Wikipedia:Reference desk/Archives/Science/2018 February 25

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February 25

A low viscosity liquid which will harden after 20+ minute working time?

I have a small hobby project in which I'm printing some keyboard keycaps with an SLA 3D printer with the intention of filling in an inset legend with some kind of paint or resin which will harden in a contrasting colour (white since the SLA resin is black) but I don't know exactly what to use. The spaces I fill will be really small so I need to use something with low viscosity which I can inject with a (blunt, narrow needle) syringe and it will self-level and harden very slowly so I have time to inject about 70 characters in total. I know two-part resins are available but I don't know their viscocity or if there are more suitable alternatives. Can anyone advise a suitable material available in small quantities for this purpose? 185.222.217.213 (talk) 14:34, 25 February 2018 (UTC)

There'll be lots of low-viscosity potting epoxy on the web. But I'd have thought some pot of enamel paint for hobbyists would do the job just as well. I think it would probably be worthwhile painting the flat area of the keycap with some masking fluid too. Dmcq (talk) 14:58, 25 February 2018 (UTC)

• Stupid-sounding idea, but what about solder, if you are OK with a metal-silvery finish? The idea is that you might already have some training and equipment for soldering. (I am assuming that since you hobby-print 3D pieces there's a good chance you have standard electronics material already. If not, follow Dmcq's advice instead.)

I would try the standard tin-lead at first on a test cap (to check that you can reliably apply the solder without melting the plastic too much; you may need to thicken the plastic cap though). If you can 3D-print freely, that is easy enough to test. If this does not work, you could switch to using a low-temperature solder (Solder#Solder_alloys lists many; I could find some Cerrolow 117 for about $40 on ebay), which should be easier to use (you can overheat the fusion temp by more, so you have more time to wipe mistakes, and viscosity is lower, while being at lower absolute temperatures for the plastic cap). Tigraan^{Click here to contact me} 13:40, 26 February 2018 (UTC)

Doesn't he need something that adheres very well to the plastic? If the label comes out of even one key it will look like a really shoddy piece of workmanship. But I don't understand why 20+ minute hardening time is needed - can't the keys be done one by one and left to harden progressively? Wnt (talk) 00:22, 1 March 2018 (UTC)

Feynman Lectures. Exercises. Exercise 19-17 JPG

. .

...

A yo-yo like spool consists of two uniform discs, each of mass M and radius R, and an axle of radius r and negligible mass. A thread wound around the axle is attached to the ceiling, and the spool is released from rest a distance D below the ceiling.

a) If there is to be no pendulum -- like swinging motion, what angle should the thread make with the vertical as the spool is released?

b) What is the downward acceleration of the center of the spool?

—  R. B. Leighton , Feynman Lectures on Physics. Exercises

I have found the acceleration with assumption the motion is vertical (with zero angle ).On time 6:16 of a video youtube.com/watch?v=kdTLZ6-hVq8 it seems there is no sidewise motion. But I don't understand why the angle is zero. The acceleration of the yo-yo is $g<a<0$. So it has apparent weight = $2M(g-a)$ like in the going down elevator. This net force must create a torque and shift the yo-yo so that the center of mass comes to be under the attachment point on the ceiling . Username160611000000 (talk) 16:05, 25 February 2018 (UTC)

The tension in the thread and the true weight of the spool (acting vertically) cannot be collinear otherwise there would be no torque to provide the angular acceleration. From the moment of inertia and the angular acceleration, you can calculate the perpendicular distance of the line of action of the tension in the thread from the centre of the spool, and hence the initial angle of the thread. From the order of the questions, I assume that you were supposed to set up simultaneous equations for linear and angular acceleration. If you have used an energy method for the acceleration, then you have probably calculated the vertical component of the tension. (I can see now that you didn't.) Dbfirs 17:13, 25 February 2018 (UTC)

"the perpendicular distance of the line of action of the tension in the thread from the centre of the spool" = r. How from this can I find the angle? Username160611000000 (talk) 18:08, 25 February 2018 (UTC)

I have calculated the acceleration form next formulas.

