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Tag: dot physics

  • What Is the Magnetic Constant and Why Does It Matter?

    This means these three values can’t be independent; if you know two of them, you can derive the third. How do physicists deal with this? We define the speed of light as exactly 299,792,458 meters per second. (How do we know it’s exact? Because we define a meter as the distance light travels in 1/299,792,458 of a second.) Then we measure the magnetic constant (μ0) and use that value along with the speed of light to calculate the electric constant (ε0).

    Maybe that seems like cheating, but to even start doing actual science, at some point we have to make up arbitrary units and define some parameters. In fact, when you come down to it, all systems of measurement are made up, just like all words are made up.

    Permeability of Free Space

    Magnetic fields (represented by the symbol B) can be created by magnets, as shown in the photo up top. But because of that interdependence we talked about, they can also be made by moving electrical charges. (I’m using the shorthand term “charges” for charged particles, like electrons.) This is described by the Biot-Savart law:

    You can see the magnetic constant (μ0) in there. We also have the value of the electric charge (q) moving with a certain velocity (v). So this says the magnetic field increases with the electric charge and decreases with the distance (r) from the moving charge—and the magnetic constant tells us precisely how much it varies.

    Of course, we don’t deal with individual moving electrons very often. But we deal with streams of moving electrons all the time: That’s electric current, which we can measure. If we know the charge on the particles in coulombs, then the number of coulombs flowing per second gives us the current (I) in amperes. And we can write the equation above in terms of current: B = μ0I/(2πr).

    It’s Everywhere

    What this tells us is that electric current generates a magnetic field. This is used in all kinds of machines. For instance, it gives us electromagnets, where the magnetic force can be turned on and off to move metal objects in factories and scrapyards. It’s also how audio speakers create sound: An electric signal vibrates a magnetic driver, which generates pressure waves in the air.

    Also magnetic fields influence electric currents. This is how motors work. There’s a current running through a coil of wire in the presence of a magnetic field that’s usually created with some permanent magnets. The force on the coil of wire causes it to turn, and there’s your motor. It could be a fan motor, part of your AC compressor, or the main drive for an electric car.

    Wait! There’s more. Just as a changing electric field creates a magnetic field, a changing magnetic field creates an electric field—and that produces an electric current. This is how most of our power is generated. Some energy source—steam, wind, moving water, whatever—spins a turbine that rotates a coil within a magnetic field. The changing magnetic flux induces a voltage in the coil, converting mechanical energy into electrical energy that can be transmitted to your home.

    Measuring the Magnetic Constant

    How can we measure μ0? One method uses what’s called a current balance. A simple version of this has two parallel wires carrying electric current (I) in opposite directions, as shown in the diagram below. Then you suspend the two wires with strings so that they can move apart, like this:

    Image may contain Triangle

    The current in each wire creates a magnetic field at the location of the other wire, and this pushes them apart. As they move away, the magnetic force decreases and the horizontal component of the tension in the support string increases (because of the change in angle). Once these two forces are equal, the wires will be “balanced.”

    If you know the value of the electric current and the distance between the wires (r), you can determine the magnetic constant, μ0. Then, as we showed above, you can use this value along with the defined speed of light to calculate the electric constant, ε0.

    So yeah, all in all, you could say the magnetic constant is pretty important. Oh, and what is that constant value? According to the International Committee for Weights and Measures, μ0 = 1.256637061272 × 10–6 N/A2. No more, no less.

    Rhett Allain

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  • The Physics Trick That Makes These New Super Cars So Insanely Fast

    The Physics Trick That Makes These New Super Cars So Insanely Fast

    You can see that it’s limited by the materials in the tires and track (captured by the frictional coefficent) and the gravitational field (so, what planet you’re on). Notice that the mass has canceled out. It doesn’t matter if you have a more massive vehicle. Yes, you get more friction, but it’s also harder to accelerate.

    Constant-Friction Model

    Since constant power doesn’t work, what about a constant acceleration due to the friction between the tires and road? Let’s say the coefficient of friction is 0.7 (reasonable for a dry road). In that case we would get the following plot of velocity versus time for the quarter-mile run.

