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In general, no. You need to know the spring constant. Think of it this way: A block of granite is a spring, albeit a very stiff one. A pile of air mattresses is also a spring, albeit a very non-stiff one. Dropping a bowling ball from the same height onto a block of granite versus dropping one from the same height but onto a pile of air mattresses will result in forces of significantly different magnitudes acting on the bowling ball. Merged post follows: Consecutive posts merged And the damping coefficient as well. Scales are obviously fairly heavily damped; ideally, they are critically damped. Suppose your mass is 160 lb. Step on an undamped scale and the weight shown on the scale will oscillate between 0 and 320 pounds and never stop. Even a lousy scale will settle to 160 lb, and do so rather quickly.

Not really, not really what? The original poster was inquiring about the maximum value that would be shown on the scale. That number depends on the spring coefficient of the scale. Terrible article, and yet another example of why wikipedia is (or can be) an awful source. There are (at least) four technical definitions of the term weight. Legally (and colloquially), weight is a synonym for mass. It is not a unit of force in this sense. This sense predates the use of the term in physics, so in a sense this is the definition that should prevail. Look at it this way: We scientists do not like it when the lay community usurps/abuses scientific terminology (e.g., "Evolution is only a theory"). We similarly should not usurp/abuse common terms. In most introductory physics texts (up to sophomore year in college) and many engineering texts, weight is a synonym for gravitational force. There is one problem with this definition: It is an immeasurable quantity. In a few introductory physics texts and some aerospace engineering texts, weight is the net sum of all forces acting on a body except the gravitational force. Most general relativity texts use a definition that is closely allied with definition #3: weight is a synonym for proper acceleration, which is what ideal accelerometers measure. Multiply this by rest mass and you get something very similar to what scales measure. Scales measure the net sum of all forces acting on a body except the gravitational force. In other words, it is definitions #3/#4 that are in play here, not the freshman physics definition of weight (which, once again is immeasurable), and not the legal/colloquial definition, either.

The first is bureaucratic overhead. Just because Gates cuts it (assuming he can cut it) does not necessarily equate to a troop reduction. It might just mean that people are transferred from bureaucratic bloat positions to operations. One reason the military has so many top-level positions is because many reach their level of incompetence after getting promoted to colonel (or equivalent). The military can't get rid of them anymore -- but they can give them an up and out. That bureaucratic overhead and top-level bloat are exactly the kind of small potatoes to which Pangloss was referring. 15 billion out of 550 billion is 2.7% -- pretty small potatoes.

Not for me, personally. Not for decades and decades and decades. (What happened in the 60s stays in the 60s.)

Depends on which ounce you use (there are several). The weight of a fluid ounce of water is just about an ounce. One imperial fluid ounce of water at 62 F weighs (weighed) exactly one avoirdupois ounce. A US customary fluid ounce, 1/128 of a US gallon, is a bit bigger than an imperial fluid ounce and weighs a bit more than an ounce. For whatever reason, the FDA uses its own definitions. From US regulation 21 CFR 101.9(b)(5)(viii), For nutrition labeling purposes, a teaspoon means 5 milliliters (mL), a tablespoon means 15 mL, a cup means 240 mL, 1 fl oz means 30 mL, and 1 oz in weight means 28 g. ============================ Nobody has mentioned stuff that some shady people illicitly sell in plastic bags.

Sociopaths know the difference between right and wrong; they just don't care about the difference. Some do care, but they revel in their wrongness. A (the?) primary purpose of criminal law is to protect the rest of us from those sickos. Mentally insane and mentally infirmed do not know the difference. That is why the law treats them very differently than it does sociopaths.

It appears that Apple has banned *all* third party APIs and third party development tools. From the iPhone Developer Program License Agreement (source: http://daringfireball.net/2010/04/iphone_agreement_bans_flash_compiler): 3.3.1 — Applications may only use Documented APIs in the manner prescribed by Apple and must not use or call any private APIs. Applications must be originally written in Objective-C, C, C++, or JavaScript as executed by the iPhone OS WebKit engine, and only code written in C, C++, and Objective-C may compile and directly link against the Documented APIs (e.g., Applications that link to Documented APIs through an intermediary translation or compatibility layer or tool are prohibited). Smart? Maybe, maybe not. I can attest that Flash has been the number one reason that Safari crashes, and that and Acrobat was the number one reason that Safari crashed on my old and not-quite standard Mac (then again, it might have been that I had an old and not-quite standard Mac). I have to wonder whether the DOJ/FTC are going after Apple because, well, they have to go after somebody; going after evildoers is there job. Banks are off-limits, and Microsoft is too big to attack.

