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137

The previous answers all restate the problem as "Work is force dot/times distance". But this is not really satisfying, because you could then ask "Why is work force dot distance?" and the mystery is the same. The only way to answer questions like this is to rely on symmetry principles, since these are more fundamental than the laws of motion. Using Galilean ...


47

The question is especially relevant from a didactical point of view because one has to learn to distingish between energy (work) and momentum (quantity of motion). The kinematic property that is proportional to $v$ is nowadays called momentum, it is the "quantity of motion" residing in a moving object, it's definition is $p:= mv$. The change of momentum ...


45

The speed of sound in an ideal gas is given by $$a = \sqrt{\gamma R T}$$ Where $\gamma = \frac{C_p}{C_v}$, $R$ is the specific ideal gas constant and $T$ is the absolute temperature. Taking standard values for air, this makes a graph like this: The linear approximation is plotted by your formula, $a = 331\ \frac{m}{s}\ +\ 0.6 \frac{m}{sK} (T - 273\ ...


31

It's true that at the speed of sound, you will have a huge amount of drag. The reason is that the air in front of you has to move out of the way, and if you are moving at the speed of sound, the pressure wave that pushes the air out of the way is moving at exactly the same speed as you. So in the continuum mechanics limit, you can't push the air out of the ...


30

At the ambient temperature and pressure (assuming atmospheric pressure), the sound speed is pretty close to $340\ \frac{\text{m}}{\text{s}}$, and it seems (from internet research) that the first contender is about $16\ \text{m}$ further away from the guy firing the gun, which comes down to a delay of about $.05\ \text{s}$ in hearing the sound if the sound is ...


27

Is it fair to judge this speedskating race by only 3 thousands of a second? Yes, it's "fair". Not only is it according to the current rules of the event**, but also: There are at least three asymmetries that have far larger impact and are all considered "fair". They happen to start in different lanes (and must cross-over thereafter). That means they ...


24

Let me start by clarifying that I assume the question is whether a superhuman or any object of human size can render itself invisible through speed alone. And that the speed of said object must be $v\ll c$. From this, I assume that the object or person being viewed must spend a reasonably long amount of time within the observer's field of view such that ...


22

The best way to solve it would be experimentally, by doing the run several times, with calibrated instrumentation by the roadside to measure your speed. The acceleration won't have been constant, so that's not an assumption we can use. Knowing the 0-60 time capability won't really help; it could be different when accelerating up hill, compared to on the ...


22

The reason is because the time taken for the two trips are different, so the average speed is not simply $\frac{v_1 + v_2}{2}$ We should go back to the definition. The average speed is always (total length) ÷ (total time). In your case, the total time can be calculated as \begin{align} \text{time}_1 &= \frac{120 \mathrm{miles}}{40 \mathrm{mph}} ...


20

There is no controversy or ambiguity. It is possible to define mass in two different ways, but: (1) the choice of definition doesn't change anything about predictions of the results of experiment, and (2) the definition has been standardized for about 50 years. All relativists today use invariant mass. If you encounter a treatment of relativity that ...


19

By special relativity, the energy needed to accelerate a particle (with mass) grow super-quadratically when the speed is close to c, and is ∞ when it is c. $$ E = \gamma mc^2 = \frac{mc^2}{\sqrt{1 - (\text{“percent of speed of light”})^2}} $$ Since you can't supply infinite energy to the particle, it is not possible to get to 100% c. Edit: ...


19

Ah, this gives me a chance to give a proper home to an analysis I first posted on Reddit. (I would much rather have first posted it here :-P) Mathematical derivation It all starts with a blog post I've written that comes very close to addressing the exact question you're asking. In the post, I calculated how fast an object would be moving after falling a ...


16

This scientific problem – well, a more general one – has been solved in the following paper: http://arxiv.org/abs/1204.0162 Because it's legal in my country to move backwards in time, I remember the future event – one minute from now – in which Andrew Gibson will mention that he has this paper hanging in his physics lounge. He will curse me. 11 minutes ...


16

I would think an object can be invisible to a human if it moves so fast that, within the time it passes the field of view of the human, it reflects too little light to be detected visually (human vision has very high, but still limited sensitivity to light). On the other hand, if the object moves so fast in air, it will produce a lot of noise and probably ...


15

I will try to adress the misunderstandings first, then answer the question. Particle exchange force model is not causal There is a flaw in your thinking, in that you are formulating the electromagnetic interaction in terms of photon emission and absorption and at the same time telling a story forward in time. These two ideas are both ok separately, but not ...