    I’ve included the constant-power curve just for comparison. You can see that with this friction model, the car will just keep increasing in speed forever with the same acceleration. That doesn’t seem correct either.

    A Better Model of Acceleration

    How about this? The car increases in velocity—however, the rate of increase (the acceleration) is the lower of the two models. So, at the beginning of the run the acceleration is limited by the friction between the tires and road. Then, when the acceleration using the constant power model is lower, we can use that method.

    Before we test this out, we need some real data for comparison. Since I don’t own a Porsche 911, I’m going to use the data from this MotorTrend race between a 911 and a Tesla Cybertruck. Here is a plot of the actual position of the Porsche over the quarter-mile track along with the combo power-friction model. (That’s now distance on the vertical axis—a quarter-mile is just about 400 meters.)

    Rhett Allain

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  • Unlock the Secret of a Gravity-Defying Parkour Stunt—With Physics!

    Unlock the Secret of a Gravity-Defying Parkour Stunt—With Physics!

    We can break that diagonal motion down into horizontal and vertical portions; for now let’s just focus on the former. Say you start with a horizontal velocity (v1) of –1 meter per second and rebound with a horizontal velocity (v2) of +1 m/s. The change of sign indicates the reversal of direction. Think of it like you’re moving back and forth along the x axis of a coordinate plane, negative to the left, positive to the right.

    Notice that your speed stays the same, but the velocity changes. (Remember, velocity has a direction.) In fact, because your horizontal velocity reverses, you get a big increase in velocity. (v2 – v1) = (1 – (–1)) = 2. This gives you a larger impact acceleration, a greater normal force, and more friction. The bouncing back and forth is the whole key to beating gravity in this stunt.

    So how much force would you need to exert to make one of these rebounding wall jumps? Let’s say you have a mass of 75 kilograms and a friction coefficient of 0.6, which is probably conservative for rubber soles.

    For starters, the frictional force (Ff) must equal or exceed the gravitational force (mg). The gravitational field strength on Earth (g) is 9.8 newtons per kilogram. So the gravitational force, (m x g) = 75 x 9.8 = 735 newtons.

    Now remember, the frictional force is the normal force times the coefficient of friction (Ff = μN). So to achieve a minimum frictional force of 735 newtons, we need a normal force of at least 1,225 newtons (Ff/μ = 735/0.6 = 1,225).

    Both of these forces, gravity and the normal force, are pushing on you, so we need to add them up to get the net force. Since they’re perpendicular, we can easily calculate the vector sum as 1,429 newtons. (Take note, kids: You want to be a parkour hero? Take linear algebra.)

    That means you need to push back with the same force (because forces are an interaction between two things). 1,429 newtons is a force of 321 pounds. That’s significant but not impossible. Doing it eight times in rapid succession, though? Not so easy.

    How much time do you have to do the turnaround? With the normal force and mass of the person, we can calculate the horizontal acceleration ax. By definition, that in turn equals the change in velocity per unit of time (Δt), so we can use that to solve for the time interval:

    Plugging in our numbers, we get a time interval of 0.12 second. In other words, if you hesitate you fall. Bottom line, if you want to do this awesome parkour stunt you gotta be strong, fast, and fearless—because if you run short of newtons halfway up, the descent is a lot faster than the ascent.

    Rhett Allain

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  • The Incredible Physics of Simone Biles’ Yurchenko Double Pike

    The Incredible Physics of Simone Biles’ Yurchenko Double Pike

    A gymnast can actually perform both of these types of rotation at the same time—that’s what makes the sport so interesting to watch. In physics, we would call this type of movement a “rigid body rotation.” But, clearly, humans aren’t rigid, so the mathematics to describe rotations like this can be quite complicated. For the sake of brevity, let’s limit our discussion just to flips.

    There are three kinds of flips. There is a layout, in which the gymnast keeps their body in a straight position. There is a pike, in which they bend at about a 90-degree angle at the hips. Finally, there is a tuck, with the knees pulled up towards the chest.

    What’s the difference, in terms of physics?

