11,99 €
Mehr erfahren.
- Herausgeber: UIT Cambridge
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
- Veröffentlichungsjahr: 2021
This is a physics book like you've never seen before: accessible and fun – perfect for anyone, young or old, with a healthy dose of curiosity. - How can you tell where a sound is coming from? - What is the human energy equivalent of a vacuum cleaner? - How does GPS work? - Why do eggs explode in the microwave? - Is there a vacuum inside double-glazed windows - Can you get less wet by cycling faster?Hundreds of full-colour photos and diagrams make the explanations super easy to follow. There are lots of home experiments, too, most of which can be done using simple items from the kitchen. For example, by using a glass full of water, a few drops of milk and a torch, you can show why the sky is blue and why the setting sun is red. If you want to dig a bit deeper, there are extra resources in the shaded boxes throughout. You can read Everyday Physics in whatever order you want, dipping in and out of the different sections. Based on Herman's Everyday physics lecture series, it combines deep physical insights with back-of-the-envelope calculations, relating abstract physics concepts to the real world, often in a surprising way. It's perfect for all ages: parents, grandparents, college students and anyone with a healthy interest in the world around them. This book will bring the magic of physics to your everyday life. Once you discover the beauty of science, ordinary things will become extraordinary.
Das E-Book können Sie in Legimi-Apps oder einer beliebigen App lesen, die das folgende Format unterstützen:
Seitenzahl: 344
Ähnliche
Everyday Physics:
Unusual insights into familiar things
Jo Hermans
To Hanneke, Reinoud and Francine, whose questions inspired me to write this book
PREFACE
Some people think that science and technology are only for people with a formal scientific education, but that’s a misconception. Our society is more and more dependent on technology, and anyone without a basic knowledge of science is at a disadvantage. Apart from that, it’s often just nice to understand a bit more about the world around us and to see how things work.
This book gives the inquiring reader scientific insights into everyday things. It contains a collection of interesting – sometimes surprising – examples, many based on questions from family, friends and students, often just motivated by curiosity. The choice of topics is therefore slightly arbitrary.
You don’t have to read this book all in one go, or even from front to back! Chapters are self-contained and can be read individually, although related topics are loosely grouped together. Some more complex topics and calculations are shown in boxes in the text, for advanced readers.
You can do almost all the experiments in the book with simple materials found at home. Some are just for fun, while others are illustrative and enlightening, but they all show that science doesn’t have to be boring!
Suggestions and errata: you can suggest new topics to include in future editions, and obtain the latest list of changes, corrections (and interesting additions) via the book’s webpage at www.uit.co.uk/everyday-physics
Continue the conversation at #EVPHYS on Twitter.
CONTENTS
01
HOW DOES GPS NAVIGATION WORK?
(WITH A NOD TO ALBERT EINSTEIN)
I’m riding on the bike paths along the southern California coast and I’ve lost my way. I do have a detailed map of the region with me, though. Fortunately there is a crossing with a sign showing that I am 14 kilometres from Santa Monica and 12 kilometres from Malibu. I am therefore on a circle around Santa Monica with a radius of 14 kilometres and at the same time on a circle around Malibu with a radius of 12 kilometres. The two circles intersect in two points. I am at one of these points. Which one? In this case I’m lucky: one of the two points lies in the Pacific, and I am not standing in the ocean, so I must be at the other point. I can now easily find the crossing on the map. If I also use the distances to the other towns on the sign in addition to Malibu and Santa Monica, my location becomes even more reliable, and the location in the ocean is eliminated.
A GPS (Global Positioning System) receiver determines position in an analogous way but it does it in three dimensions: not just the location on the map but the height as well, and with astounding precision. So how does GPS (or its European counterpart, Galileo) work?
Broadly speaking it works like this: GPS has 24 satellites orbiting at a distance of 20,000 km above the Earth (Fig. 1) and making two revolutions about the Earth per day. (The satellites are not geosynchronous/geostationary, by the way.) Each sends a radio 2signal that can be picked up by the GPS receiver in your car, on your bike or in your phone.
Fig. 1: GPS uses a network of 24 satellites.
Credit: After commons.wikimedia.org/wiki/User:Yuma
You need two things to determine your position: (1) the position of each satellite that is visible to your GPS receiver and (2) the distance to each.
(1) The position of each satellite is accurately monitored by a number of ground stations spread over the Earth and coordinated from the “mother station” in the US, where the system was originally developed for military purposes. These data are transmitted from Earth to the satellites. In this way each satellite knows its own position and reports this to your GPS receiver.
(2) Now you need to know the distance to each satellite. Your receiver finds this by measuring the time it takes for a radio signal from the satellite to reach the receiver; this is the difference between the time when the satellite sent the signal and the time your GPS received it. Multiply the time by the speed of the radio signal (i.e. by the speed of light) to give the distance. If you know the distance for (at least) three satellites, then you can calculate your position, just as in the road-sign story: 3
(a) The distance to the first satellite tells you that you are on an imaginary sphere around that satellite, with a radius equal to the measured distance.
(b) Similarly, the second satellite yields another imaginary sphere – around the second satellite (Fig. 2). So you must be on both spheres simultaneously, that is, on the intersection of these two spheres. This is a circle, just like two adhering soap bubbles form a circle.
(c) The third satellite yields yet another sphere, which intersects the circle in two points. Fortunately one of those drops out: it lies deep in the Earth or far above it. The remaining point is your position. Of course there is always a margin of error in the measurement; if your GPS receiver can see more satellites and takes them into account, the error margin will be smaller.
Fig. 2: The intersection of two spheres is a circle.
It all comes down to measuring time. That has to be very accurate because the radio signals travel at the speed of light (300,000 km per second). A timing error of one millionth of a second would mean an error of 300 metres in your position.
To achieve the required accuracy all satellites and ground stations have precision clocks (but note – not the GPS receivers) that are based on an extremely precise and stable transition within a caesium atom. Clocks of this type attain fabulous accuracies: the best ones on Earth run so precisely that in 1,000 years from now they will be out by less than one tenth of one millisecond! The satellite clocks 4need not be that good, but they must be synchronized to within one billionth of a second.
The clock in your GPS receiver isn’t an atomic clock like the ones in the satellites and ground stations, and in fact it doesn’t need to be. By using an extra satellite (i.e. four instead of three), the GPS receiver can precisely synchronize its (cheap, quartz) clock with the atomic clocks in the satellites, and so measure the times accurately, and therefore the distances.
See the Resources appendix for an animation of GPS satellites orbiting the Earth.
GPS and relativity
We’ve seen that GPS depends on precise time measurement. Now something unexpected happens: we need Einstein and his theory of relativity. Einstein himself would never have guessed that his theory – such an elusive piece of theoretical physics – would ever play such an important role in something as practical as GPS. It’s a lovely example of an unexpected and unintended application of cuttingedge fundamental science.
Here’s how it works: according to relativity theory, the clocks in the satellites don’t run at the rate they would when sitting on Earth, for two reasons: (1) because they are moving at high speed, they run somewhat slower, and (2) because they are so high up they feel less gravity (only a quarter of what they would feel on Earth), so they run somewhat faster.
The second effect is the greater, and the satellite clocks get ahead of the clocks in the ground stations by 38 millionths of a second per day. That does not sound like much, but it means that after one day the error in calculating a position would be more than 11 km, which would render your GPS useless.
To compensate for this relativistic effect, before launch the clocks in the satellites are set to run at a slightly slow rate – exactly slow enough so that after launch and once they are in orbit, they are precisely synchronous with the clocks in the monitoring stations on Earth.
Problem solved. Destination reached. With a nod to Einstein.
02
WHY ARE SOME ALPINE WINDS SO WARM?
In the Alps, the Föhn is the warm wind that blows from the mountains into the valleys, especially in winter. Curiously, even though it comes down from the mountains it’s warm and dry. Why?
To see what’s happening, let’s first look what happens to dry air that comes over the mountains (Fig. 1). The air pressure at the top of the mountain is lower than in the valley below, because there is less air pressing down, to cause the pressure. So air that streams up a mountain expands and therefore cools down. (This is the opposite of what happens in a bicycle pump: in the pump, air is compressed and therefore warms up.) By rising and expanding, air cools about 1°C per 100 metres, which explains why it gets colder when you hike up into the mountains. When air rises, say, 2,000 metres, 6it cools by about 20°C. When it comes down the other side of the mountains it warms at the same rate. The net effect is therefore zero: no Föhn (Fig. 1).
