#fast calculation

[masterminddabacusforum]

Abacus Tutorials | Lesson - Addition and Subtraction on Abacus Tool | Abacus Online Classes

This is the 2nd Abacus tutorial in the series, Here you will learn how to do simple addition and Subtraction on Abacus Tool.For learning to do Addition on Abacus you need to join Abacus Classes.

Get a brief understanding about Abacus Addition and Subtraction in this video. To become an expert at using Abacus for Addition and subtraction join Mastermind Abacus online classes or offline classes. Learning Abacus improves a child's Mental Math. Abacus training triggers Whole Brain development. You can also start Abacus Classes in both Offline & Online mode.

[srslylini]

Mel Medarda is one of THE characters of Arcane and I'm tired of pretending she isn't.

who ever designed her, decided what her story will be and just simply who she is gonna be, will see heaven I'm so serious

[barachiki]

Another Christmas, another night where Sherlock fails to stay up and see Santa.

Maybe next year.

[frankiebirds]

LOOK AT THEM READING TOGETHER,,,i can hear them bickering already. jj constantly telling reid she wasnt done and him bitching before turning the page back. the reason theyre making the faces they are is because reid has read this page five times already and jj has told him a thousand times to wait until she says she's done before turning the page but he doesn't LISTEN!!!

[nomnomroko]

Heyo, I wanted to let you all know that I have a Ko-fi page where I offer commissions for those that have been wondering about wether I take them or not :D

In this case a "sketch" commission is a colored clean sketch and very basic shading, no background.

The exceptions are the Quick Sketch, which is a timed rough monochrome portait sketch, and the Lower Decks style (a fullbody artwork in the STLD style)

Maybe there's something there for you :D !

(delivery times may vary, as I have to watch my wirst pain)

[nights-at-crystarium]

wolqotd

Your WoL fights a random enemy, a random npc/civilian happens to witness that. How would they describe the encounter?

[gayofthefae]

Thinking about the inclusion of Will remembering Dustin's birthday

The inclusion of more birthdays at all. The inclusion of someone's partner remembering to the hour.

[bokettochild]

Me: Happily working on TBoHH

*realizes I am coming up to the point where I have to broach the Marin subjct*

Me:

[pseudospectre]

Sent an application for a kitten on Petfinder tonight. I'm irrationally scared they'll reject me for some reason :/ but Selkie needs a buddy and I've been scrolling looking for a little face that calls to me. And she does. So I hope I hope!

[diltonsstrangescience]

DANG. Absolutely cold-blooded.

[masterminddabacusforum]

What is Abacus Mental Math? Benefits of Abacus Classes

Get brief information about how abacus training triggers the 'Whole brain Development' in children. Mastermind Abacus training activates both the left and right brain. Attending an abacus class regularly augments in the student's skills like visualization, photographic memory, recall, logical thinking, and overall learning abilities.

[raiiny-bay]

monster boyz thoughts...

[network-rail]

Why are obstacles on the tracks a problem?

Previously, I mentioned that when a train encounters an obstacle on the line such as a tree branch, what happens is a complicated physics process that results in the train pushing the branch along the line. Here I will explain that process, but be aware that complicated physics things are about to happen. There are some pretty diagrams to look at though, so if you want you can look at those and then skip to the end for a summary. They're even in color!!

First of all, some basic setup (before putting some numbers in):

We have a train travelling at an initial velocity u, with mass M, and an engine capable of producing a constant power P (we will use this to restore the train's velocity to u if it decreases for some reason).

The train encounters an obstacle on the line, such as a tree branch of mass m. We will assume (for now) that the collision is elastic - that is, no energy was lost (for instance, as sound).

We are also assuming a frictionless vacuum, cylindrical tree branch, and rectangular train.

To start with, we look at conservation of momentum (figure 1):

Since the train has elastically collided with a branch, its speed is reduced, given as Vtrain . As trains are typically much heavier than a single tree branch, we take M >> m, and so Vtrain ≈ u.

However, this is somewhat unrealistic, as when a train hits an obstacle, energy is lost –as a crunch sound, for instance– so it may be more appropriate to assume an inelastic collision. Since I said that the branch sticks to the train (and I am right), we should assume a completely inelastic collision, where as much kinetic energy as possible is lost.

Again, we look at conservation of momentum (figure 2):

In this case, if we again assume M>>m, we still get v ≈ u.

Since we know from reality that problems will happen if the train collides with the branch, this tells us that we have made an unrealistic assumption somewhere. In this case, it must be the assumption that the train's mass, M, is large enough that the branch's mass m can be ignored. So, without this assumption, we look at how long it takes the train to get back to its initial speed, using the equations for motion under constant power (equations derived from Taylor, 1930 and shown in figure 3):

To find how much energy is used in each case, simply multiply the time by the power.

By now, you may be wondering what the point of all this is – after all, I haven't actually shown you if this is meaningful. So let's add some numbers to this and see how reasonable all of our assumptions were!