    Rotations and the Moment of Inertia

    If you want to understand the physics of a rotation, you need to consider the moment of inertia. I know that’s a strange-sounding term. Let’s start with an example involving boats. (Yes, boats.)

    Suppose you’re standing on a dock next to a small boat that’s just floating there, and isn’t tied up. If you put your foot onto the boat and push it, what happens? Yes, the boat moves away—but it does something else. The boat also speeds up as it moves away. This change in speed is an acceleration.

    Now imagine that you move along the dock and pick a much larger boat, like a yacht. If you put your foot on it and push it, using the same force for the same amount of time as you did for the smaller boat, does it move? Yes, it does. However, it doesn’t increase in speed as much as the smaller boat because it has a larger mass.

    The key property in this example is the boat’s mass. With more mass, it’s more difficult to change an object’s motion. Sometimes we call this property of objects the inertia (which is not to be confused with the moment of inertia—we will get to that soon).

    When you push on the boat, we can describe this force-motion interaction with a form of Newton’s Second Law. It looks like this:

    Illustration: Rhett Allain

    Rhett Allain

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  • No, You Can’t Have a Solar-Powered Passenger Plane

    No, You Can’t Have a Solar-Powered Passenger Plane

    The angle at which the light hits the panel, θ, is measured from a line perpendicular to the surface. This means you will get a maximum solar panel power when the light is shining straight-on (θ = 0), since cosine(0) = 1.

    OK, let’s do a quick calculation. The intensity of sunlight at the location of the Earth is about 1,361 watts per square meter. So, let’s say our solar panel is 1 meter by 1 meter with an efficiency of 25 percent (which is very optimistic). If the light hits at a 30-degree angle, this solar panel would give us a power of 294.7 watts.

    Well, our solar-powered 737 is going to need a lot more power than that. We can calculate the surface area needed to generate 10 million watts. For simplicity, let’s assume the light is perpendicular to the panels (obviously not realistic). With this, we’d need 29,000 square meters of panels.

    Just for comparison, the 737 has a wing area of 125 square meters. If it was covered with solar panels it would generate 42 kilowatts. That’s nice, but not nearly nice enough for a passenger airliner. To be specific, it’s 0.4 percent of the power you’d need to remain in the sky.

    Bottom line, it’s pretty hard to envision any way of making a solar-powered passenger liner. However, that doesn’t rule out electric airplanes altogether! We might have some nice battery-powered planes someday.

    Oh, but what about those real solar-powered planes? The key is to fly slower with a lower mass so that the drag force is smaller. If the wings are big enough, it’s possible to get enough power to fly—until it gets cloudy.

    Rhett Allain

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  • How to Run on the Moon

    How to Run on the Moon

    When the elevator is stopped, the two forces are equal and opposite, and the net force is zero. But if you’re accelerating upward, the net force must also be upward. This means the normal force exceeds the gravitational force (shown by the lengths of the two arrows above). So you feel heavier when the normal force increases. We can call the normal force your “apparent weight.”

    Get it? You’re in this box and it looks like nothing’s changing, but you feel yourself being pulled downward by stronger gravity. That’s because your frame of reference, the seemingly motionless elevator car, is in fact zooming upward. Basically, we’re shifting from how you see it inside the system to how someone outside the system sees it.

    Could you build an elevator on the moon and have it accelerate fast enough to regain your earthly weight? Theoretically, yeah. This is what Einstein’s equivalence principle states: There is no difference between a gravitational field and an accelerating reference frame.

    A Roundabout Solution

    But you see the problem: To keep accelerating upward for even a few minutes, the elevator shaft would have to be absurdly tall, and you’d soon reach equally ridiculous speeds. But wait! There’s another way to produce an acceleration: move in a circle.

    Here’s a physics riddle for you: What are the three controls in a car that make it accelerate? Answer: the gas pedal (to speed up), the brake (to slow down), and the steering wheel (to change direction). Yes, all of these are accelerations!

    Remember, acceleration is the rate of change of velocity, and here’s the key thing: Velocity in physics is a vector. It has a magnitude, which we call its speed, but it also has a specific direction. Turn the car and you’re accelerating, even if your speed is unchanged.