Tachyons are purely hypothetical entities.

Oops. I misread your post. I thought you said f(x) = 1 if x is irrational, 0 if x is rational. That function integrates to F(x)=x+c. That is the standard gotcha problem used to introduce Lebesgue integration. You switched the values so that f(x)=1 if x is rational, 0 if x is irrational. This function is zero almost everywhere. It integrates to a constant.

This integrates to F(x)=x+c.

If you mean something like [math]f(x) = \Biggl\{\array{ll} 0 & x=0 \\ \pi & x\ne 0\endarray[/math] then yes, [math]f(x)dx[/math] is exact. It integrates to [math]F(x) = \pi x + c[/math] Note that [math]\frac {dF}{dx} = f(x) \,\text{a.e.}[/math]

From the OP, (emphasis mine): In other words, [math]\int_C\vec F\cdot d\vec l[/math]. We are talking about exactly the same thing here, triclino. I am being explicit in showing that the integral is a path integral. A differential will always be exact if the underlying space truly is one dimensional (which is implicit in what you wrote). Inexact differentials only appear in higher dimensional spaces. A differential [math]\partial F \equiv \sum_i f_i(x) dx_i[/math] is exact if There exists some differentiable function [math]\phi(x_1,...,x_n)[/math] such that [math]\nabla \phi(\vec x) = \vec f(\vec x)[/math], or The integral [math]\int_{\vec a}^{\vec b} \partial F[/math] is the same for all paths that start at point [math]\vec a[/math] and end at point [math]\vec b[/math]. There are many other tests for an exact (or total) differential.

OK, so we're just showin' off? The u-substitution [math]u = -\sqrt{x/4+1}[/math] works quite nicely here. With this substitution, [math]\frac 1 {x\sqrt{x+4}}\,dx\,\rightarrow\,\frac{du}{1-u^2}[/math] This integrates to tanh-1u for u<1, coth-1u for u>1, or more compactly, [math]\int \frac{du}{1-u^2} = \frac 1 2 \ln \left|\frac{u+1}{u-1}\right|[/math] Undoing the u-substitution, [math]\int\frac 1 {x\sqrt{x+4}}\,dx = \frac 1 2 \ln \frac {|\sqrt{x/4+1}-1|}{\sqrt{x/4+1}+1} = \frac 1 2 \ln \frac {|\sqrt{x+4}-2|}{\sqrt{x+4}+2}[/math]

No. You cannot do that. I posted this earlier, but my post was mistakenly moved along many other posts in the cleanup of the hijack of this thread. A better way to express work is [math]W = \int_C \vec F \cdot d\vec l[/math] Force [math]\vec F[/math] and the differential length [math]d\vec l[/math] are vectors. What you did is invalid. You are once again treating vectors as if they are scalars.

No, it is not. Suppose you need to bring a gas from pressure P0 and volume V0 to pressure P1 and volume V1. The amount of work done depends on the path taken through the P,V phase state. For example, consider these two paths: Change the volume from V0 to V1 while maintaining a constant pressure P0, then change the pressure from P0 to P1 at constant volume V1. Change the pressure from P0 to P1 at constant volume V0, then change the volume from V0 to V1 while maintaining a constant pressure P1. Both paths achieve the desired goal. The work done is P0*(V1-V0) for the first path, P1*(V1-V0) for the second. Clearly these are not the same except for the trivial cases V1=V0 or P1=P0. That the result of some integration depends not only on the initial and final states but also on the path taken from the initial state to the final state is one of the signature characteristics of an inexact differential.

You cannot consider [math]\partial W[/math] an exact differential because it is not an exact differential. Do you know what the phrase "exact differential" means?