$\alpha ={\tfrac {\tau }{I}}={\tfrac {2Mgr}{{\tfrac {2MR^{2}}{2}}+2Mr^{2}}}$

$a=r\alpha ={\tfrac {gr^{2}}{{\tfrac {R^{2}}{2}}+r^{2}}}$

The moment of inertia $I$ and the torque $\tau$ were calculated around a point A (see image PNG) where the thread touched the spool. From answers it is correct jpg. The tension is then $T=2M(g-a)$, but again using the assumption that the spool is moving vertically.

In The Solutions is said:

...

The spool is acted upon by gravity, directed vertically downward, and the tension force T along the thread. The spool will not swing if there are no horizontal forces, i.e. if the thread is vertical.

—  MEPhI , Solutions (Google Translate)

But it does not explain the case when the thread is fixed , then the spool will go so that the center of mass is under the point on the ceiling PNG . I.e. we hold the spool with fixed thread by hand in position, showed in the exercise PNG; then the spool is let fall. The spool then 100% will go to the right, but in the absence of horizontal forces at starting moment. I can understand it like next: the spool starts rotation and pulls the thread away from the vertical. The inclined thread generate a horizontal force. It proves that absence of horizontal forces CAN produce horizontal motion and it demolishes the arguments from The Solutions. Username160611000000 (talk) 18:20, 25 February 2018 (UTC)

• • From assumption that the center of mass must be under the ceiling fixing point I can calculate the angle: $\sin(\theta )={\tfrac {r}{OC}}$ (see image). It is not clear from the statement of the exercise is $D=OC$ or $D=AC$, but it is not a problem. The problem is how to prove that the center of mass must be under the point on the ceiling, moreover the experiment shows that it's not the case. Username160611000000 (talk) 08:18, 26 February 2018 (UTC)

Now I'm confused. It's too long since I did this type of problem. Perhaps someone else can help? I had assumed that the spool was released with the thread vertical, but there will be horizontal motion in this case as the spool rotates about the lower end of the thread. Perhaps you were meant to assume that the centre of mass is moved to be under the point of suspension before release, but then the tension in the string will cause a swing the other way. Dbfirs 10:11, 26 February 2018 (UTC)

@Dbfirs:but then the tension in the string will cause a swing the other way. The tension will create a torque about point O only in O - reference frame (ref. frame in which point O is at rest). First, the tension will simply increase angular velocity about point O, there is no guarantee that the point O will move horizontally. Second, O - ref. frame is an accelerating frame, so there may be some complications. On the other hand point A is at rest in ceiling ref. frame (at least during small time at start). Username160611000000 (talk) 17:09, 26 February 2018 (UTC)

Hmmm. I think the thread, wherever unspooled, does not actually move; thus all downward force on it is opposed by upward force. And at the moment of release, the spool has no downward velocity. Therefore, it applies a torque according to the newtons (M * g) multiplied by the lever arm = radius r. To oppose the torque, the string can be non-vertical, applying a contrary lever arm. That puts the center of mass of the spool directly under the string, AFAICT - in other words, the center of mass is stable when directly below the suspension point, like with anything else. That makes the angle sin-1(r/D).

Now as for the downward acceleration, we know it can move only r * however many radians it turns by. From the list of moments of inertia, I = 1/2 mr^2 for a disk. We use the quation from moment of inertia that tau = I alpha, where tau (the torque) is that M*g*r thing. So alpha = M*g*r / (1/2 MR^2) given that R is the disk radius and M is I think the same M, or alpha = 2*g*r/R^2. The distance, velocity, and acceleration should all be r* the angular versions I think, so I get 2*g*r^2/R^2 ... hmmm, units should be acceleration, it tends to zero for a very thin axle -- but, I get double speed falling if you wrap a string around a soup can, which is wrong. Sigh. This time I'll post my detritus in hope someone finds a fix, with apologies. Wnt (talk) 02:11, 27 February 2018 (UTC)

@Wnt: With the non-vertical thread, I'm pretty sure the spool would swing in the direction of the horizontal component of the string tension. Compare this with picture frame wires, which typically have two attachments with opposing tensions that can be adjusted (they tend to get misaligned anyway). Take away one of the attachments and the frame swings. Assuming an infinite thread and fall of the spool (with gravity not changing), the spool's mass should oscillate about the thread's vertical position as the horizontal tension is a restoring force towards vertical with each swing. -Modocc (talk) 19:14, 27 February 2018 (UTC)

So with the picture frame we have something like this , where last position is the one when oscillations stop. I'm not sure the frame center of mass will go left.