    So what if you just drove in a circle? Then you’d be constantly accelerating without going anywhere. This is called centripetal acceleration (ac), which means center-pointing: An object moving in a circle is accelerating toward the center, and the magnitude of this acceleration depends on the speed (v) and the radius (R):

    Courtesy of Rhett Allain

    Rhett Allain

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  • Can You Really Run on Top of a Train, Like in the Movies?

    Can You Really Run on Top of a Train, Like in the Movies?

    Just because you see something done in a movie, that doesn’t mean you should try it yourself. Take, for example, a human running on top of a moving train. For starters, you can’t be sure it’s real. In early Westerns, they used moving backdrops to make fake trains look like they were in motion. Now there’s CGI. Or they might speed the film up to make a real train look faster than it really is.

    So here’s a question for you: Is it possible to run on a train roof and leap from one car to the next? Or will the train zoom ahead of you while you’re in the air, so that you land behind where you took off? Or worse, would you end up falling between the cars because the gap is moving forward, lengthening the distance you have to traverse? This, my friend, is why stunt actors study physics.

    Framing the Action

    What is physics anyway? Basically it’s a set of models of the real world, which we can use to calculate forces and predict how the position and velocity of things will change. However, we can’t find the position or velocity of anything without a reference frame.

    Suppose I’m standing in a room, holding a ball, and I want to describe its location. I can use Cartesian coordinates for a 3D space to give the ball an (x, y, z) value. But these numbers depend on the origin and orientation of my axes. It seems natural to use a corner of the room as the origin, with x and y axes running along the base of two adjacent walls and the z axis running vertically upward. Using this system (with units in meters), I find that the ball is at the point (1, 1, 1).

    What if my pal Bob is there, and he measures the ball’s location in a different way? Maybe he puts the origin where the ball starts, in my hand, giving it an initial position of (0, 0, 0). That seems logical too. We could argue about who’s right, but that would be silly. We just have different frames of reference, and they’re both arbitrary. (Don’t worry, we’ll get back to trains.)

    Now I toss that ball straight up in the air. After a short time interval of 0.1 second, my coordinate system has the ball at the location (1, 1, 2), meaning it’s 1 meter higher. Bob also has a new location, (0, 0, 1). But notice that in both systems, the ball rose by 1 meter in the z direction. So we would agree that the ball has an upward velocity of 10 meters per second.

    A Moving Reference Frame

    Now suppose I take that ball on a train traveling at 10 meters per second (22.4 miles per hour). I again toss the ball straight up—what will happen? I’m inside the railcar, so I use a coordinate system that moves along with the train. In this moving reference frame, I am stationary. Bob is standing on the side of the tracks (he can see the ball through the windows), so he uses a stationary coordinate system, in which I am moving.

    Courtesy of Rhett Allain

    Rhett Allain

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  • Can You View a Round Solar Eclipse Through a Square Hole?

    Can You View a Round Solar Eclipse Through a Square Hole?

    If you live in the US and missed the last total solar eclipse in 2017, good news! You’re about to get another chance. There will be a total solar eclipse passing through Texas and the Midwest states on April 8. Remember that in a solar eclipse, the moon’s shadow falls on the Earth. If you’re in this shadow, it’s going to look really weird. But also awesome.

    Even if you’re not in the path of totality, you can still see something. All of the continental states will get at least a partial eclipse. (Check out the map here at NASA’s eclipse page.) And do I need to tell you this? Never look at the sun without special glasses, even when it’s mostly blocked by the moon. You may still be able to get some safe solar viewers before the big event.

    But there’s another way to view the solar eclipse without glasses: using a pinhole projector. It’s super simple to make and easy to use. All you need is something flat like a piece of cardboard. Then you poke a hole in it with a pin. That’s pretty much it. When light from the sun passes through the hole, it will project an image onto some flat surface (like a sidewalk).

    If you did this on a normal day you’d see a circular dot of light. You might think that’s because the hole is round. But during the eclipse you will see a crescent shape caused by the moon passing in front of the sun. It’s both awesome and safe for your eyes.

