Imagine driving your car in a circle, like you would when take a clover-leaf type of freeway exit, or make a right turn on a green light. Here’s how the forces play out during the motion:
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For any object that goes in a circle (or you can approximate it to a circle), you’ll want to use this approach when solving problems. You can feel the effect of circular motion if you’ve ever been in a car that suddenly turns right or left. You feel a push to the opposite side, right? If you are going fast enough and you take the turn hard enough, you can actually get slammed against the door. So my question to you is: who pushed you? Let’s find out!
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An object that moves in a circle with constant speed (like driving your car in a big circle at 30 mph) is called uniform circular motion. Although the speed is constant (30 mph), the velocity, which is a vector and made up of speed and direction, is not constant. The velocity vector has the same speed (magnitude), but the direction keeps changing as your car moves around the circle. The direction is an arrow that’s tangent to the circle as long as the car is moving on a circular path. This means that the tangent arrow is constantly changing and pointing in a new direction.
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A common misconception in science is that centrifugal and centripetal force (or acceleration) are the same thing. These two terms constantly throw students into frenzy, mostly because there is no clear definition in most textbooks. Here’s the scoop: centripetal and centrifugal force are NOT the same thing!
This experiment is mostly for Advanced Students, but here's a quick lesson you can do with your younger students...
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This experiment is mostly for Advanced Students, but here's a quick lesson you can do with your younger students...
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Now this next experiment is a little dangerous (we’re going to be spinning flames in a circle), so I found a video by MIT that has a row of five candles sitting on a rotating platform (like a “lazy susan”) so you can see how it works.
The candles are placed inside a dome (or a glass jar) so that when we spin them, they aren’t affected by the moving air but purely by acceleration. So for this video above, a row of candles are inside a clear dome on a rotating platform. When the platform rotates, air inside the dome gets swung to the outer part of the dome, creating higher density air at the outer rim, and lower density air in the middle. The candle flames point inwards towards the middle because the hot gas in the flames always points towards lower density air. Source: http://video.mit.edu
Now you’re beginning to understand how an object moving in a circle experiences acceleration, even if the speed is constant.
So what direction is the acceleration vector?
It’s pointed straight toward the center of that circle.
Velocity is always tangent to the circle in the direction of the motion, and acceleration is always directed radially inward. Because of these two things, the acceleration that arises from traveling in a circle is called centripetal acceleration (a word created by Sir Isaac Newton). There’s no direct relationship between the acceleration and velocity vectors for a moving particle.
Click here to go to next lesson on Centripetal Force.
Do you remember when I asked you “Who pushed you?” when you were riding in a car that took a sharp turn? Well, the answer has to do with centripetal force. Centripetal (translation = “center-seeking” ) is the force needed to keep an object following a curved path.
Remember how objects will travel in a straight line unless they bump into something or have another force acting on it like gravity, friction, or drag force? Imagine a car moving in a straight line at a constant speed. You’re inside the car, no seat belt, and the seat is slick enough for you to slide across easily. Now the car turns and drives again at constant speed but now on a circular path. When viewed from above the car, we see the car following a circle, and we see you wanting to keep moving in a straight line, but the car wall (door), moves into your path and exerts a force on you to keep you moving in a circle. The car door is pushing you into the circle.
According to Newton’s second law of motion, if you are experiencing an acceleration you must also be experiencing a net force (F=ma). The direction of the net force is in the same direction as the acceleration, so for the example with you inside the car, there’s an inward force acting on you (from the car door) keeping you moving in a circle.
If you have a bucket of water and you’re swinging it around your head, in order to keep a bucket of water swinging in a circle, the centripetal force can be felt in the tension experienced by the handle. Swinging an object around on a string will cause the rope to undergo tension (centripetal force), and if your rope isn’t strong enough, it will snap and break, sending the mass flying off in a tangential straight line until gravity and drag force pull the object to a stop.
This force is proportional to the square of the speed, meaning that the faster you swing the object, the higher the magnitude of the force will be.
Remember Newton’s First Law? The law of inertia? It states that objects in motion tend to stay in motion with the same speed and direction unless acted upon by an unbalanced/external force. Which means that objects naturally want to continue going their straight and merry way (like you did in a straight line when you were inside the car) until an unbalanced force causes it to turn speed up or stop. Can you see how an unbalanced force is required for objects to move in a circle? There has to be a force pushing on the object, keeping in on a circular path because otherwise, it’ll go off in a straight line!