Also I checked cylinder with fixed thread : 12345678 Username160611000000 (talk) 12:20, 28 February 2018 (UTC)

If the tension is very small or negligible compared to the mass so is the lateral motion of the swing (or the rocking) of that mass. With the picture frame you are simply showing the very end result... a stationary frame and not the oscillations that had to first be dampened due to the spring tension that was on the wire and became free to set the frame in motion. I can't quite make out what your dropped spool test shows. If it is swinging rather than dropping straight down the string is not spooling very well, too tightly wound or not enough spool mass etc. Try again by wrapping it around a heavy jar and see if you get the same result. There are different factors that will influence any experiment or test. But to get an idea of the magnitude of the forces involved, consider a bicycle. If one lifts it at the handle bars straight up the bike rotates about its rear wheel which will stay put, but if one does this at the slightest angle toward the center of the bike it will roll backward even with a slight pull. -Modocc (talk) 13:29, 28 February 2018 (UTC)

• • • • • I can't quite make out what your dropped spool test shows. As I told, experiment with the wound thread gives strictly vertical thread during unwinding. Snapshots show that the cylinder CM goes sidewise only on 6th snapshot (each snapshot time = 1/24 sec). So the inclined thread doesn't imply horizontal motion and the vertical thread doesn't imply absence of horizontal motion. Username160611000000 (talk) 17:10, 28 February 2018 (UTC)

I see. You placed the spool in such a way that is reversed from what was expected; thus the spool is not spun initially for half a turn without any significant tension (other than to remove the thread), thus it gets a large pendulum kick to the right when it undergoes tension... which should be expected because the string happens to be no longer vertical at that point when it actually starts unspooling normally. -Modocc (talk) 17:46, 28 February 2018 (UTC)

I still do not trust The Solution reasoning (and so I can't explain the experiment theoretically). How to model the motion of the spool (or disk) by numerical methods shown in lecture 9? To do this, we need to know the expression for the tension force (in terms of coordinates or velocities and independent from 2nd Newton's law), but it is unknown. Username160611000000 (talk) 19:02, 28 February 2018 (UTC)

The picture isn't the same as the spool, because the thread's attachment can *rotate* freely. Of course, the thread is not rigidly attached to the spool... but so long as it supports the spool as it unrolls, it has to remain at a fixed angle that meets almost perpendicularly at one end. Its attachment point can never be right on top of the spool, unless it runs out and reaches the point where it's tacked on to something. Wnt (talk) 14:49, 28 February 2018 (UTC)

True, the thread's vertical component of the spring tension supports the spool or counters gravity and that is true for the frame's wire. The horizontal component of the tension in both do not. The point I am making with the picture is that its horizontal tension is divided between left and right tensions that balance each other, thus preventing lateral motion and swing of the mass center. Replace the wires with springs and the ensuing oscillations become very apparent. With the spool, without any lateral force acting on it, it drops straight down and this should be the cased as diagrammed in the problem statement with that shows a vertical thread. Add an unbalanced lateral force and there is lateral movement that has to change the angle of the thread (in part, because the thread remains attached to the ceiling) which changes the lateral force which is always a component of the tension vector. The magnitude of the changing horizontal component then has to oscillate as pendulums tend to do and it doesn't take much force to set them off. --Modocc (talk) 16:17, 28 February 2018 (UTC)

Maybe I'm missing what you're saying, but if you pull up a picture that is hanging off a bent wire coat hanger, then (barring bending of the hanger...) you expect to be able to pull it straight up even though the hanger makes an extreme angle. In this case the lower leg of the hanger is the near-horizontal radius from where the thread separates from the spool to the center of the spool. And the upper leg of the bent hanger is the string deviating from vertical to meet the spool. Wnt (talk) 00:01, 1 March 2018 (UTC)

The coat hanger is rigid, but the spool is free to separate from the thread. Elastic tension is all that is needed here anyway and you calculated the string tension with the string vertical, but then moved the contact point from vertical to non-vertical. However, the string tension is zero if the thread starts out horizontal and the spool has to drop and swing a bit before the torque increases significantly. Since the spool is free to separate from the thread, the unopposed horizontal component of that tension accelerates the spool's mass center laterally as the spool continues to move downward. Modocc (talk) 15:50, 1 March 2018 (UTC)

