Rolling a 14-sided die - Physics Stack Exchange
WEBJan 10, 2017 · 2. Suppose we make a 14 sided die by taking a cube and slicing a triangular pyramid off each corner, such that there are now 6 square faces and 8 triangular faces, each with unit side length (in other words, a cuboctahedron). Assuming that the die is an evenly weighted solid and rolled with plenty of energy, what is the probability of it ...
"Regular" 20-sided die, vs "life counter" 20-sided die. Same …
WEBRegular dice are made such that opposite sides of the die add to 1+the number of sides. For example, a 20-sided die has 14 and 7 opposite of each other, adding to 21. For certain types of games, "life counter" die are used. In these, sides are numbered sequentially, so that 1 is next to 2, which is next to 3, which is next to 4, and so on.
Creating a fair 3 sided coin - Physics Stack Exchange
WEBThe easier solution than a three sided prism is a three sided top, the side that is on the ground is the one that is counted. Seriously, by far the easiest way is to find it empirically. Take several coins and find the number of coins it is required to make a fair one by piling them together. The problem seems to be hard from the theoretical ...
Why is pressure in a liquid the same in all directions?
WEBJul 11, 2012 · 12. I'd like answers both in the more intuitive side an on the more precise side. Thinking of water as "cubes" of water, for example, would allow pressure in the z axis to be independent of the y or x axis. Choosing other "shapes", like a triangular prism, yield different results. Will this fact, then, be dependent on the format of the ...
How to determine the probabilities for a cuboid die?
WEBFor a cuboid, we can figure out the solid angle of a face by doing an integral, Ω = ∬Sˆr ⋅ dA r2. as given on MathWorld. Take the face to lie in the plane z = Z (capital letters will be constants) and to have dimensions 2X × 2Y. The integral then becomes.
How does a half-life work? - Physics Stack Exchange
WEBJun 10, 2015 · The right way to think about this is that, over 5,730 years, each single carbon-14 atom has a 50% chance of decaying. Since a typical sample has a huge number of atoms 1 , and since they decay more or less independently 2 , we can statistically say, with a very high accuracy, that after 5,730 years half of all the original carbon-14 atoms …
Total Entropy and Entropy per trial - Physics Stack Exchange
WEBJan 24, 2018 · It's a bit unclear which part of it has had you confused, and I don't have access to your book, but from your equations $(5.1)$ and $(5.2)$ I reckon the author is simply showing how the definition of entropy in terms of log of multiplicity (number of microstates), can be re-expressed in terms of a probability distribution.
radioactivity - Why does a collection of radioactive atoms show ...
WEBJul 19, 2020 · Think about a six sided die. The die has a very specific structure. It's highly symmetrical. Because of this, we can say with a great deal of certainty that if you roll that die 10,000 times, about 1/6th of the time it will show a 2. The radioactive decay process for billions of identical atoms is just like rolling billions of uniformly ...
statistical mechanics - Can the second law of thermodynamics be ...
WEBApr 28, 2016 · Does it also mean that negative entropy change in a closed system can occur if the system is small enough and it's tried repeatedly enough? Kind of like if you keep guessing the outcome of a 6-sided dice several times at some point you'll get it right. If yes, has it been demonstrated by experiment?
radioactivity - Why is radioactive decay dependent on amount of ...
WEBIt's like rolling lots dice, the number of dice showing a certain digit will be proportional to the number of dice you roll. Continuing this analogy, say you remove a die if it shows 1. This correspond to a nucleus decaying. Then at first many dice will be removed, but as the number of dice grow smaller so will the number that are removed.