I don't know what charlatan was babbling on about, triclino. [math]\partial W = \vec F \cdot d\vec l[/math] is correct. The only difference between what you wrote in the OP and what I just wrote about is that I am explicitly showing that [math]\vec F[/math] and [math]d\vec l[/math] are vectors.

OK, then. We agree then that the policy right now is that nuclear weapons are off the table as a response to an attack with non-nuclear WMD. Isn't that exactly what Fox News said? Continuing (emphasis mine): Now we are venturing into the realm of opinion rather than fact. My opinion: Changing the policy after the fact and reacting with this newly changed policy would be a case of "too late". A nuclear response might start a nuclear exchange with countries that truly can wipe us (and all of humanity) off the map. There you go again, bascule. You ofttimes are the first to accuse someone of using fallacies. Why then do you have such a proclivity to employ them yourself? Here you are quoting out of context to create a straw man. Putting your quote of my statement in context, Stop with the fallacies, bascule.

That you are moving of the goal posts is a bit obvious. You have claimed that the entire quote is baseless. Your basis for this claim was a statement made by Hillary Clinton rather than Robert Gates. So, "mea culpa", but lets move the goal posts anyhow and attack again. The fallacy is that your are using a straw man argument. I explicitly said that the policy is "If any state eligible for this assurance were to use chemical or biological weapons against the United States or its allies or partners, it would face the prospect of a devastating conventional military response," not some waffle words about how this weak administration might change this verbose statement in some hypothetical future. The issue is not what the policy might be in some hypothetical future; the issue is what the policy is now. Do you deny that the policy right now is that nuclear weapons are off the table even if a Non Proliferation Treaty signatory attacks us with non-nuclear WMD?

All right then. So, what will bascule do next: Move the goal posts, or use some fallacy? Which one, which one? We have a winner! Both!

Well there you go again, bascule. Bzzzt, wrong! Last time I checked Robert Gates and Hillary Clinton are not the same person. Let's see what Robert Gates said: http://www.jcs.mil/speech.aspx?ID=1355 To these ends, the NPR [Nuclear Policy Review] includes significant changes to the U.S. nuclear posture. New declaratory policies remove some of the calculated ambiguity in previous U.S. declaratory policy. If a non-nuclear-weapon state is in compliance with the nonproliferation treaty and its obligations, the U.S. pledges not to use or threaten to use nuclear weapons against it. If any state eligible for this assurance were to use chemical or biological weapons against the United States or its allies or partners, it would face the prospect of a devastating conventional military response. Still, given the catastrophic potential of biological weapons and the rapid pace of biotechnology development, the United States reserves the right to make any adjustment to this policy that may be warranted by the evolution and proliferation of biological weapons. The second paragraph is IMHO a useless appendage. The Executive branch always has the right to make adjustments to policies that are strictly the domain of the Executive branch. All Gates was saying in that paragraph was that, like past Democratic and Republican administrations, this current administration reserves the right to renege on its promises. The first paragraph summarizes the new policy. Straight from the horse's mouth, "the NPR includes significant changes to the U.S. nuclear posture." Again continuing with the horse's mouth, "If a non-nuclear-weapon state is in compliance with the nonproliferation treaty and its obligations, the U.S. pledges not to use or threaten to use nuclear weapons against it. If any state eligible for this assurance were to use chemical or biological weapons against the United States or its allies or partners, it would face the prospect of a devastating conventional military response." The only quibble then is the meaning of the verbose "If any state eligible for this assurance were to use chemical or biological weapons against the United States or its allies or partners, it would face the prospect of a devastating conventional military response" versus the summarized version "-- even in the case of a biological or chemical attack."

