Is it necessary that if we concider a system then always work done by internal forces would be equal to zero? I am getting confused in between these two cases: Case 1: When we solve pulley-block problems using work-energy theorem then the work done by tension force gets cancelled out because in one block tension and displacement is in same direction while the other end these two will be in opposite direction so work done by tension +TS and -TS gets cancelled out. Case 2: Concider 2 electrons in space. These two have a repulsive electrostatic force in between them and both have work done positive (qe) (S) where S is displacement. So in case 1 when we considered a system the internal forces turned out to be zero and when we considered case 2 when the internal forces didn't get cancelled out but got added up.. So isn't it wrong to say that work done by internal forces is always 0 if we concider a system.
Can internal forces do work? My Mechanics textbook claims that the sum of the work by internal forces is not generally zero.  translated to English the paragraph reads:     Notice about the work by internal forces: the work by the internal forces is in general not equal to zero although the sum of the internal forces is always equal to zero. Since the work also depends on the relative displacement of the two pointmasses in the material system, the work provided by these 2 internal forces will generally not be equal to zero.   Other sources claim that the work done by internal forces is always zero.  (answer by Mark Eichenlaub)     Then I didn't do any work on the system at all since, by definition, only external forces can do work.        the net work done by internal forces is zero since they do not cause motion of the object.   To me it would seem that these sources contradict eachother. Do they? If so, which one is correct? If not, please explain why they don't contradict eachother.
I usually try to avoid lens flare, usually by avoiding shooting directly into bright lights (or using  to minimize it). However, sometimes I find a situation where lens flare actually adds to the image.  What can I do to effectively incorporate lens flare into my image? Also, are there any ways to do so while minimizing loss of contrast? Is it true that quantum mechanics technically allows anything to happen? Maybe this is a silly question (I think it is), but it's a question I'm arguing with some of my friends for a long time.  The ultimate question is: Is everything (in our Universe) possible ?  I've read some books (Penrose, Hawking, Greene, etc.) where it was clearly stated several times that quantum mechanics allows any situation to happen (e.g. everything is possible) - even with absurdly tiny probabilities?  Does this mean only physically possible - or "ultimate" possible ?  For example (I know this example seems really absurd, but I'm saying this so you get the idea) what my friends clame it is possible:   If I ask my friend(s): "Is it possible there is a Sun-sized star in my pocket right now?" They will respond: "Yes, there is very very tiny possibility this can be true!" Etc. We are asked the following:      let $f(x)$ be a continuous function on $[0, 1]$ such that   $$\int _ {0} ^ {1} \ f(y) dy = 1$$   prove that $f(x) = 1$ for some $x ∈ [0, 1]$   The question asks to take into account Rolle's Theorem and Mean Value Theorem.  I'm aware of the definitions, but I am really unsure how to answer this question and my tutors are not really responding till after easter.    Could someone please help? Why is there a "y" involved?  Thanks you How to close view windows? How do I shuffle cards for a card game? I am trying to develop an card game for Android Can anyone suggest me how to write code for effectively shuffling the playing cards? How to determine if the specific time is between given time range in javascript Say i have this PHP code:  $FooBar = "a string";   i then need a function like this:  print_var_name($FooBar);   which prints:  FooBar   Any Ideas how to achieve this? Is this even possible in PHP? After update, get "error: file not found." followed by "grub rescue> _" UTF-8 encoding a servlet form submission with Tomcat Why does my bread keep 'blowing out'? Instead of swelling as a whole loaf, my loaf will often expand in the oven off to the side or the bottom - looking 'blown out', a big tear.  This results in a loaf that leans to one side, doesn't rise well, or generally doesn't look good.    Why is this happening and what can I do about it? How to change from csh to bash as default shell I have csh as my default shell, as shown by echo $SHELL. I want to switch to bash as my default shell. I tried the following approaches to no avail:   With chsh I get:  chsh: can only change local entries; use ypchsh instead.  With ypchsh I get:  ypchsh: yppasswdd not running on NIS master host ("dcsun2").    I only have .chsrc in my home directory and I cannot find any .profile files in /etc. How can I change my default shell to bash? How to access object attribute given string corresponding to name of that attribute A person that professes discrimination based on race is a racist.  