, but also that you don’t need fancy equations to solve a problem and that you really have to understand what the problem is asking for, so you don’t waste time calculating stuff you don’t need.
This problem will show you how a soccer ball can also be a projectile, and how by knowing a couple of simple things, you can find out everything you need about the problem, including how far and how high the ball traveled in addition to its time of flight.
This is a simple, fun, and sneaky way of throwing tiny objects. It’s from one of our spy-kit projects. Just remember, keep it under-cover. Here’s what you need:
Okay now, back to work! Here’s a neat problem involving a pirate ship and a cannon ball. I seriously doubt pirates would be able to calculate this kind of problem when being fired at by a fortress, but you might have a captain that had a good sense based on experience of how far and fast that cannon ball could travel.
When you drop a ball, it falls 16 feet the first second you release it. If you throw the ball horizontally, it will also fall 16 feet in the first second, even though it is moving horizontally… it moves both away from you and down toward the ground. Think about a bullet shot horizontally. It travels a lot faster than you can throw (about 2,000 feet each second). But it will still fall 16 feet during that first second. Gravity pulls on all objects (like the ball and the bullet) the same way, no matter how fast they go.
What if you shoot the bullet faster and faster? Gravity will still pull it down 16 feet during the first second, but remember that the surface of the Earth is round. Can you imagine how fast we’d need to shoot the bullet so that when the bullet falls 16 feet in one second, the Earth curves away from the bullet at the same rate of 16 feet each second?
Answer: that bullet needs to travel nearly 5 miles per second. (This is also how satellites stay in orbit – going just fast enough to keep from falling inward and not too fast that they fly out of orbit.)
Catapults are a nifty way to fire things both vertically and horizontally, so you can get a better feel for how objects fly through the air. Notice when you launch how the balls always fall at the same rate – about 16 feet in the first second. What about the energy involved?
When you fire a ball through the air, it moves both vertically and horizontally (up and out). When you toss it upwards, you store the (moving) kinetic energy as potential energy, which transfers back to kinetic when it comes whizzing back down. If you throw it only outwards, the energy is completely lost due to friction.
The higher you pitch a ball upwards, the more energy you store in it. Instead of breaking our arms trying to toss balls into the air, let’s make a simple machine that will do it for us. This catapult uses elastic kinetic energy stored in the rubber band to launch the ball skyward.
Since you've worked so hard, I thought you'd enjoy making a marshmallow launcher just for fun. You can calculate the horizontal and vertical acceleration based on the time of flight, you can also figure out the initial speed based on how far it went, or you can just make it and have fun with it. Here it is:So now let’s look ahead and sneak a peek into your future. Are you nervous about taking Calculus? Or if you have, have you wondered what Calculus could possibly be useful for? Here’s a two part video that shows you what Calculus is (and will even have you doing it before the end of the second video!) and how it’s used all the time in physics. Sir Isaac Newton was so frustrated that he couldn’t solve his physics problems with the math that was already developed at that time (algebra) that he set them aside to invent a branch of mathematics that could support his work in science, and that’s where Calculus came from. Here’s how we use it today in physics…
This experiment is for Advanced Students. For ages, people have been hurling rocks, sticks, and other objects through the air. The trebuchet came around during the Middle Ages as a way to break through the massive defenses of castles and cities. It’s basically a gigantic sling that uses a lever arm to quickly speed up the rocks before letting go. A trebuchet is typically more accurate than a catapult, and won’t knock your kid’s teeth out while they try to load it.
Trebuchets are really levers in action. You’ll find a fulcrum carefully positioned so that a small motion near the weight transforms into a huge swinging motion near the sling. Some mis-named trebuchets are really ‘torsion engines’, and you can tell the difference because the torsion engine uses the energy stored in twisted rope or twine (or animal sinew) to launch objects, whereas true trebuchets use heavy counterweights.
Vectors are different from scalar numbers because they also include information about direction. Velocity, acceleration, force, and displacement are all vectors. Speed, time, and mass are all scalar quantities. Acceleration can be either a scalar or a vector, although in physics it’s usually considered a vector. For example, a car traveling at 45 mph is a speed, whereas a car traveling 45 mph NW is a vector. When you draw a vector, it’s an arrow that has a head and a tail, where the head points in the direction the force is pulling or the object is moving.
The coordinate system you use can be a compass (north, south, east and west) which is good for problems involving maps and geography, rectangular coordinates (x and y axes) which is good for most problems with objects traveling in two directions, or polar coordinates (radius and angle) which is good for objects that spin or rotate.
We have to get really good at vectors and modeling real world problems down on paper with them, because that’s how we’ll break things down to solve for our answers. If you’re already comfortable with vectors, feel free to skip ahead to the next lesson. If you find you need to brush up or practice a little more, this section is for you.
A resultant is the vector sum of all of the vectors, usually force vectors. You can’t just add the numbers (magnitudes) together! You have to account for the direction that you’re pushing the box in. Here’s what you need to know about vector diagrams and how to add vectors together:
deals with problems where one object moves with respect to another. For example, an airplane might be traveling at 300 knots according to its airspeed indicator, but since it has a 20 knot headwind, the speed you see the airplane traveling at is actually 280 knots. You’ve seen this in action if you’ve ever noticed a bird flapping its wings but not moving forward on a really windy day. In that case, the velocity of the wind is equal and opposite to the bird’s velocity, so it looks like the bird’s not moving.
But what if the airplane encounters a crosswind? Something that’s not straight-on light a head or tail wind? Here’s how you break it down with vectors:
