Imagine two objects of mass $m$ each (both of them in outer space), with initial velocities $v_0$ and $0$. Now I apply a constant force $F$ on both of them for time $t$. Now the change in energies of the masses are $$\Delta E_1=m v_0\Delta v + \frac{1}{2}m\Delta v^2$$ $$\Delta E_2=\frac{1}{2}m\Delta v^2$$ What these equations are saying is that I lose more energy when I try to accelerate an already moving object (same amount of momentum transfer doesn't mean same amount of energy transfer). This doesn't make sense. If I look at it mathematically, i.e $dW = \vec{F} \cdot \vec{ds}$, I completely understand why I'll have to spend more energy on the moving object. But for some reason my intuition says if I apply same force on objects moving at different velocity for the same amount of time, I'll lose the same amount of calories. Where is my intuition wrong?
Consider a rocket in deep space with no external forces. Using the formula for linear kinetic energy $$\text{KE} = mv^2/2$$ we find that adding $100\ \text{m/s}$ while initially travelling at $1000\ \text{m/s}$ will add a great deal more energy to the ship than adding $100 \ \text{m/s}$ while initially at rest: $$(1100^2 - 1000^2) \frac{m}{2} \gg (100^2) \frac{m}{2}.$$ In both cases, the $\Delta v$ is the same, and is dependent on the mass of fuel used, hence the same mass and number of molecules is used in the combustion process to obtain this $\Delta v$. So I'd wager the same quantity of chemical energy is converted to kinetic energy, yet I'm left with this seemingly unexplained $200,000\ \text{J/kg}$ more energy, and I'm clueless as to where it could have come from.
Causes of hexagonal shape of Saturn's jet stream NASA has just shown a more detailed picture of the hexagonal vortex/storm on Saturn:           Is that theoretically understood what is the cause behind this eye-catching nontrivial, regular yet not circular, shape? If so, what is the cause? I expect some explanation in terms of "nonlinear equations" of "mathematical physics" and "solitons".  P.S. (added a day after this question and the first answer was posted): On  where I posted the same question, people came up with some articles and phrases like "Rossby waves" and "resonance of latitude-dependence Coriolis frequency". /review tab not accessible on a private beta How to extract pixel value counts from a raster in QGIS? Introductory Calculus textbook for physics? Do you use "a" or "an" before acronyms / initialisms? 99% of the time, I'm clear on when I should use "a" versus "an." There's one case, though, where people &amp; references I respect disagree.  Which of the following would you precede with "a" or "an," and why?   FAQ FUBAR SCUBA   [Note: I've read the questions  and , but the rules given there don't necessarily apply here.]    [Edited to add]  Here's a shorter (and hopefully clearer) version of the question…  In written English, which is correct (and why): "a FAQ" or "an FAQ"?  Some references with differing opinions:   an: the  and  a: the Microsoft Manual of Style for Tech Publications, 3e either: the  and Create 128 Barcodes within Excel Is there a way to create Barcodes (128 standard) on a Mac, preferably via an add-in?  I need it to create barcodes in Excel sheets (or moreso a friend of mine needs it).   I have tried all VBA macros and fonts I found on Google, but none give me a scannable result (usually there are weird characters like ó's mixed in). Does anybody have a working solution? Motley fool says you can make $15,978 more per year with Social Security. Is this for real? The Motley fool has an ad campaign that says you can make $15,978 more per year on Social Security by doing 17 minutes of work using a legal loophole.  I don't want to link to their ad (although, you can find it by searching ).  What are they talking about here?  Is there any truth to this?  If someone could explain it to me without me having to watch the entire ad video or subscribe to their newsletter, I'd appreciate it. I have Raster data for a country which has Evaporation Data in its pixels. I also have Vector layer which has the 30 cities of the country.   What I need is the average Evaporation value of each city from the raster data using ArcGIS?  I have access to the spatial analyst extension. 1970s scifi/horror novel where protagonist is used by a crablike creature to feed its larvae, goes mad, and is defeated by retraumatising him I read this book once as a teenager, I think it might have been written in the 1970s but could be late 1960s or early 1980s.  