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Tag: forces

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

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

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    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.)

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    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!

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    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.

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    Rhett Allain

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  • The Incredible Physics of Simone Biles’ Yurchenko Double Pike

    The Incredible Physics of Simone Biles’ Yurchenko Double Pike

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    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

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    Rhett Allain

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  • How to Run on the Moon

    How to Run on the Moon

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    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

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    Rhett Allain

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  • The Quest to Map the Inside of the Proton

    The Quest to Map the Inside of the Proton

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    “How are matter and energy distributed?” asked Peter Schweitzer, a theoretical physicist at the University of Connecticut. “We don’t know.”

    Schweitzer has spent most of his career thinking about the gravitational side of the proton. Specifically, he’s interested in a matrix of properties of the proton called the energy-momentum tensor. “The energy-momentum tensor knows everything there is to be known about the particle,” he said.

    In Albert Einstein’s theory of general relativity, which casts gravitational attraction as objects following curves in space-time, the energy-momentum tensor tells space-time how to bend. It describes, for instance, the arrangement of energy (or, equivalently, mass)—the source of the lion’s share of space-time twisting. It also tracks information about how momentum is distributed, as well as where there will be compression or expansion, which can also lightly curve space-time.

    If we could learn the shape of space-time surrounding a proton, Russian and American physicists independently worked out in the 1960s, we could infer all the properties indexed in its energy-momentum tensor. Those include the proton’s mass and spin, which are already known, along with the arrangement of the proton’s pressures and forces, a collective property physicists refer to as the “Druck term,” after the word for pressure in German. This term is “as important as mass and spin, and nobody knows what it is,” Schweitzer said—though that’s starting to change.

    In the ’60s, it seemed as if measuring the energy-momentum tensor and calculating the Druck term would require a gravitational version of the usual scattering experiment: You fire a massive particle at a proton and let the two exchange a graviton—the hypothetical particle that makes up gravitational waves—rather than a photon. But due to the extreme weakness of gravity, physicists expect graviton scattering to occur 39 orders of magnitude more rarely than photon scattering. Experiments can’t possibly detect such a weak effect.

    “I remember reading about this when I was a student,” said Volker Burkert, a member of the Jefferson Lab team. The takeaway was that “we probably will never be able to learn anything about mechanical properties of particles.”

    Gravity Without Gravity

    Gravitational experiments are still unimaginable today. But research in the late 1990s and early 2000s by the physicists Xiangdong Ji and, working separately, the late Maxim Polyakov revealed a workaround.

    The general scheme is the following. When you fire an electron lightly at a proton, it usually delivers a photon to one of the quarks and glances off. But in fewer than one in a billion events, something special happens. The incoming electron sends in a photon. A quark absorbs it and then emits another photon a heartbeat later. The key difference is that this rare event involves two photons instead of one—both incoming and outgoing photons. Ji’s and Polyakov’s calculations showed that if experimentalists could collect the resulting electron, proton and photon, they could infer from the energies and momentums of these particles what happened with the two photons. And that two-photon experiment would be essentially as informative as the impossible graviton-scattering experiment.

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    Charlie Wood

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