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84

Alright, let's start with your direct question. Since $d = vt$ the time it takes to travel a certain distance is inversely proportional to your speed $ t \propto v^{-1} $, and so the fractional change in time is proportional to the negative fractional change in your speed. $$ \frac{dt}{t} = - \frac{dv}{v} $$ So, if we consider typical a typical highway ...


52

I think that most of the answers here are incorrect since it has nothing to do with decreasing resistance of rubber. In fact, the force required to stretch the balloon increases, not decreases while inflating. It's similar to stretching a string, ie. the reaction force is proportional to the increase in length of the string - this is why there is a point ...


32

Firstly, a Fibonacci spiral and a golden spiral are not quite the same thing, although they are pretty close. In this image from Wikipedia, the green curve is a Fibonacci spiral, and the red curve a golden spiral, with overlapping areas in yellow: They are close enough that for the purposes of your question we can consider them to be the same. In any ...


31

Take a strip of balloon rubber and pull it. It will get harder the more you pull. So why is it that inflating the balloon gets easier (at least long before the breaking point)? The balloon starts with very high curvature, so the air pressure is distorting each spot on its surface a lot relative to its 1cm neighbors for example. All the rubber's tension ...


28

The thing that makes a mirror a mirror is a that it has a high reflectivity (and is very smooth of course, but that doesn't enter into this issue), but all optical properties including reflectivity are functions of wavelength. The mirror is not reflective in the x-ray band, so it looks like a layer of glass (moderately dense) and a very thin layer of heavy ...


23

After much investigation, simulation and a deep literature search, I've figured out the true answer. You perceive a chirp because you are being hit with the echos of the sharp noise that generated the sound. The times between the arrival of those echos is decreasing inversely with time, so it sounds as if it were a tone with a fundamental frequency ...


22

dmckee points out that an ordinary mirror doesn't reflect X-rays, but if you could find an X-ray mirror and put it in your case it would just appear black. When you look at yourself in the mirror you're seeing light from your skin/clothes that hits the mirror and is reflected back towards your eyes. But airport X-ray machines work by passing X-rays through ...


22

The answer is a combination of physics and physiology. The warm water in the shower very quickly heats up the air in the shower, and warms up your skin. It also drives up the humidity of the air in the shower. You acclimate very quickly to the temperature/humidity conditions in the shower as being "normal". With the door left open a crack, you allow ...


21

No, this is not a golden-ratio spiral. Its closest relative is the Archimedean spiral, whose fundamental equation is $$r=a+b\,\theta.$$ This is the spiral traced out by the water thrown out by a horizontal sprinkler as it rotates: because its horizontal velocity is constant, the radius $r(t)$ of a given drop at time $t$ increases linearly with $t$, whereas ...


17

As others have noted, an ordinary mirror will not reflect x-rays. X-ray mirrors do exist, but will also probably not do what you want here. It's very difficult to manipulate the optical trajectory of an x-ray. The critical angle of typical metal foils at x-ray wavelengths is a few degrees at most -- that means that the x-ray is only reflected if it hits the ...


16

The type of headlight lenses shown in the images, with the rows of fringes, look like Fresnel lenses. This is essentially a lens with a series of fringes that act as prisms, each at a slightly different angle but with the same focal length. That has the effect of reflecting the non-directional light from the bulb in a particular direction. I'd think the ...


16

The air pressure inside the (intact) bubble is larger than in the surrounding. This pressure difference is called Laplace pressure and is caused by the surface tension between the soap film and the air. When the bubble pops the compressed air expands, thus creating a pressure wave, which you ultimately hear as the typical popping sound.


16

When in doubt, use mathematics. Imagine the balloon as a sphere (close enough for this answer) of initial radius $r_0$ and thickness $t$. Let's inflate it just a little bit (to radius $r_0 + \Delta r$). Now we can take a look at what happens by taking a cut through the equator of the sphere. The total circumference at the equator is $2\pi r$; with the ...


15

Like Dev said above, the material your typical round balloon is made from has a non-linear stress strain curve. When just starting to inflate it is fairly stiff, but then as it starts to blow up the stiffness goes down somewhat until it approaches its maximum size. We measured this in my undergraduate advanced lab class, and while I don't have the data ...