What is the word for defining a person that discriminates based on culture (pretty sure it is not culturist) or social habits?  E.g., Eric Cartman doesn't like hippies, he discriminates against them. But a hippie is not a race, an ethnic, a religion or a nationality. It is a life style not related to any of these. Why was a fox able to think about the hobbits on the road to Rivendell? $\int_0^{\infty} f(x)dx$ converges and $\lim_{x\rightarrow \infty} f(x)$ exists, then $\lim_{x\rightarrow \infty} f(x)=0$? How can I write a unit test to determine whether an object can be garbage collected? If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$. Having some trouble proving this:     If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show: $\lim _{x\to \infty } (f(x+1)-f(x))=0$   Attempt: from $\int \lim _{x\rightarrow \infty } f^\prime(x) \mathrm{d}x=0$ we can say that $f^\prime(x)=const$ would we then have to show that  $\lim _{x\to \infty } (f(x+1))$ is also a constant? From there if we show that both are equal then the difference is zero. I am on the right track?  Thank you for the help. I looked up a few grammar-teaching websites (in Chinese language). The website says many people do not use the phrase "A xxx of" correctly because they do not identify the subject of the phrase correctly.   The website says phrases like "A range of; A high percentage of" is singular, while "a number of; a group of; a couple of; a total of" is plural.  Therefore according to the website, the correct sentences should be as follows.     A wide range of courses is available. ("A wide range" is the subject)      A high percentage of peptides that are made of amino acids is present   in the sample. ("A high percentage" is the subject)      A number/ group/ couple of people were killed in the earthquake.("people" is the subject )       A total of 230 employees were laid off. ("employees" is the subject)   I don't get the pattern here. All of this looks (or should I use "look"?) arbitrary to me. In fact I thought this phrase is supposed to be arbitrary and whether the phrase is plural or singular should depend on the the person's own judgment.   How do I identify the correct subject in the "A xxx of" phrase? This is an attempt to gather together the various questions about time that have been asked on this site and provide a single set of hopefully authoritative answers. Specifically we attempt to address issues such as:   What do physicists mean by time? How does time flow? Why is there an arrow of time? Make it cost more to downvote without comment; make it hurt to leave a crap comment Possible Duplicate:    In the spirit of &quot;encouraging&quot; people to leave comments on downvoting, I would propose that if someone downvotes without a comment, I propose a heavy point tax, say 3x the current point cost for a downvote. If he or she downvotes and leaves a comment, then it costs the current amount. If someone leaves a crap comment (to avoid the &quot;charge&quot;) they get a painful spank (100 points gone or whatever the community decides) if and only if:  The comment is flagged Three (five? whatever) moderators agree it is crap  Common complaints Or, why my proposal is different.  &quot;  a &quot;   No it isn't. I specifically address the issue of leaving garbage comments to avoid the downvote tax, unlike the other proposals.   &quot;Some people want to leave anonymous (down)votes.&quot;  I understand that some might be fearful of retaliation. Is retaliation a real problem or a &quot;what if&quot; conjecture? (Where's the data?) What if we try it for 3-6 months and then circle back to see how well it works?  If a user starts retaliating against another user, they will be dealt with as are all other problem users. Nothing else is anonymous - asking questions, answering questions, editing questions, leaving comments, etc. and there is a clear benefit. What is the benefit to the community for having anonymous voting? I would argue &quot;none.&quot; Even though some people might want to leave anonymous questions, answer anonymously or anonymously edit a question, it is not allowed, because it is not good for the community.   &quot;But this will discourage downvoting&quot;  I agree, and I think that's a good thing, which goes to the philosophy of the site: promote good questions and answers. If a question or answer is poor, few will up-vote it. If is is really poor, it will get flagged and . If someone really wants to downvote, no one is stopping him or her. Just as we want quality questions and answers, we need quality voting.   It will require too much work to implement  Maybe. Let's ask if it is worth the effort. What benefit does anonymous, no-comment downvoting add to the site? It certainly doesn't allow the author to improve. What benefit would owned, commented downvoting add? It would hopefully allow authors to improve and discourage drive-by downvoting. Would me (or someone else) submitting a patch alleviate this complaint?   Jeff (or Joel) thinks this is a stupid feature, and you're stupid for suggesting it.  &quot;&quot; Is this a true statement?    Thanks for reading.