We were asked in class to use a physics simulator beforehand to test the conditions of an experiment we are going to do and save it to use in our report. The experiment involves the dropping of a ball and measuring its efficiency afterwards Is there any configurable simulator that would allow us to change the height and spin on the ball being dropped, while taking into account air resistance, natural forces, etc? And is it able to give values of kinetic and gravitational energy as well as outputs of the set configuration at any point the ball may be at? Something like  would be good I know an experiment like this doesn't typically need a simulator and the math can be figured out by hand but our teacher has asked us to develop one and share it with him all the same
I'm a physics teacher and I would like to find a simulation software that could be used to give exact numerical answers to high school level problems in Newtonian mechanics.  I want the students to first calcultate a numerical answer to a physics problem and then use the simulator to visualize the problem in order to understand it better and verify that the simlator gives the same answer that they got when doing the calculation themselves.  Here are some examples of what kind of problems I want the students to be able to solve with the simulator:   A slope with a specific angle of inclination and a ball starts rolling at a certain point. Determine the speed, angular momentum and total mechanical energy of the ball after a specific time t. A ladder of known mass and length is leaning against the wall at a specific angle. The contact between the ladder and the wall is frictionless. Calcultate the x and y components of the force between the floor and the ladder.   I would like the software to have the following features:  - Simulation in 2D. No 3D simulations are necessary and the software should at least have the option of doing simulations only in 2D.  - Position all objects exactly by writing numbers (just positioning the objects using the mouse is not precise enough).  - Show animations of the time evolution of the system.  - Show forces, velocities and accelerations as arrows.  - Give exact numerical results so that the students can use the software to verify their calculation.  Ideally the software would have a graphical user interface, but if no suitable software with graphical interface exixts, I could also consider a software with text-based inputs. I would consider both free and commercial software.  My question is: Is there any software that would meet these requirements and if there is, where could I get it?
Does every set have a group structure? I know that there is no vector space having precisely $6$ elements. Does every set have a group structure? Does it just vanish into space leaving nothing behind or does it expel some material?    Also, talking more about black holes, as far as I understand the term "temperature", it is defined by the amount of kinetic energy of the particles of a body and from what I have read, there are no particles inside a black hole, I know that you can find the temperature of a black hole by analyzing its Hawking radiation but I cant really understand how the term "temperature" can be applied to a black hole. Does it mean that whatever is that it is inside a black hole has kinetic energy? Have physicist already experienced the death of any regular black hole (by regular I mean space-sized black holes not micro ones created in labs)? Also, where is the Hawking radiation form? Because if it is released by the black hole I bet it must have formed outside the event horizon, but how exactly? I'm using BibLaTeX to handle my bibliography and I want a reference to be placed in a footnote on every page where I cite the same work and have the same number. Also I want to be able to cite the same work on one page several times. The latter could be done by using  from the Joseph Wright's blog. However, it puts a reference in a footnote only once. So, I know that there is a race in Lord of the Rings of Peredhil  (half elf). Also, in the Hobbit (film trilogy, not book), there is a romance between a dwarf and an elf.  My question is, how do man/elf or dwarf/elf offspring work? Can they not be born? Are they born infertile because they are from parents of two different species? Are elves, dwarves, and men only different "races" of one single primordial species, and can thus reproduce any number of ways? To my knowledge, this isn't addressed in the books or films. My website's google cache copy looks broken.   Below is link to cache.  http://webcache.googleusercontent.com/search?q=cache:http://paintcollar.com  Can this affect the SERPs and crawling by google?  What can I do to rectify it?  PS. Few pages are being cached properly though.Below is URL to one such page. http://webcache.googleusercontent.com/search?q=cache:http://paintcollar.com/aneel How do I find out command line arguments of a running program? I'm looking for a tool or method to find out what command line parameters have been passed to a program, for example when it was run by another program (launcher-application scenario). How to find the sum of this series?  $$\sum_{k=0}^{\infty}\cfrac{{2}^{k}}{\binom{2k+1}{k}}$$  It seems very easy. But I still can not work it out, can anyone help? Let $G$ pe a $p$ group. I have to show that         the number of nonnormal subgroups is divisible by $p$       the number of subgroups differs from the number of normal subgroups by a power of $p$.   Are there any theorem that can help me to prove this ? We have discussed the Sylow theorems but I don't know how to apply them - if those are the theorems I need. (Does this theorem also hold for infinite groups $G$ ?) Can I have 2x2 workspaces in GNOME 3? Recently I created a website with hundreds of thousands of unique pages. A week ago, Google had indexed about 250,000 pages. It has now decreased to 90k URLs (using a site:domain.com query).   