13

Let me just throw in an intuitive explanation. You could re-phrase your question as: Why does velocity only increase as the square root of kinetic energy, not linearly? Well, drop a ball from a height of 1 meter, and it has velocity v when it hits the ground. Now, drop it from a height of 2 meters. Will it have a velocity of 2v when it hits the ...


12

You've seen the speed of light quoted as roughly $3*10^8\, \text{m/s}$, so the speed of light is very fast compared to one meter and one second. This is roughly a human walking speed, so your question could be interpreted as asking why light is few hundred million times faster than a walking speed. The speed people walk is rather anthropocentric, though. ...


12

A photon does not "reach" light speed, it is "born" with that velocity. And because the photon has no rest mass, there is no problem inherent.


12

Velocity does indeed have to be measured relative to something. We can measure our radial velocity relative to any other astronomical object we care to, by measuring Doppler shifts. But if you want to know our velocity "relative to the Universe as a whole" rather than relative to any one object, we have to be a bit careful to define our terms. Because the ...


12

Why can't a space ship accelerate infinitely? Because a space ship needs to carry fuel, and because that fuel needs to be contained in a fuel tank. That need to carry the fuel needed to make the spacecraft accelerate leads to the very nasty ideal rocket equation, $$\Delta v = v_e \ln \left( \frac {m_{\text{initial}}} {m_{\text{final}}} \right)$$ The ...


11

SPEED OF LIGHT: This is a very interesting question. Going through the foundations of electromagnetism and the theory that led to Maxwell’s equations, there is an interesting element that can grab your attention. You can see that the speed of light is not as abstract and mysterious as it appears to be, but only if you look from a different perspective. I ...


11

If you consider a rotating propeller, it has the following properties: you can see that something is there you cannot see what it is; you just happen to know it you cannot count the blades or really distinguish the features at all you cannot even tell the distance to the blurry "thing" in front of you people are known to walk into running propellers ...


11

What you want to do is keep the angle between your direction of motion and the line of sight to police car the same as the angle between the truck's direction of motion and the truck's line of sight to the police car. In other words, we want to keep $a1=a2$ in the picture above. This is a problem in similar triangles. The answer will be that the ratio of ...


11

The Red Bull Stratos project involving the 43-year-old Austrian man Felix Baumgartner is to break the sound barrier. Within the first 15,000 feet of his jump he was traveling well over the cruising speed of a commercial jetliner, reaching some 625 mph. The maximum velocity reached by Felix is about some 380 km/s. How did he do that? During a free-fall, ...


10

Unsurprisingly this has been the subject of several scientific papers. In particular Google for papers by J. W. Glasheen and T. A. McMahon. They studied the basilisk lizard, but their results can be extrapolated to humans. It's debatable how reliable such a large extrapolation is, but the result is that the required speed is so far beyond human ability that ...


10

This derivation is often neglected, because it is slightly involved (for an ungergraduate presentation) in Newton's way of thinking, with explicit forces, although this is how Newton did it, and it is a little too trivial if you use stress tensor concepts. I will use the stress tensor concept. Momentum is a conserved quantity, and you should be familiar ...


10

It's a bit misleading to simply say the speed of sound is proportional to $\sqrt{T}$ because life is a bit more complicated than that. You've probably seen http://en.wikipedia.org/wiki/Speed_of_sound and this does indeed say in the introduction that the speed of sound is a function of the square root of the absolute temperature. However if you read on you'll ...


9

The only real physical reason (which is not really a fully satisfying answer) is that $E \sim v^2$ is what experiments tell us. For example, gravitational potential energy on the Earth's surface is proportional to height, and if you drop an object, you can measure that the height it falls is proportional to the square of its speed. Thus, if energy is to be ...


9

I'm going to dare to give a very brief answer that's likely not what most folks would expect, but is deeply rooted in experiment: The speed of time is just the speed of a clock -- that is, of how fast some kind of a repeated cycle can be done. Clocks thus only have meaning relative to each other. You can set one as a standard, then measure other by it, but ...


9

So here is the question, is it physically possible for a "human" (human size object) to move in a CONFINED environment (lets say, 20 m×20 m×10 m ) so fast that a regular person would be unable to SEE? If it is possible, how fast must this "person" be? The human eye relies on reception of photons to "see" something. There is no speed below the speed of ...



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