    Actually, you don’t even need to make a pinhole viewer—they already exist all around us. If you stand under a tree, the small spaces between the leaves will act as pinholes to project a bunch of little crescent images. Here’s a picture I took during the 2017 eclipse:

    Images of a solar eclipse projected through the gaps in overhead leaves.

    Courtesy of Rhett Allain

    Fun With Pinholes

    Just for fun, here’s a question for you. Most pinholes are round (because pins have cylindrical shafts). But what if you replaced the circular hole with a square one? What shape would a round sun project onto the ground? Would it be a circle? Would it be a square? Or maybe it would be a squircle! What about a triangular hole? What would happen then?

    I actually have a card from PUNCH (Polarimeter to Unify the Corona and Heliosphere) that demonstrates this with three holes—circular, triangular and square. Check it out.

    Rhett Allain

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  • Stumped by Heat Pumps?

    Stumped by Heat Pumps?

    Now stretch it really hard and quickly hold it to your upper lip, which is sensitive to temperature. You will feel that it’s warmer than it was before. That’s because you’re adding energy to the rubber band, which increases its temperature.

    Are you ready for the awesome part? Keep it stretched for a little while until it returns to room temperature. Now let the rubber band relax and quickly touch it to your lip again. It’s now colder than room temperature! Seriously, try this for yourself.

    So if you had a big enough rubber band, could you use this to cool your house? Wait a minute, you’re gonna say: In the first stage, when we stretched the rubber band, it got hot, and then it cooled back to its original temperature—and in doing that it heated the air. You’re right. But what if we could vent that warmer air outside? Then you could keep just the cooling phase inside.

    Boom. You just re-invented the air conditioner! Instead of a rubber band, an AC has a fluid called a refrigerant that circulates in a closed loop from inside to outside. This fluid has a low specific heat, so it changes temperature quickly, and a very low boiling point—turning into a gas at something like –15 Fahrenheit.

    How’s it work? The gas is first compressed, causing it to heat up to like 150 degrees. The hot gas circulates in a set of copper coils outside, with a fan blowing over them, so the gas loses thermal energy to the atmosphere. (Copper also has a low specific heat.)

    Then it’s pumped back inside, where the pressure is quickly reduced, causing it to expand and instantly cool down to around 40 degrees. As the now cold fluid circulates through indoor coils, a fan blows warm inside air over it, heating the fluid again and cooling the indoor air in the process. As the system circulates, it basically picks up thermal energy indoors and carries it outdoors.

    By the way, this is exactly the same process that your fridge uses to keep your cheese and soda cold. In both cases, the process makes something inside cooler and something outside warmer. Put your hand behind the fridge and you’ll see what I mean. Just for kicks, here’s a guy who actually built a refrigerator that runs on rubber bands.

    So Heat Pumps Aren’t New!

    You thought this was going to be an article about heat pumps, right? Well guess what. We’ve been talking about heat pumps this whole time, because they run on the same principles. A heat pump cools your home just like an air conditioner, by circulating a refrigerant and varying the pressure to change its temperature, so it takes thermal energy from one place and puts it in a different place.

    So back to the big mystery: How can a heat pump increase the temperature of indoor air on a cold day without actually generating any heat? Simple: Just run it in reverse! This time we let the hot compressed refrigerant cool off inside the house to raise the indoor air temperature. The low-pressure, cold gas then goes outside to warm up.

    Warm up outside? Yep. Even on a freezing day, the air still has thermal energy. So long as it’s above absolute zero—which, believe me, it is, since that’s around –460 Fahrenheit—the air molecules are in motion. And since we’re cooling the refrigerant to, say, –15 degrees, which is lower than winter temperatures in most places, it will wring thermal energy out of even frigid air.

    Of course, you can’t get energy for free. Heat pumps rely on electricity to drive the compressor and fans. But if you have solar panels at home, or if the electricity in your area is even partly from non-carbon sources, replacing a gas furnace with a heat pump can make a big difference in reducing greenhouse gas emissions. And it’ll probably lower your utility bills in the process.

    Rhett Allain

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