Fig. 1: In this model example the dry air starts out in the valley at 20°C, cools to 0°C at the top of the mountain, and warms again to 20°C in the valley.
With moist air (as in the Föhn) things are different (Fig. 2). As the air rises up the mountain it cools, just as the dry air did. But something else happens too: as the air cools, the water vapour in the air condenses and forms rain, just like morning mist can form above a meadow as the temperature goes down, or like the water vapour in your breath condenses if you blow on a cold windowpane. Heat is released when vapour condenses – the opposite of evaporation which absorbs heat.
Because of the heat that is released at condensation the rising moist air doesn’t cool as much as the dry air did. The net result is that the temperature rises to 27°C as it comes down the other side of the mountain. And the air is not only warm: it is also dry because it dropped most of its moisture as rain on the slope while rising. The relative humidity (the amount of water vapour the air contains divided by the amount that it can contain) can easily get below 20% this way. Warm and dry air, that’s what you get.
Fig. 2: The rising moist air cools down by only 13°C rather than 20°C. But as it descends the other side of the mountain, it warms up by the full 20°C, just as the dry air did in Fig. 1.
03
WHAT IS WIND CHILL?
The weatherman reports that the temperature is 0°C, but that the “wind chill” factor is minus 17. What does this mean?
When it is cold outside you feel particularly chilly if there is a strong wind blowing. The moving wind cools your body more than stationary air does. This is often called “wind chill”, i.e. subjective temperature. It is important whenever you skate, ride your bike, sail or ski; if you ignore it, you could end up with frostbite.
There is a lot of misunderstanding about wind chill. One newspaper said that if there is enough wind the water in a car radiator can freeze, even when the temperatures is above 0°C. 8That’s wrong. The radiator temperature will drop until it is the same temperature as the air and it can’t become colder than that. What is true, however, is that in a wind the radiator will cool down more quickly than in stationary air. And what’s true for the radiator is true for any object suspended in the wind: it will reach the temperature of the air, period. (The only exception is where something is wet; then evaporation takes away heat and can lead to excess cooling, but that’s not what we are talking about here.)
However, for a human being who has to generate heat constantly to maintain their body temperature of about 37°C the rate of heat loss is important. The environment is normally cooler than your body, so your body loses heat to the environment. In still air, the heat loss is relatively small: even exposed skin is still enveloped by an insulating air layer a few millimetres thick, which you carry with you as though it were a sweater (see How do you keep your temperature constant? p49). That air layer limits the heat losses and keeps your skin relatively warm.
In contrast, when there’s a wind, it blows away the insulating air layer, so that the cold gets right up to your skin, which becomes colder quicker. It becomes just as cold as it would be at a lower air temperature without wind. That lower temperature is the subjective temperature or “wind chill”. In other words: it is the temperature that still air would be to cause the same heat loss as the real temperature does in the wind.
9Fig. 1 shows the wind chill for various temperatures and wind speeds in average conditions. The left-hand column shows the real air temperature; the other columns give the subjective temperatures in degrees Celsius for various wind speeds. Note that the wind speed is relative: if you are standing still, and the wind is blowing at 25 km/h, the effective wind speed is 25 km/h. But if the air is stationary, and you are cycling through the air at 25 km/h, the effective wind speed is again 25 km/h, so a moving cyclist will cool down a lot more than someone standing still.
Fig. 1: Wind chill values under different conditions. Wind speeds of 13 and 20 m/s roughly correspond to the speed of a professional cycling time triallist (47 km/h) and a skier on a fast slope (72 km/h).
We see that it makes a lot of difference whether or not there is a wind blowing. At 0°C with a 72 km/h wind (or when skiing down the mountain at 72 km/h), it feels as cold as −20°C would be without wind. And if the temperature is −12°C at that speed, it feels like −39°C. It’s like being in Siberia!
If the air temperature is 37°C (i.e. at body temperature), there is no wind chill. However, you will probably find moving air more comfortable than still air, because the moving air evaporates some of your perspiration, and cools you a bit.
10A different way of looking at all this is to realize that while wind chill doesn’t reduce the temperature, it does increases the rate of heat loss and this matters to humans and animals. For example, say you are sitting at rest in still air at 0°C. Depending on body mass and clothing, you use about 120 joules/second, i.e. 120 watts. However, when there’s a wind of 20 m/s, you will need 185 watts to keep your body at constant temperature. If your internal heat production doesn’t increase fast enough, your temperature will fall and that’s how you get hypothermia.
