# Is there always a Planck length between the particles

## Big Bang HTL 1, textbook

Solutions 153 Solutions 2 The seven basic units of the SI F2 The following conversions apply: 1 inch (or inch) is 2.54cm. If your computer monitor is 17 inches diagonal, that's 43.18 cm. One foot is 12 inches. So a meter is 3.28 feet or 3 feet and 3 3/8 inches. One yard is 91.44 cm. F3 The term dpi means dots per inch, i.e. how many dots per inch (2.54 cm) are printed out. 600 dpi means that a single point is only an incredible 0.0423mm. F4 In Austria, fathoms (1.8965 m), cubits (the large Viennese cubit was 0.7775 m), yokes (5754.642 m 2), buckets (56.589 l) or hundredweight (56.006 kg) were common. F5 144, or a dozen dozen, was called a major. And then there was a shock (60, so 5 dozen) and a big dozen (120). How many dozen are 99? Stupid to calculate, huh? Q9 Our home planet is constantly hit by particles from space, from tiny particles in the solar wind to meteorites. It is roughly estimated that around 40,000 tons of meteorite material fall on the earth every year. But the mass of the earth is so great that you don't even notice it. Why? Simply compare the orders of magnitude: Earth's mass 10 25 kg, increase in mass per year 10 4 kg. Even since the earth began to exist (around 4 billion years ago), its mass has only increased by 10 14 kg. F10 The architecture of a PC is based on the dual system and the numbers are always powers of 2. That is why a kilobyte is not 1000, but 1024 bytes, i.e. 2 10 bytes. A megabyte is 1024 kilobytes and thus 1024 2 or 1 048 576 bytes, one gigabyte is 1 073 741 824 bytes. If you are accurate! But you can also get by with the fact that 1 gigabyte is about 10 9 bytes. FLOP is the abbreviation for "Floating Point Operations per Second", ie floating point operations per second. The computing speed is given in teraflops. The super supercomputers in 2015 had over 33,000 teraflops, i.e. over 33 quadrillion arithmetic operations per second. F13 F16 Every object expands when heated. In the case of metal, this effect is very large, by the way. On the other hand, metal is very robust. The problem is that you have to pay attention to the temperature when measuring length. If the original meter is heated from 0 ° C to 20 ° C, it is extended by 0.3mm. Q17 Is there a largest and smallest length? In theory not, but in purely practical terms there is an upper and lower limit. The sensible upper limit results from the diameter of the visible universe. According to today's view, it is around 10 26 m. If something were even longer, it could not be accommodated in the visible universe. At the lower end of the meaningfulness is the Planck length of 10–35 m. Every object that would be smaller than Planck's length would have so much energy or mass due to the so-called uncertainty relation (see Volume III) that it would collapse into a black hole whose gravity is so high that not even light can escape can (see Volume III). What is smaller cannot be measured. And not because our technology is too bad, but because the laws of nature do not allow it. (Note: The uncertainty principle states that the momentum and location of a particle cannot be measured with unlimited precision and is a core part of quantum mechanics. A black hole is a burned-out and collapsed star whose gravity becomes so high that not even light can escape. ) F18 The objects have a thickness of 4.6mm and 15.5mm. F20 From 1983 is the current definition for the meter. At that time it was determined with the help of the time that the light needs for 1 m. As a result, meters and the speed of light are inextricably linked. Measuring the speed of light has become meaningless because the definition of the meter can be used to calculate the speed of light without measurement: c = s / t = 1 m / (1/299 792 458) s = 299 792 458 m / s. The measurement only makes sense to calibrate a device! F22 The sun (apparently of course) rotates around the earth once every 24 hours, so that's 360 °. So in one hour it rotates 360 ° / 24 = 15 °. Q24 The shortest sensible time is the Planck time (see also question 17). This is the time it takes for light to travel the Planck length, and it is in the order of magnitude of 10–43 s: a) 3.7 · 10 6 d) 12 · 10 3 = 1.2 · 10 4 g) 7 · 10 -2 j) 6.37 · 10 6 mb) 52 · 10 9 = 5.2 · 10 10 e) 2 · 10 -6 h) 3 · 10 -3 k) 0.37 · 10 9 mc) 2 · 10 5 f) 7 · 10 –9 i) 5 · 10 –7 ml) 0.3 · 10 –9 m The greatest meaningful time is the age of the universe. There can't be anything older! According to today's view, the age of the universe is 13.8 billion years, that is about 4 · 10 17 seconds. F25 / 26 The period of oscillation of a thread pendulum is independent of the mass and, in the case of small deflections, also of the oscillation amplitude. Perhaps you have also found out that t depends on the root of the pendulum length, i.e. four times the pendulum length, twice the oscillation period. The equation that can be used to calculate the period of oscillation is: g is the acceleration due to gravity (see Section 4.4.1) and is 9.81 ms –2. You want a pendulum that swings back and forth once in 2 seconds. For a half oscillation it is therefore 1 second and that is why it is also called a second pendulum. Shape around: A seconds pendulum is therefore almost 1 m long. Q27 The answer is a). The mass of an object always remains the same. What can change is weight. The weight of the astronauts on the moon is about 1/6 of that on earth, but the mass is the same! The astronaut's mass is still the same even when he is floating weightlessly in space. So mass is immutable. F29 The volume of a sphere can be calculated with V = (4 r 3 π) / 3 and is approximately 4.2 m 3 for a sphere with a radius of 1 m. Since one cubic meter of cork has a mass of 300kg, that adds up to 1260kg! Q31 You can see from the table that air has a mass of around 1.2kg per m 3. So you just have to estimate the volume of the physics room. For example, if it is 12 m long, 6 m wide and 3.5 m high, its volume is 252 m 3 and the air mass is therefore around 300 kg. Surprisingly too, isn't it? 3 Vector and Scalar F8 Only the unit Newton belongs to a vector quantity, the force. 4 Straight movements F7 It doesn't matter in which direction the stick is thrown. The distance run depends only on the dog's running speed. If he runs at about 15 km / h for an hour, then he covers 15 km. F10 F21 The speed of light is always the same, no matter what movement you make. That is why the trucks also measure the same speed. If they measured different speeds, then the theory of relativity would be wrong. F22 v = s / t, therefore t = s / v. The result is in seconds and has to be converted first. The values from the table then result in around 2 hours and 16 minutes for women and 2 hours and 5 minutes for men. F23 The circumference of the earth is about 40 · 10 6 m and the light has 3 · 10 8 m / s. So that makes pretty much 7.5 laps per second. Very fast! F25 The equation for the depth of fall is s = (a / 2) t 2. In this case you just have to insert 3.72 m / s 2 for the acceleration a. This results in the following depths of fall for the first 6 seconds: 1.86 m, 7.44 m, 16.74 m, 29.76 m, 46.5 m and 66.96 m. The acceleration due to gravity is about 1/3 of the earth, therefore the depth of fall per time is only 1/3 of the value on earth. t l g = 2 π l t g m cm = = ≈ 2 2 4 0 99 396 99 4,, π For testing purposes only - property of the publisher öbv

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