If we take the train's mass to be M=30 tonnes (30,000kg), its power P=1500kW, and its initial speed u=40 m/s (144 km/hr) respectively; and assume the branch has a mass m=5kg (that seems reasonable, right? Trees are mostly water, which is 1kg per cubic meter, and if it has a radius of 0.5m and a length of 1.435m, it should be about that much), we can calculate all the various things we need:

First, the final velocity of the train and branch in the inelastic case (see figure 2 for the equation):

v≈39.99m/s which is pretty close to the initial velocity.

The time taken to return to speed (fig. 3) for the train/branch system is:

t≈0.0053s

This is quite fast, but hold on: the energy used to do this is about 8000 joules, which is probably quite expensive at current electricity prices, but those are given in kWh and I really don't feel like converting between them. (8000 is a big number, right?)

For the elastic case, things are a little bit more complicated, as we have two different velocities to calculate (figure 4):

If you were just looking at the pictures and are upset that the last two have been equations, don't worry, the next one isn't.

Vbranch ≈ 79.99 m/s

Vtrain ≈ 39.98 m/s

The time taken to return to speed:

t≈0.0094s

This is almost double that of the inelastic case, resulting in the energy used increasing to the enormous –and probably expensive– value of 14 kJ. (I even needed to use an SI prefix this time! And one of the ones that makes things bigger!)

However, both of these cases also reveal some interesting things about the situation: the elastic case has the tree branch launched away from the train at 80m/s, which is about 288 km/hr. Since the train and branch are likely irregularly shaped, the branch probably won't be pushed along the tracks at 290km/hr, and could instead be launched into the air space towards you. Nobody wants to be in the situation where a tree branch is flying towards you at almost 300 km/hr. I could do some math to see how much it would hurt, or if you could reasonably expect to dodge it, but I think we can just assume it will be quite painful.

Historically, trains avoided flinging branches at nearby passengers at almost 500km/hr (that's half the speed of sound) by employing a triangular device on the front of the train to deflect objects such as cows off the tracks. These were particularly common in North America, where lineside fences have yet to be discovered outside of the Northeast Corridor and it is easy for things to wander onto the tracks. However, thanks to innovations by the Budd company and others, more recent american trains are basically indestructible, rendering obstacle deflectors unnecessary. The effects of the obstacle deflector are shown below (figure 5):

This device is known in America as a burgerizer, since it can provide an easy meal for the train crew –two of the five ingredients for a cheeseburger right on the front of the train, more if you're lucky– although since usually the obstacle is shoved off the track, the British name of "cowcatcher" is misleading, especially if you hit a truck instead. The burgerizer's physics can easily be calculated using conservation of momentum, but this involves vectors, and I don't want to deal with vectors right now is left as an excercise for the reader.

In the inelastic case, we note that the branch sticks to the front of the train. Since the inelastic case is more realistic (I will not justify this statement), this means that other things will also stick to the train. By the time the train reaches the end of the line, the mass of the things stuck to it may end up not being negligible (figure 6):

If the train is electric, this will strain the power grid and could lead to power cuts elsewhere as more energy is given to keep the train running at speed. If the train is diesel, it will be unable to provide constant power and could slow down (an electric train has access to every power station in the country if the need arises, a diesel train just has its onboard generator or motor AND a limited amount of fuel).

This mess is also difficult to clean up, and could damage the track as it is pushed along. Also, although we have been ignoring friction (since trains have very little rolling resistance) this pile of stuff will cause friction to be very noticeable, and could even obstruct the driver's visibility – potentially leading to more collisions.

–//–

Now that you have read through all of the calculations (or looked at the pictures and skipped the rest), you should have a thorough understanding of why we have to stop trains to clear things off the line, and can't just plow through them like in the movies. (I assume this happens in movies, I have not checked)

TL;DR: When the train hits a branch, either the branch goes flying towards you really quickly, at basically 1000km/hr, which is approximately the speed of sound; or it sticks to the front of the train and becomes part of a massive pile of things that gets in the way and slows down the train.

Finally:

I put the images together using the shapes in my computer's word processor (except the various rail logos); while the equations of motion under constant power are from this paper by Lloyd W. Taylor (published in 1930, I believe). Also thanks to @cosmos-dot-semicolon for peer reviewing this, any errors are not my fault.

[ssreeder]

Hiii I'm sorry if you've answered this before, I'm just wondering if you have an idea (vague or otherwise) about how many chapters ITF is going to be? I'm just curious. Thank you, hope you have a great day ^^

I have? Maybe? I’m not sure! But after this we’ll have probably 10 chapters left! I’m guessing we’ll end up at 31 total chapters but that’s just my guess! We’re on the home stretch!!

[chialattea]

me: omg I love lab work!! I love doing procedures🥰🥰 it’s so interesting and rewarding I wanna keep doing it forever!!🥺

me whenever I’m at the lab:

[computersucker]