What factual inaccuracies? The quoted phase is exact, and the non-quoted phrase is a fair summary of Gates statements regarding using conventional means to redress non-nuclear WMD attacks on the US. Whether this represents a major change in policy is a matter of opinion. Fox News was far from alone in deeming this to represent a sea change. Fox News was far from alone in mingling reporting and editorializing. From several articles that I read, other news sources tended to editorialize that this was but a minor change, still others thought this was not near enough of a change. Now I am going to turn the table. You, not Fox, are the one who is obfuscating here. You are talking about hypothetical changes to the policy, not what the policy is now. The only thing wrong with my statement is that I should qualified "That is a huge change in policy" with "in my opinion". I verified the text I quoted from multiple sources. Gates did say what Fox claimed he said -- including the paraphrased 'even in the case of a biological or chemical attack.' Hypothetical changes to the policy in the future are just that: hypothetical. They are not what the policy is now. BTW, believe it or not I do not get my news from Fox. The first time I saw that article was after reading toastywombel's opening post. Good for you. That is your free choice. What is sad is your insistence on enforcing your views on everyone else. =================================== Thanks for that voice of reason. Between this thread, the thread on killing rich people (which I find to be absolutely repugnant), and other recent threads here, I was on the verge of abandoning my position at this site.

Are you sure about that? There are venues where the people with the best strength+technique cannot be selected because those venues specifically rule out selecting said 'best' individuals. I don't know if challenges to the legality of these venues have been made, but nonetheless such organizations certainly do exist. Merged post follows: Consecutive posts mergedHmmm. I don't particularly like it when other users come in with an ambush post and here I did just that. So, being upfront, I am talking about profession women sports venues. The NBA, NFL, MLB and the PGA (amongst others) do not have rules against women competing with the men in professional basketball, football, baseball, and golf. The WNBA, IWFL, National Pro Fastpitch, and LPGA do have rules against men competing with the women in professional basketball, football, softball, and golf.

Short answer: Because that is the only value that makes sense. Long answer: Let's start with the truth table for implication, if P then Q, or [math]P\rightarrow Q[/math], or [math]P \Rightarrow Q[/math]. Here I am using 0 to indicate false, 1 to indicate true. [math] \begin{array}{l|ll} \multicolumn{1}{c}{}&\multicolumn{2}{c}{Q} \\ P & 0 & 1 \\ \hline 0& 1 & 1 \\ 1& 0 & 1 \end{array} [/math] How to construct that? There are two valid production rules associated with implication. These are modus ponens and modus tollens. The first is what lets us derive Q from knowledge that both P and if P then Q are true statements. The latter is what lets us derive ~P from knowledge that Q is a false statement but if P then Q is a true statement. Modus ponens tells us that the bottom row (P=1) of the truth table must be 0 for Q=0 and 1 for Q=1. Modus tollens tells us that the left column (Q=0) of the truth table must be 1 for P=0 and 0 for P=1. Thus the truth table for implication must look like [math] \begin{array}{l|ll} \multicolumn{1}{c}{}&\multicolumn{2}{c}{Q} \\ P & 0 & 1 \\ \hline 0& 1 & ? \\ 1& 0 & 1 \end{array} [/math] There are also two invalid production rules that people try to associate with implication. These are affirming the consequent and denying the antecedent. The first says that trying to draw a conclusion from if P then Q given that Q is a true statement is invalid, while the second says that trying to draw a conclusion from if P then Q given that P is a false statement is invalid. These mean respectively that the two entries in the top row (P=0) must be equal to one another and that the two entries in the right column (Q=1) must be equal to one another. There is one unknown element in the as-constructed truth table, and the above says this must be 1 (true). The completed truth table is thus [math] \begin{array}{l|ll} \multicolumn{1}{c}{}&\multicolumn{2}{c}{Q} \\ P & 0 & 1 \\ \hline 0& 1 & 1 \\ 1& 0 & 1 \end{array} [/math]

One is a difference of degree, the other a difference of kind. There is a difference between men and women (and long live the difference), but in terms of mental differences, those differences relatively small. All men are not equally good at physics skills. They fall in a spectrum, roughly a bell curve. Women's physics/math capabilities similarly fall in a spectrum that is roughly a bell curve. These two curves might have different means and variances, but there is an incredible overlap as well. If you lump these two populations together you will still see something that is very close to a bell curve. Now compare the people who have a physics degree from MIT versus those with the same degree from 4th tier podunk U. Some curve will characterize the diversity of physics/math skills in each of these two groups. If you lump these two populations together you will see two distinct populations. The lumped population will be bimodal. There might be some overlap at the extremes, but in general it is easy to guess whether someone came from MIT or Podunk based solely on their skills. Conversely, it is easy to accurately predict future performance based on the school they attended.