Where the problem statement states "no pendulum -- like swinging motion" is a bit unclear, however the solution that the string (or thread) needs to be vertical such that the net horizontal force acting on the disks' axle is zero is a reasonable interpretation of that... any angle from vertical gives a measurable horizontal force component from the string's total tension and without any other horizontal force also acting on the mass center, that lateral string tension results in its horizontal acceleration. Now if the string is "fixed at point A" as in your diagram, the spool thread is essentially stuck as the spool rotates without the thread being released, creating a pendulum with lateral string tension acting on the spool and which you didn't account for and the motion of which is to be avoided. --Modocc (talk) 17:30, 27 February 2018 (UTC)

The on-line handouts and examples from major educational establishments (Browns, MIT etc) all seem to assume that the thread remains vertical. I'm trying to convince myself that this will be the case for all values of moment of inertia, then it does make the calculations much simpler. Maybe it can be proved that the moment of the weight about the (moving) point of contact of the lower end of the string always produces a rotation at exactly the rate to match the downward speed of the centre of mass. If so, then careful release with the string vertical will always produce a pure unrolling motion without any swing. Dbfirs 11:37, 1 March 2018 (UTC)

I think you meant a pure rolling motion. Gears, wheels, balls or tires can also be set rolling down a vertical wall with minimal contact. Of course when the wall is not vertical, the angle is set opposite of vertical than that of the spool here since the force acting on their mass centers is compression and not tension. For a given angle from vertical, the component force due to gravity that accelerates an object down an incline contributes to the thread tension. In particular, if they were to oppose one another there is no acceleration and the object is held stationary on the incline and the force of that tension is mg*the sine or cosine of which ever angle one is referring to (calculated here). For the spool, there is no incline thus no compression force, but there is also centripetal acceleration to consider too. In any case, the tension vector can also be broken down into two components, vertical and horizontal, to determine the horizontal acceleration of the bob at any given moment. -Modocc (talk) 18:35, 1 March 2018 (UTC)

See this reference for calculating an ordinary pendulum rod's tension. --Modocc (talk) 19:43, 1 March 2018 (UTC)

Modocc, I was discussing the original question. I've no problem with the rotational dynamics of rolling down a rough slope where the acceleration depends on the moment of inertia. I'm also fully familiar with the dynamics of a pendulum for a small angle of swing. I'm just trying to convince myself that this problem can be treated in the same way. Dbfirs 07:49, 2 March 2018 (UTC)

The pendulum reference is valid for large angles not just small angle swings and the original problem involves leverage of an object while under the influence of gravity and these other cases should help the OP, Wnt and others understand how to work it and why, especially since the OP asked about how the thread tension can be calculated. In addition, the applied force on the spool acts on its mass center. An example is the firing of a projectile from an unmoored ship's cannon. It does not matter where on board one places the cannon, conservation of momentum requires the ship's mass center to be acted on by the cannon recoil in a direction opposite that of the projectile even when the cannon is somewhere in a far corner such that it sets the ship spinning too. Here, the thread tension does the same, torquing the spool while it acts on the spool's mass center. -Modocc (talk) 13:06, 2 March 2018 (UTC)

True about the pendulum, except for the usual calculation of the period of swing. Your ship example is a good illustration. The rotational behaviour of the ship varies with the positioning of the canon, and in this case the swinging behaviour varies with the initial release configuration. I would like to be able to prove that if the thread starts vertical then it remains vertical, assuming no snagging. I used to prove every year from first principles that the motion can be separated into the linear acceleration of the centre of mass plus the rotation about the centre of mass, and this principle applies here in exactly the same way if we are allowed to assume that the thread remains vertical. I'm just worried about the assumption. Dbfirs 14:35, 2 March 2018 (UTC)

• In the simple pendulum problem the tension can be easily found from centripetal acceleration formula $v^{2}/R$, coordinates and velocity of a bob. In the spool problem constraint is still present and as I can see I can find one tension component from another , e.g. $T_{y}$ from $T_{x}$ , but I cannot find $T_{x}$ (so I should use $T_{x}(t+\Delta t)=T_{x}(t)$ ).Username160611000000 (talk) 19:42, 2 March 2018 (UTC)

How well do Tanks and other tracked vehicles coast?

I was talking to a buddy of mine about tanks the other week, and we were wondering how well tanks coast and if it is possible to put regen braking on a tracked vehicle. Does anyone have any experience with tanks here? Our Tank steering article wasn't much help, and neither was Google. Thanks, L3X1 ◊distænt write◊ 16:36, 25 February 2018 (UTC)

I can't find any in service, but this paper discusses the concept and notes that there are some hybrid-electric tracked vehicle development programs in the works. I don't know how well tanks coast, but regenerative braking definitely seems to be seen as a non-laughable concept. TenOfAllTrades(talk) 17:49, 25 February 2018 (UTC)

Considering that the M1 Abrams gets only .6 miles per gallon, I doubt "coasting" is even the right word; it barely budges without eating a lot of fuel. Matt Deres (talk) 21:05, 25 February 2018 (UTC)

Well, the thing weighs 60-70 tons, so unless there is some jake or automatic engine braking going on, if you let off the throttle at 30 or 45mph inertia says it will keep on going for a little bit. I've driven some hydraulic transmission construction vehicles, but they always would come to a halt pretty quick if you let off the gas. Thanks, L3X1 ◊distænt write◊ 22:21, 25 February 2018 (UTC)

Common Tanks are very ineffective vehicles because of their weight and Caterpillar tracks. They also lose their speed fast, even on streets, because the traks are very sturdy and stiff. A recuperation system would not be worth the extra weight and besides it would have to be absurdly huge to take up and feed back the braking energy of 60+ tons at 60-70 km/h. Because of their ineffectiveness most modern Armoured personnel carrier constructions went back to wheels. --Kharon (talk) 05:39, 27 February 2018 (UTC)

This is kind of an aside, but why hasn't anyone come out with wheels covered in retractable spikes or more sophisticated specialized grabbers or pseudopods? I'd think each could have its own little computer brain and (at least at military funding levels) its own camera. I'm picturing whizzing down the road on spikes that drive into ice for traction, stop short to sail over speed bumps without a jiggle, and go the extra two inches to cross a problem pothole. But conceivably each one could drive its own little pitons this way and that, hundreds of times a second, and allow you to drive straight up the wall, maybe even along the ceiling. One of the few things you could actually do with all this cheap computing/surveillance technology. Wnt (talk) 00:28, 1 March 2018 (UTC)

10-4 to that, I like the way you think! L3X1 ◊distænt write◊ 02:23, 1 March 2018 (UTC)

Why do humans have body hair?

Why?86.8.202.234 (talk) 22:10, 25 February 2018 (UTC)

Because mammal! "It [ hair ] is a definitive characteristic of the class." {The poster formerly known as 87.81.230.195} 90.220.212.253 (talk) 03:16, 26 February 2018 (UTC)

For the lack of body hair in humans, see What is the latest theory of why humans lost their body hair? Why are we the only hairless primate? from Scientific American. Alansplodge (talk) 09:10, 26 February 2018 (UTC)

We're not hairless. ←Baseball Bugs ^{What's up, Doc?} carrots→ 10:34, 26 February 2018 (UTC)

Indeed, but a lot less hairy than all other primates (most people anyway). Alansplodge (talk) 11:20, 26 February 2018 (UTC)

"Hairless" does not simply mean "less hair". I'm reminded of Richard Armour's comment about the wireless, i.e. the radio: "Although it had a great many wires, it had less than it might have." ←Baseball Bugs ^{What's up, Doc?} carrots→ 12:21, 26 February 2018 (UTC)

Still, the concept of the human as a hairless ape is a common enough trope, see, for example, the sentiment in the title of the famous book by Desmond Morris, The Naked Ape. --Jayron32 17:41, 26 February 2018 (UTC)

This is the bloke who wrote the offending article. Alansplodge (talk) 18:05, 26 February 2018 (UTC)

FWIW, the Aquatic ape hypothesis mentioned in that article is not really supported by any paleontological or archaeological evidence and is generally dismissed by most anthropologists (outside of a few proponents) as an interesting thought experiment. In terms of body hair, of course, we have about the same number of hairs per square inch as a chimp, it's just that the hairs are shorter and finer. Matt Deres (talk) 14:36, 26 February 2018 (UTC)

Thank you. Yes, some of us have particularly fine hair. Drmies (talk) 17:42, 26 February 2018 (UTC)