What should I do to have Google index all the pages again? Why did all these pages get de-indexed from Google?. I've been try to download Xcode for work, but for some reason the Mac App Store is giving me a bit of trouble. Activity monitor shows some network usage, but in Launchpad it seems the download isn't moving.   When I go to the purchases panel of the Mac App Store, I see this.     No status, no pause button, in fact - the button has no text on it! I've tried restarting the App Store, restarting my computer, even removing the com.apple.appstore folder in /var/folders but alas, no luck.  Can anyone diagnose the issue? When I removed com.apple.appstore, Xcode still showed up on Launchpad, and clicking on it did nothing - it was frozen in time. So can I kill off this partial download and start new? How do you check if a JavaScript Object is a DOM Object? I'm trying to get:  document.createElement('div')  //=&gt; true {tagName: 'foobar something'}  //=&gt; false   In my own scripts, I used to just use this since I never needed tagName as a property:  if (!object.tagName) throw ...;   So for the second object, I came up with the following as a quick solution -- which mostly works. ;)  The problem is, it depends on browsers enforcing read-only properties, which not all do.  function isDOM(obj) {   var tag = obj.tagName;   try {     obj.tagName = '';  // Read-only for DOM, should throw exception     obj.tagName = tag; // Restore for normal objects     return false;   } catch (e) {     return true;   } }   Is there a good substitute? $\displaystyle \int\nolimits_0^8 \sqrt{x^4+4x^2}\,dx$.   Alright, so I thought I had this figured out. Here's what I did:   I factor out an $x^2$ to get $\sqrt{x^2(x^2+4)}$. I let $x = 2\tan(\theta)$, therefore the integrand is $\sqrt{4\tan^2(\theta)  (4\tan^2(\theta) + 4)}$. Factor out a 4 and it becomes $\sqrt{(16\tan^2(\theta)  (\tan^2(\theta) + 1))}$ Which equals $\sqrt{16\tan^2(\theta) \sec^2(\theta)}$ This is easy to take the sqrt of. The integrand becomes $4\tan(\theta)\sec(\theta)$. Now, the integral of this is $4\sec(\theta)$ And it's evaluated from $0$ to $\arctan(4)$ right? Because as $x$ goes to $0$, so does $\theta$, and as $x$ goes to $8$, $\theta$ goes to $\arctan(4)$... But the end result $(4 (\sec(\arctan(4)) - 1) )$ isn't the correct answer   I put it into WolframAlpha and I get $(8/3) (17\sqrt{17} - 1)$, which is the right answer. How did they get that? (there's no "show steps" option)  Any help is greatly appreciated!  PS, what's the syntax for doing sqrts and exponentials? Does copying a spell from a scroll into your spellbook consume the scroll? The text on page 32 of the Basic Rules that talks about copying spells does not explicitly state that the process consumes the scroll. Does it? Cannot remove a repository that complains it has no public key When exactly does combat start and surprise take effect? So say I'm going to ambush an orc. I successfully sneak up on him and I attack. The DM determines that the orc is surprised. The orc happens to get an initiative roll of 19, while I get a 10. How would this work? I can only think of two reasonable resolutions to this.   The orc, having a higher initiative, goes first. Since he's surprised, he does nothing. Then it's my turn. If the orc survives my attack, it is now his turn, and being that the orc has already gone through his round of surprise, he can now attack me or whatever, and combat proceeds as normal. I, having started the combat, go first. If the orc survives my attack, but he is surprised, so he does nothing. It is now my turn again, I attack again. If the orc survives my second attack, it is now his turn, and being that the orc has already gone through his round of surprise, he can now attack me or whatever, and combat proceeds as normal.   Which one of these is correct? neither? Does starting combat secure me a turn/action at the start of initiative order like in option 2? If option 1 is correct, could I ready an action to shoot the orc, effectively granting me a similar first attack as in option 2?  Sorry if this makes no sense. What will Sony do if someone uses my account as primary on another ps4 without my knowledge? What will Sony do if someone uses my account as primary on another ps4 without my knowledge? Will the account be banned? Or will the other guy that has my account as primary be banned? After how long? I have no credit card on my account so I don't care too much but I want to know.   He uses my account on his ps4 as a primary account. I think to use my digital games as free (Sharing, but without my knowledge). How do Minecraft biomes work? I've never seen any information about the distribution of biomes in a generated world.   First, are all types of biomes, guaranteed to exist in a world? Will I always find snow somewhere, and desert somewhere? I've got one world that doesn't seem to have cactus (so I guess the sand is beaches, no actual desert).  Second, is there any kind of pattern or relation to biomes? Is snow to the North, and desert South, for example?  Third, how about density of biomes? If all types do exist, would I find them all within distance X of my spawnpoint, or have to travel for weeks to find a given type? Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$ Let $m,n$ be two integers such that, $m\ge n$. Compute the number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$   There are $n^m$ functions (total).  we subtract from $n^m$ the number of non-surjective functions.  There are $\binom{n}{1}(n-1)^m$ functions missing one element.  There are $\binom{n}{2}(n-2)^m$ functions missing two elements, but how many times did we count this in the previous count ?  Then we have to add this again by inclusion-exclusion but why is the difference always 1? How to test a power supply? My computer powered off the other day on its own, and now when I push the power button, nothing happens. My assumption would naturally be that the power supply is done (possibly well done) but is there any good way to test this before I buy a new one?