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Every object moving in a circle will experience a force pushing or pulling it toward the center of the circle. Whether it’s a car making a turn and the friction force from the road are acting on the wheels of the car, or a bucket is swung around your head and the tension of the rope keeps it moving in a circle, they all have to have a force keeping them moving in that circle, and that force is called centripetal force. Without it, objects could never change their direction. Because centripetal force is tangent to the velocity vector, the force can change the direction of an object without changing the magnitude.
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Centrifugal (translation = “center-fleeing”) force has two different definitions, which causes even more confusion. The inertial centrifugal force is the most widely referred to, and is purely mathematical, having to do with calculating kinetic forces using reference frames, and is used with Newton’s laws of motion. It’s often referred to as the ‘fictitious force’.
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You’ve come so far with your analysis that I really want to give you the “real way” to solve these types of problems. Normally, this method isn’t introduced to you until your second year in college, and that’s only if you’re an engineer taking Statics and Dynamics classes (the next level after this course).
Here’s a step-by-step method that really puts all the pieces we’ve been working on all together into one:
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We’re going to build monster roller coasters in your house using just a couple of simple materials. You might have heard how energy cannot be created or destroyed, but it can be transferred or transformed (if you haven’t that’s okay – you’ll pick it up while doing this activity).
Roller coasters are a prime example of energy transfer: You start at the top of a big hill at low speeds (high gravitational potential energy), then race down a slope at break-neck speed (potential transforming into kinetic) until you bottom out and enter a loop (highest kinetic energy, lowest potential energy). At the top of the loop, your speed slows (increasing your potential energy), but then you speed up again and you zoom near the bottom exit of the loop (increasing your kinetic energy), and you’re off again!
Here’s what you need:
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You can find circular motion everywhere, including football, car racing, ice skating, and baseball. An ice skater spins on ice, or a competition speed skater makes a turn… they are both examples of circular motion. A turn happens when there’s a force component directed inward from the circular path. Let me show you a couple of examples:
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We’ve already studied the different types of forces and learned how to draw free body diagrams. We’re going to use those concepts to put forces into two different categories: internal and external forces. Internal forces include forces due to gravity, magnetism, electricity, and springs. External forces include applied, normal, tension, friction, drag and air resistance forces.
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The reason why we put the forces into two different categories will be obvious when we start solving physics problems, but for now, you can think of it like this: when total amount of work is done on an object is done by only internal forces, energy will change forms (like going from kinetic to potential energy), and the total amount of mechanical energy is conserved, and the forces are also conserved. When the total amount of work done is done by an external force, the forces are not conserved and the object with either gain or lose energy.
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This is a nit-picky experiment that focuses on the energy transfer of rolling cars. You’ll be placing objects and moving them about to gather information about the potential and kinetic energy.
We’ll also be taking data and recording the results as well as doing a few math calculations, so if math isn’t your thing, feel free to skip it.
Here’s what you need:
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What’s an inclined plane? Jar lids, spiral staircases, light bulbs, and key rings. These are all examples of inclined planes that wind around themselves. Some inclined planes are used to lower and raise things (like a jack or ramp), but they can also used to hold objects together (like jar lids or light bulb threads).
Here’s a quick experiment you can do to show yourself how something straight, like a ramp, is really the same as a spiral staircase.
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When you toss down a ball, gravity pulls on the ball as it falls (creating kinetic energy) until it smacks the pavement, converting it back to potential energy as it bounces up again. This cycles between kinetic and potential energy as long as the ball continues to bounce.
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Note: Do the pendulum experiment first, and when you’re done with the heavy nut from that activity, just use it in this experiment.
You can easily create one of these mystery toys out of an old baking powder can, a heavy rock, two paper clips, and a rubber band (at least 3″ x 1/4″). It will keep small kids and cats busy for hours.
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This is a very simple yet powerful demonstration that shows how potential energy and kinetic energy transfer from one to the other and back again, over and over. Once you wrap your head around this concept, you’ll be well on your way to designing world-class roller coasters.
For these experiments, find your materials:
- some string
- a bit of tape
- a washer or a weight of some kind
- set of magnets (at least 6, but more is better)
This experiment is for Advanced Students.There are several different ways of throwing objects. This is the only potato cannon we’ve found that does NOT use explosives, so you can be assured your kid will still have their face attached at the end of the day. (We’ll do more when we get to chemistry, so don’t worry!)
These nifty devices give off a satisfying *POP!!* when they fire and your backyard will look like an invasion of aliens from the French Fry planet when you’re done. Have your kids use a set of goggles and do all your experimenting outside.