15

This is not an advertisement. Under the rubric of "do try this at home", I wanted to share one more thing that I discovered after writing my previous answer - but it is so unrelated to that answer that I thought it better to write this as a separate post. I discovered two interesting things. First, when you spin a coin on a hard surface, it "rings" with ...


15

First, it must be said that the picture you provided in your question is extreme. The concept of light bending is true, but the amount that the light bends is nowhere near as large as the picture shows it. The quantification of how much light bends when transferring from one medium to another is called the "index of refraction," and air's index of ...


14

The volume of a balloon grows linear, while the surface (which you actually stretch) doesn't. So although you're blowing the same amount of air into a balloon, you don't stretch the surface as much as in the beginning.


11

The heat energy being moved does not contribute to any global warming. The A/C is simply moving energy from inside to outside; the heat just turns around and flows back into the room, and the total stays the same. It's like someone trying to keep a leaky boat from sinking; you dump some water over the side, and it (or some just like it) leaks back in. A ...


9

Based on your comment, I think you are indeed asking a more profund question than your teabag suggests: Why is it that gravity is so weak compared to the other forces? The answer is: We don't know. Seriously, that is one of the holy grails: To first find the Grand Unified Theory of nature in which all forces except gravity are explained as coming from one ...


7

To figure out why this happens, you need to think about what boiling is, and how it works. As you would know, the water in the pot boils because its temperature was raised above the boiling point by the flame. This required a net transfer of heat from the flame, through the pot, to the water in the pot. Why did the heat flow in this direction? Because the ...


7

You don't even need highly specialised equipment to see the colour separation of the sun at low sun angles, a decent zoom lens on a camera will see it, and it's the origin of the "green flash" effect as the sun drops below the horizon. This site offers a good image: http://www.atoptics.co.uk/atoptics/gf15.htm


7

Unfortunately X-ray and gamma mirrors are impossible to build the way you think - mainly because there is much less interaction with the matter comparing to UV - it will go through all materials commonly used for making mirrors. Even for EUV light (wavelength of 13.5nm) building effective mirrors is a royal pain. As wavelength of X-Rays is very small (down ...


6

There are two parts to those lights: the reflector, which gathers the bulb's output and creates as focused a beam as possible the lens, which modifies that beam as desired. A focused beam makes a lousy headlight. You only see a small patch way in front. The extra ridges in the pictured lenses are vertical, which means they will spread the beam ...


6

Let us first summarize what do we actually experience when inflating the balloon. For the very first bit of volume, we have to exert a lot of energy. Or alternatively, we have to apply a lot of pressure coming from our lungs because for the change of energy $\delta E$, change of volume $\delta V$ and extra pressure $\Delta P$ (that is the difference between ...


6

That's not quite correct. You may have noticed that during summer the days are longer (and the nights shorter) than during winter. That is because the earth's axis is tilted about $23^o$ from the plane of it's orbit around the sun. With this tilt, as the earth travels around the sun the northern hemisphere gets longer days is the north pole is tilted ...


6

The answer is NO. (with the help from Antonio's comment) Any golden ratio spiral is tangential to rectangles at vertexes, which is not the case with spiral created by water in this picture. There are other discrepancies, but this is the easiest to spot and explain.


5

If the speed limit is 60 mph, it would take 60 min to go 60 miles. To go the same 60 miles at 65 mph, it takes 55.4 minutes. A time savings of 4.6 minutes. Is it really worthwhile to speed if all you are going to save is a few minutes (even less for shorter distances).


5

Aside from the effect on one driver you might consider the effect on traffic in general, that is what happens when everyone breaks the speed limit. As far as fluid dynamics is concerned, the side-effects of your speeding (if any) are felt by the people behind you. Reaction distance increases linearly with speed, but stopping distance must include a term ...


5

There are better answers than this, but I just want to contribute. As Joshua said, The quantification of how much light bends when transferring from one medium to another is called the "index of refraction," and air's index of refraction is very very close to that of a vacuum, so the bending of the light is very small, and the spreading apart of the ...


4

As everyone else is saying, if you assume Newton's law of cooling: $$ \dot Q = m c_p \dot T = h A \Delta T $$ The equation for how you heat or cool is an exponential $$ T(t) = T_\infty + \Delta T e^{ -\frac{hA}{mc_p} t } $$ The rate constant for growth (or dying) of temperature is the same (assuming other details of the material don't change much), so ...



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