DerSpooky

(with a little refresher from a text book) L'Hopitals rule says that if you have two functions f and g that are differentiable over an interval (a,b) except maybe at a point c within the interval, and given that the lim(x to c) f(x)/g(x) is in the indeterminate form 0/0 or infinity/infinity, then if the lim (x to c) f'(x)/g'(x)=L (or +/- infinity) where the g'(x) doesn't equal 0 we can say limf(x)/g(x)=limf'(x)/g'(x) translation...when your limit goes to 0/0, or infinity/infinity, you can take the limit of the derivatives of both functions (don't use the quotient rule!) and you will get the same answer, as long as the derivative of the denominater doesn't equal zero. (this cuts out some of the finer details above that are still important!)

I can't think of any web sites, but here are some tips: 1. When converting between standard and metric units, or any other identity relationship like Avogadros number (i.e. molecules/mole or inches/cm), multiply your quantity by the identity ratio (like inches/cm) that will cross cancel your units and leave behind the ones you want. ex. 10in(2.54cm/1in)=25.4cm...my inches cancel and im left with cm in the numerator. 2. When using SI units it is just a shift of the decimal. Sometimes you may have to do a number of conversions and this is simplified by using scientific notation where everything is multiplied by magnitudes of ten. Conversions then become addition and subtraction problems as you divide or multiply by orders of ten, with the occasional multiplication problem when raising a conversion to a power (like 10^4cm^2/m^2=[10^2cm/m]^2). This is a lot easier then dealing with the evil tyrant that is the standard(US) system.

I do what pulkit does. If you have two positive roots of 2, I would only say that it has a root of positive two, one unique solution. If instead it were 2 and 3, than I would say it had the roots of 2 and 3.

http://ocw.mit.edu/OcwWeb/Physics/index.htm I just found this site on a thread. It is great! Click on different physics courses listed and you will find lecture notes, problem sets with solutions, and old quizzes for different physics courses. There are even fully taped (I think the whole semester, 35 each) lectures for the undergrad lower division mechanics and electromagnetism.

Another way to think about this is to consider conservation principles. As everyone has said, momentum is conserved, and in your case the constant of the total momentum is zero. This means that just as long as the two bullets have the same magnitude of speed in opposite directions, or none at all, we are happy and momentum is conserved. The second consideration is the conservation of mechanical energy, or simply kinetic and thermal energy. The energy of our two bullet system cannot simply disappear, and depending on thermometric properties and environmental conditions, you can speculate on the outcome of this event. I would expect a ricochet at lesser speeds than approaching, and considering the symmetry of the problem with identical bullets, they would bounce back in opposite directions and follow parabolic paths.

It is common to distinguish between unique roots.

I think you meant that when you change the path of light by a very small amount there will ne no first order (substantial) change in the time it takes for light to follow the new path, only a second order (less substantial) change in time (approximately). Think about binomial series approximations. Feynman sums up in the next sentence that light follows a path that is surrounded other paths that take just a little bit different time to traverse, but not substantially.

The mass could vary depending on the velocity and liberation of energy during the collision. The atomic bomb is a large number of collisions (Uranium 235)releasing a substantial amount of energy into the environment. This causes a noticable difference in mass (about two grams less) in surrounding material samples. Energy transfer is the relation between mass and collisions.

...evil...my picture is destroyed... ...it was a masterpiece...

This is a Centimeter... This is an Erg... _______ __ __ / \ _;;_ || || ____ / \/ 0 0 \ __||___||___/ \ ||_______|| \____/ \ /\_x_x_/ ||__ ||__ \________/ ;; So what exactly is an erg? ... ...An Erg is a Dyne Centimer!

maybe dave did it for part three, with Bob and Carl telling the truth...

Many physicists of the recent past concerned themselves with the limitations technology may play in our understanding of nature. One example of this would be the degree of uncertainty maintained as an axiom of quantum mechanics, stating that the more we try to see what nature does, the more she will lie and say that its none of our business. It seems that we have reached a point in that our presence has become a significant disturbance to the behavior of certain natural phenomena. Technological advances may improve our "poking sticks" a little more here and there, which could have a significant impact on current research in progress; However, the scientific method, based so much on the greeks, may have to adapt to the conundrums that present scientific investigation must face. An example would be to use technological advances to understand an area such as supersymmetry, and if nature permits, then using this knowledge to peer into an even smaller world where we could only indirectly test or infer the theory's of such a tiny and labyrinthine world.

Four suspects of a crime made the following statements to the police: Andy: Carl did it. Bob: I did it. Carl: Dave did it. Dave: Carl lied when he said i did it. 1.) given that one of them "did it" and that exactly one of them told the truth, who did it? 2.) given that one of them "did it" and that exactly one of the statements was false, who did it? 3.) If exactly two answers were true, who could have done it? 1. Dave said, "Carl lied when he said i did it," but whom is referred to as "the variable" i? Well, all you have to do is look at what Carl had said. Carl said, "Dave did it." So i must refer to Dave. But, there is also an ambiguity in Bob's statement in the case of i. Bob said, "I did it." Does Bob mean himself, Dave, or can it be interpreted as either Bob or Dave? If this ambiguity is considered, Andy is the only one who could have "done it", with Dave telling the truth, and everyone else lying. 2. The only two statements which are specific, meaning that they identify the culprit by name, would be from Andy and Carl. They should be the focus of our attention, rather than the statements of Bob and Dave. The only solution would then be that Dave had done it, Andy lied, and everyone else told the truth (with the ambiguity of I). It won't work out if you switch the roles of Carl and Andy as either telling the truth or lying. 3. Finally, Bob is the culprit. Bob and Dave both tell the truth, while Andy and Carl are both lying through their teeth.

correction i = Dave and I= Bob ... its late... Andy did it ....

Carl: Dave did it. Dave: Carl lied when he said I did it. Therefore: Dave = I 1. If Andy did it, then Dave is the only person who told the truth. The same goes for Bob. If Carl did it, Andy and Dave told the truth. If Dave did it, Carl and Bob told the truth. However, Bob: I did it. Therefore I = Bob = Dave If Bob did it, then he and Dave told the truth. So Andy did it. ...