Here’s what you need:
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Bobsleds use the low-friction surface of ice to coast downhill at ridiculous speeds. You start at the top of a high hill (with loads of potential energy) then slide down a icy hill til you transform all that potential energy into kinetic energy. It’s one of the most efficient ways of energy transformation on planet Earth. Ready to give it a try?
This is one of those quick-yet-highly-satisfying activities which utilizes ordinary materials and turns it into something highly unusual… for example, taking aluminum foil and marbles and making it into a racecar.
While you can make a tube out of gift wrap tubes, it’s much more fun to use clear plastic tubes (such as the ones that protect the long overhead fluorescent lights). Find the longest ones you can at your local hardware store. In a pinch, you can slit the gift wrap tubes in half lengthwise and tape either the lengths together for a longer run or side-by-side for multiple tracks for races. (Poke a skewer through the rolls horizontally to make a quick-release gate.)
Here’s what you need:
- aluminum foil
- marbles (at least four the same size)
- long tube (gift wrapping tube or the clear protective tube that covers fluorescent lighting is great)
We’re going to build monster roller coasters in your house using just a couple of simple materials. You might have heard how energy cannot be created or destroyed, but it can be transferred or transformed (if you haven’t that’s okay – you’ll pick it up while doing this activity).
Roller coasters are a prime example of energy transfer: You start at the top of a big hill at low speeds (high gravitational potential energy), then race down a slope at break-neck speed (potential transforming into kinetic) until you bottom out and enter a loop (highest kinetic energy, lowest potential energy). At the top of the loop, your speed slows (increasing your potential energy), but then you speed up again and you zoom near the bottom exit of the loop (increasing your kinetic energy), and you’re off again!
Here’s what you need:
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Nothing says summer time fun than a home-built go-kart that can race down the driveway with just as much thrill as two story roller coasters.
A go-karts (also called “go-cart”) can be gravity powered (without a motor) or include electric or gas powered motors. The gravity powered kind are also known as Soap Box Derby racers, and are the simplest kind to make since all you need is wheels, a frame, and a good hill (and a helmet!).
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If you’ve ever thrown a ball down into the sand, you know it can bury itself below the surface. Here’s how you figure out the non-conservative forces into the equation of the sand exerting a force on the ball as it slows down and stops deep in the sand.
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Have you learned how to drive yet, or are you excited to learn? Here’s a question on the driver’s test that is really kind of scary from a physics point of view, but it will make a lot of sense once you see how it works. And might even keep you from speeding, now that you understand what can happen if you lock up your brakes while going too fast.
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How do you calculate the energies of particles going near the speed of light? It’s a little tricky, but you can do it if you have the right equation. Since the kinetic energy equation comes from Newton’s Laws of Motion, which don’t apply to particles moving near the speed of light, we have to add a correction factor from Einstein’s Theory of Relativity in order to compensate and make the equations accurate. Here’s the equation for particles going close to light speed:
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Work is not that hard… it’s force that can be difficult. Imagine getting up a 10-step flight of stairs without a set of stairs. Your legs don’t have the strength or force for you to jump up… you’d have to climb up or find a ladder or a rope. The stairs allow you to, slowly but surely, lift yourself from the bottom to the top. Now imagine you are riding your bike and a friend of yours is running beside you.
Who’s got the tougher job? Your friend, right? You could go for many miles on your bike but your friend will tire out after only a few miles. The bike is easier (requires less force) to do as much work as the runner has to do. Now here’s an important point, you and your friend do about the same amount of work.
You also do the same amount of work when you go up the stairs versus climbing up the rope. The work is the same, but the force needed to make it happen is much different. Don’t worry if that doesn’t make sense now. As we move forward, it will become clearer. Before we start solving physics problems, we first have to accurately define a couple of terms we’re going to be using a lot that you might already have a different definition for.
Here are three concepts we’re going to be working with in this section:
- Work
- Energy
- Power
Energy is the ability to do work. Work is done on an object when a force acts on it so the object moves somewhere. It can be a large or small displacement, but as long as it’s not in its original position when it’s done, work is said to be done on the object. An example of work is when an apple falls off the tree and hits the ground. The apple falls because the gravitational force is acting on it, and it went from the tree to the ground. If you carry a heavy box up a flight of stairs, you are doing work on the box.
An example of what is not work is if you push really hard against a brick wall. The wall didn’t go anywhere, so you didn’t do any work at all (even though your muscles may not agree!). Mathematically, work is a vector, and is defined as the force multiplied by the distance like this: W = F d
If there’s an angle between the force and displacement vectors, then you’ll need to also multiply by the cosine of the angle between the two vectors. This is an important concept: Notice that the force has to cause the displacement. If you’re carrying a heavy box across the room (no stairs) at a constant speed, then you are not doing work on the box.