04
WHY IS ICE SO SLIPPERY?
Why is ice so slippery? It sounds obvious: of course ice is slippery – that’s why you skate on it. But what exactly makes it so slippery? It’s not just because it is smooth: glass is very smooth, but it’s not a good surface to skate on. “As smooth as glass” isn’t the same as “slippery as ice”.
To slide on a surface you need more than just smoothness – a layer of water, for example: a surface that is smooth becomes slippery only when it is wet. You slip on a wet floor, not on a dry one, so a bit of water is what you need. And indeed, that is precisely what makes ice slippery: a thin layer of water between skate and solid ice acts as a lubricant.
The next question is: why would there be water under the skate when the ice is below freezing? An old misconception is that this is due to the pressure that the skater puts on the ice: the weight 12of the skater is concentrated on a tiny area – on the few square centimetres of the skate that touch the ice – and that produces a lot of pressure. It’s true that, when under pressure, ice melts below the normal freezing point. That is just plain logic: ice has a larger volume than liquid water (which is why ice floats). So if you compress ice, it tends to become liquid, which means that the melting point has dropped a bit. However, if we calculate that change in melting temperature, we find it’s very little in the case of the skater – a few tenths of a degree at most. So the fun of skating would be over as soon as the temperature is a few degrees below the freezing point. (Incidentally, this pressure argument would also fail to explain why a light object like an ice hockey puck slides so well on ice.)
The real answer is that ice has a layer of water at its surface by nature. Ice is made up of a lattice of water molecules, tightly bound to their neighbours all around. But at the outermost layer of molecules things are different. The molecules at the surface have no neighbours on the outside. Therefore, they are less tightly bound, have a high mobility and behave like fluid water even at freezing temperatures. At freezing point, this layer of water on ice has a thickness of some 200 molecules – about 70 nanometres (roughly one thousandth of the thickness of a human hair.) That’s not exactly thick, but it is enough to act as a lubricant. In addition, the friction between skate and ice releases heat which, in turn, melts some extra ice, making sliding even easier.
However, as the temperature goes down, the water layer becomes thinner and the lubrication reduces. If it gets sufficiently cold, far below −40°C, even the outermost molecules freeze, and there is no water layer left.
You might now be tempted to conclude that skating is best at temperatures just below freezing point, but this is not the case. The ice gets a little soft and loses mechanical strength since it’s closer to the melting point, and the skate cuts into it, causing some extra resistance. To skate really fast you therefore must go down a bit in temperature. The optimum – depending on the type of skate – is around −7°C or −8°C. That is cold enough to keep the skate from cutting into the ice too much, but not so cold that the water layer becomes too thin. So the recipe for beating the world speed skating record is no wind and −7°C.
06
HOW FAST DO RAINDROPS FALL?
In a heavy rain shower it is quite striking that the big drops come first and as the shower wanes the drops are smaller. So it seems that big drops fall faster than small ones, which is strange, because in a vacuum everything falls equally rapidly, as we remember from school. For example, a feather in a vacuum tube falls as fast as a marble or a coin.
The explanation is that raindrops aren’t falling in a vacuum; they’re falling in air, so friction (or “air resistance”) plays a role, acting against gravity. To understand the difference between large and small drops we have to look at the process of falling. That process starts as gravity makes the drop accelerate. But as the speed increases, so does the friction, directed upward, against the force of gravity. So the net force downward becomes smaller, and therefore the speed increases less rapidly – according to Newton’s “force is mass times acceleration”. The speed continues to increase until the net force becomes zero, at which point the speed remains constant: there is equilibrium between the downward gravity force and the upward friction.
The size of the drops is critical. For a falling drop bigger than about 1 mm, air resistance is proportional to area, i.e. to the square of the diameter (D2). So a drop 2 times the diameter of another will feel a resistance 4 times as large at the same speed, and a drop 3 times the diameter will feel 9 times as much resistance. It is the area 16that counts because the air stream becomes turbulent, just as it does for a cyclist (as we will see on p59) and for a car (p87).