The problem about the lack of paleontological or archaeological evidence for the Aquatic ape hypothesis is that it would be extremely difficult to find any even if it were true. The hypothesis supposes the aquatic behaviour (leading to various physical adaptations) was practiced on marine shores, but since the postulated period in question sea levels have risen by hundreds of feet, so any such evidence will have been almost if not entirely obliterated, and any that remains would be almost impossible to find and excavate, even if we were looking in the right places (which we're not). In this case, the maxim "absence of evidence is not evidence of absence" is particularly apt. {The poster formerly known as 87.81.230.195} 90.220.212.253 (talk) 23:28, 26 February 2018 (UTC)

I think a "mud ape" hypothesis is more interesting. After all, polar bears can swim with thick body hair, but we are constantly reading about well-meaning humans pulling things out of mud pits. In earlier times they would also have meant well... meant to eat well. The Okavango delta in particular is known for periods of flooding and periods of mud and periods of wildfire, and seems like an interesting possible ancestral situation. The feet of humans, like lechwe, seem elongated -- could it have been for crossing that mud? Wnt (talk) 01:46, 27 February 2018 (UTC)

So you're saying it's unfalsifiable? Then I'm afraid it's not science. We have found and studied numerous human settlements that are now underwater, having been submerged by rising sea levels, so the implication that "evidence may be underwater so we just have to throw up our hands" is nonsense. All conclusions in science are provisional, so it's possible in the future we could unearth some stunning evidence for the hypothesis, and if we do, it will presumably be revisited. Until then, it fails in explanatory power relative to other hypotheses. RationalWiki has a good summary of its problems. Although as noted, a problem is that people often seem to mean different things when talking about the "aquatic ape hypothesis". The notion that marine environments may have played some role in human evolution is, I don't think, very crazy, though we need stronger evidence to state that more definitely. The idea that human ancestors at some point lived entirely in the water like whales or dolphins is ludicrous. --47.146.60.177 (talk) 08:23, 27 February 2018 (UTC)

Yes, that site is a good overview of the problems with the AAH, but the problem it goes deeper than that. We all have hooded noses, we all have sebaceous glands, we all have all those items that proponents of the theory say were likely derived from a semi-aquatic existence. In order to be true, aquaticism would have to have been a massively important evolutionary feature where divergence from that adaptation meant complete lack of procreation. It would require a bottleneck where all non-aquatic people were wiped out to the point where even recessive non-aquatic genes were virtually eliminated. Matt Deres (talk) 13:33, 27 February 2018 (UTC)

That's not really a valid argument at the end. Many racial features and even more substantial cosmetic alterations in the lineage leading to humans (such as hooded noses) can be seen as cosmetic features that potentially might have been basically under no selection at all. If on average a person had to dive into a creek once a generation to avoid a barrage of rocks, spears, or arrows, that would be enough selection to make big changes in even a thousand years. Wnt (talk) 15:14, 27 February 2018 (UTC)

I'm sorry, but that's just ridiculous - you don't develop subcutaneous fat and a "hairless body" because you jump in a lake every few months. We're talking about a massive evolutionary pressure here - one that hasn't seen itself reset despite millennia since it proved advantageous. We're all different shapes and sizes and colours, but whatever selected for hooded noses did so with such survival differentiation that essentially nobody gets born without them any more. You can't have it both ways; it might hang on if there's no longer a survival bias, but something hugely significant must have selected for it at some point. Matt Deres (talk) 14:37, 28 February 2018 (UTC)

[In answer to 47.146.60.177] "The idea that human ancestors at some point lived entirely in the water like whales or dolphins is ludicrous": yes, I agree with that entirely, but I'm not aware that anybody has ever suggested such an extreme version of AAH. As for the inaccessibility of evidence making it unfalsifiable and therefore unscientific: no, not in principle, just extremely difficult (like, for example, Einstein's theorised gravity waves which eventually were detected against his own expectations). And yes, we have found and excavated submerged human settlement sites, but not, I think, any sites a million or so years old, and also some 300 feet below current sea levels, and also many miles from current coastlines (as most potential sites would now be). However, we're now just exchanging opinions without reliable sources, so we perhaps ought to draw the discussion to a close. {The poster formerly known as 87.81.230.195} 90.220.212.253 (talk) 06:48, 28 February 2018 (UTC)