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We’ll cover power in a little bit, but first we need to have a unit of measurement for work. The units for work and energy are the same, but note that energy and work are not the same. (Remember, energy is the ability to do work.)
For energy, a couple of units are the Joule (J) and the calorie (cal or Cal). A Joule is the energy needed to lift one Newton one meter. A Newton is a unit of force. One Newton is about the amount of force it takes to lift 100 grams or 4 ounces or an apple.
It takes about 66 Newtons to lift a 15-pound bowling ball and it would take a 250-pound linebacker about 1000 Newtons to lift himself up the stairs! So, if you lifted an apple one meter (about 3 feet) into the air you would have exerted one Joule of energy to do it.
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This experiment is for Advanced Students. We’re going to really get a good feel for energy and power as it shows up in real life. For this experiment, you need:
- Something that weighs about 100 grams or 4 ounces, or just grab an apple.
- A meter or yard stick
This might seem sort of silly but it’s a good way to get the feeling for what a Joule is and what work is.
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A peanut is not a nut, but actually a seed. In addition to containing protein, a peanut is rich in fats and carbohydrates. Fats and carbohydrates are the major sources of energy for plants and animals.
The energy contained in the peanut actually came from the sun. Green plants absorb solar energy and use it in photosynthesis. During photosynthesis, carbon dioxide and water are combined to make glucose. Glucose is a simple sugar that is a type of carbohydrate. Oxygen gas is also made during photosynthesis.
The glucose made during photosynthesis is used by plants to make other important chemical substances needed for living and growing. Some of the chemical substances made from glucose include fats, carbohydrates (such as various sugars, starch, and cellulose), and proteins.
Photosynthesis is the way in which green plants make their food, and ultimately, all the food available on earth. All animals and nongreen plants (such as fungi and bacteria) depend on the stored energy of green plants to live. Photosynthesis is the most important way animals obtain energy from the sun.
Oil squeezed from nuts and seeds is a potential source of fuel. In some parts of the world, oil squeezed from seeds-particularly sunflower seeds-is burned as a motor fuel in some farm equipment. In the United States, some people have modified diesel cars and trucks to run on vegetable oils.
Fuels from vegetable oils are particularly attractive because, unlike fossil fuels, these fuels are renewable. They come from plants that can be grown in a reasonable amount of time.
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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.
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We’re going to learn how to calculate the amount of work done by forces by looking at how the force acts on the object, and if it causes a displacement. Have you spotted the three things you need to know in order to calculate the work done?
- Force
- Displacement
- Angle between the force and displacement vector (called theta)
The easiest way to do this is to show you by working a set of physics problems. So take out your notebook and a pencil, and do these problems right along with me. Here we go!
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Work done by friction is never conserved, since it’s turned into heat or sound, and we can’t get that back. It’s a non-conservative force. Other forces like gravity and speed are said to be conservative, since we can transfer that energy to a different form for a useful purpose. When you pull back a swing and then let go, you’re using the energy created by the gravitational force on the swing and transforming it into the forward motion of the swing as it moves through its arc. Energy from friction forces cannot be recovered, so we say that it’s an external energy, or work done by an external force.
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All the different forms of energy (heat, electrical, nuclear, sound, and so forth) can be broken down into two main categories: potential and kinetic energy. Kinetic energy is the energy of motion. Kinetic energy is an expression of the fact that a moving object can do work on anything it hits; it describes the amount of work the object could do as a result of its motion. Whether something is zooming, racing, spinning, rotating, speeding, flying, or diving… if it’s moving, it has kinetic energy.
How much energy it has depends on two important things: how fast it’s going and how much it weighs. A bowling ball cruising at 100 mph has a lot more kinetic energy than a cotton ball moving at the same speed.
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Imagine an arrow is shot from a bow and by the time it hits an apple it is traveling with 10 Joules of kinetic energy (kinetic energy is the energy of motion). What’s meant by kinetic energy is that when it hits something, it can do that much work on whatever is hit.
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.
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The rubber band can also show how energy is converted from one form to another. If you place the rubber band against a part of you that is sensitive to temperature changes (like a cheek or upper lip), you can sense when the band heats up. Simply stretch and release the rubber band over and over, testing the temperature as you go. Does it feel warmer in certain spots, or in just one location?
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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:
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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.)
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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!
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!
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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?
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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.
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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.
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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.
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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:
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Indoor Rain Clouds
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.
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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:
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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.
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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.
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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.
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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.)
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