The protagonist is left to die hideously by enemies. He is paralysed and left on some planet (I don't believe it was earth) in the habitat of some kind of crablike creature, which injects him with its young, and periodically returns to force nutrient and a paralytic agent down his throat, as the larvae grows inside him.  He is rescued, and his body rebuilt to some kind of superhuman abilities, but he is traumatised and bent on indiscriminate revenge for his suffering. He proves hard to defeat.   He is eventually defeated by trickery, when he is shown (or demands to see) something by some kind of video link or remote TV/monitor - perhaps he is told that people he wants revenge on, are held captive for him, I can't be sure.   I think maybe he takes hostages or makes a severe threat, and his demands relate to the people he wants revenge on. But he can't be physically reached, so what can be done?  They set up a video feed, to negotiate, or more likely, to purportedly show him they have what (or who) he wants, and he looks to see.  When he looks at the video stream, it's actually an image of the crablike creature. The shock of repressed memories flooding back, renders him re-traumatised and perhaps catatonic, and defeats him. In the PGF/TikZ manual, sometimes I see the option right of=somenode instead of right=of somenode. They look very similar, but the effects are different.  The distance between nodes positioned with the latter option is boundary-to-boundary, as stated in the manual. However, with the first option, it seems that the distance is shorter. I couldn't find any explanation of the first option in the manual.  My question is: what is the difference between the two options? Is there any explanation in the manual that I missed? When I tried to run , I got the below screen:    The captcha is missing!  I tried in other browsers too.    Update:  From @Oded's comments, I changed to HTTP and it was working perfectly.  Out of curiosity I would like to know why the captcha isn't working when accessing Data Explorer over HTTPS. Prove the set of all infinite binary sequences is uncountable by using Cantor's theorem. This is different then the other versions of the questions here. I'm not supposed to use the diagonal argument. I'm looking to write a proof based on Cantor's theorem, and power sets. Is there a \subsubsubsection command? I could do \subsection{} and \subsubsection{} but not \subsubsubsection{}. This command does not seem to be available in LaTeX. Is there an alternative command? How to create an interactive bash script to collect arguments for a command in linux? I'm trying to create an interactive bash script where I can collect user input variables to be used as arguments in another command. Can someone provide me an example of this?  Currently i want to do:   what type of content you want to delete? what is the status?   then feed it into a mysql delete query command. Remove Punctuation When Checking for Duplicate Titled Questions I recently saw a question titled "" (10k+ users only). I thought, "surely someone has asked this question before", and began looking for a duplicate.  is a question with the exact same title, just with a little different punctuation and casing. It was "Jquery vs Javascript" and "jQuery vs. Javascript?". The only difference being the ., ?, and the casing.  Since we now , I propose that when checking for questions with duplicate names, certain punctuation be striped out to prevent the duplicate from occurring in the first place.  As pointed out in the comments, if isn't already, white-space and non-printable characters may want to be removed for duplicate detection as well. What is this story about 20 y.o. inexperienced "kids" fighting against a stronger foe in space? Can I run my CPU at 100% usage for a long time? I have a Dell XPS 15 9570, 32 GB ram, 2.2 ghz and 6 cores. When i use an application (The parsim command on MATLAB) ()  then my fan starts running fast , during this my PC doesn't seem to be heating but it never got this noisy in the past so it got me worried. In my task manager , the CPU usage shows 100% when this application is running.   Is it a problem for the life of laptop, if I run the PC at CPU 100% for like 4 hours in a day? Do I need to be worried about the noisy fan during the application? How do I hide the GRUB menu showing up at the beginning of boot? I stopped dual booting and I don't want to have to choose the OS any more. I want to boot into Ubuntu 12.04 directly without seeing the GRUB menu.  How can I achieve that? Ubuntu 18.04 bond with netplan duplicate MAC address after cloning Do objects rotate around the torque vector or its center? If a sphere has a torque vector coming out of it at point A, would the sphere rotate about its center or the axis of the torque vector?