Now suppose a drop falls at a certain speed and suddenly grows to twice the diameter (because it merges with several other drops, say). The friction force becomes 4 times as big. But since mass is proportional to the cube of the diameter (D3), the mass has becomes 8 times as big and thus the gravity force becomes 8 times as big. So there is now suddenly a greater net downward force, and immediately the drop starts to accelerate. This continues until the speed has increased so much that the forces are in balance again. That’s why large raindrops fall faster than small ones.
17How large do raindrops actually become? Could we have raindrops that are 10 cm in diameter? To answer that question we first have to look at how drops behave. Just like a balloon, water drops like to be spherical, because this gives the smallest possible surface area for a given volume. It is the attractive forces among molecules that minimize a drop’s surface area. These forces are the basis of surface tension, which acts as though an elastic membrane (like a balloon’s) were wrapped around the drop.
18As a drop falls, it feels the air resistance. For larger and faster drops the increasing air resistance causes the drops to flatten on the downward side (Fig. 1). As the drop reaches a diameter of 5 mm it becomes so unstable that it breaks into smaller drops, which is why we don’t get raindrops the size of footballs. (This can be nicely observed in a vertical wind tunnel, in an air stream at just the right speed to make the drops hang stationary in the air.)
Raindrops stay nice and round up to a diameter of about 3 mm. If they become larger, they flatten on the downward side, the resistance increases and the drops no longer gain speed (Fig. 1).
Fig. 1: As raindrops get bigger they tend to flatten on the underside.
How high are those speeds? For drops 1 mm in diameter the speed turns out to be 16 km/h and for 3 mm drops it’s 28 km/h, which is nearly the maximum. For larger drops any further increase of speed is resisted by the flattening. The fastest drops are those that approach 5 mm in diameter, which achieve about 29 km/h – very little faster than 3 mm drops.
So if you cycle fast, you can travel at the same speed as the fastest raindrops. Of course, they fall vertically and you go horizontally, so the drops strike you at exactly 45°, from the front, which is good to know if you want to use an umbrella on your bike.
07
WHY DON’T FOG DROPS FALL?
Rain and fog both consist of water drops, but rain falls whereas fog just hangs in the air. The only difference is the size of the drops. Large drops fall much faster than small ones (as we just saw in the preceding chapter, which dealt with drops bigger than about 1 mm diameter). Fog drops fall very slowly if at all. The reason is that the gravity force on such tiny drops is very small – because it’s proportional to the mass of the drop, i.e. to the cube of the diameter.
20So far this looks just like the raindrops story. However, the fog drops are so much smaller and fall so much more slowly that a different law of friction applies. The air that flows around the little fog drops is well-behaved, forming nice streamlines that run more or less parallel; this is called laminar flow, and is less turbulent than with larger and faster objects. For droplets smaller than 0.1 mm the friction is directly proportional to the diameter. So when a droplet becomes half the diameter, it will also feel half the air resistance at the same speed, but the force of gravity is only one eighth (because that’s proportional to D3).
Does this mean the fog droplets fall eventually?
Probably, but only very slowly. Take fog droplets of 0.002 mm diameter. That’s about four times the wavelength of light and therefore large enough to be seen with your eyes. (You see the drops as a white cloud.) If you do the fairly complex calculation, you get a speed of 0.1 mm/s (or 36 cm per hour – a bit more than a foot per hour). That is not much – less than 10 m in a whole day. A breath of air will overwhelm the small force of gravity and keep such droplets afloat.
However, some fog droplets really will continue floating even if the air is perfectly still, provided they are small enough! This isn’t so strange – after all, the molecules of air and water don’t fall to the ground either; instead they form the Earth’s atmosphere. Because of thermal motion, gas molecules and other small particles continue floating, so that the atmosphere does not fall on your head, but stretches above you for many kilometres.
You can calculate how small the droplets must be in order to continue floating in the Earth’s atmosphere, like gas molecules do. Because fog drops are much heavier than individual molecules we cannot expect that they will float just as high and form as thick a layer as the atmosphere. To form a “droplet atmosphere” of modest thickness (say one thousandth of the thickness of the real atmosphere, i.e. a layer of fog having an effective thickness of 8 m instead of 8 km) the water droplets will contain some 1,600 water molecules. The diameter of such drops is 4.5 nanometres – about one ten thousandth of the thickness of a human hair. These are tiny droplets, so small that individual drops are invisible to the naked eye. But they don’t fall.
