#physics of collisions

[er-cryptid]

Inelastic Collisions [Ex. 1]

A 4.98 kg box moves at 2.5 m/s and collides and sticks to a 4.80 kg box moving at -2.5 m/s. What is the velocity of the objects after they collide?

-- Since the objects stick together, you know the collision is inelastic

-- Use conservation of momentum

-- p = mv

-- This can be simplified for inelastic collisions

-- Plug in values and solve for Vf

-- The velocity after the collision is 0.05 m/s

.

Patreon

[fuckyeahfluiddynamics]

Instabilities in Competition

When two liquid jets collide, they form a thin liquid sheet with a thicker rim. That rim breaks into threads and then droplets, forming a well-known fishbone pattern as the Plateau-Rayleigh instability breaks up the flow. (Image credit: S. Dighe et al.) Read the full article

[omegalomania]

we are such a fucking tragedy, you and i

[network-rail]

Always Learning

Here at Network Rail, we are always learning new things about how the railways work, and about new problems that can happen. For instance, recently I learned that when solar storms induce electrical currents in wires, they also induce currents in track circuits, making them think that there's a train there when there isn't. So, sometimes if your train is delayed by a signal failure, it's because of the sun. Previously, we had no idea this could happen, we just thought that either someone had stolen a train or there were ghost trains.

[bleue-flora]

just a random thought/idea: where I'm from, parents used to make their kids kneel on mongo beans or rice grains for a while as a punishment. I wonder if that's how it feels like to kneel on the obsidian in the cell

Oh yea, 100% I love this. When I’ve gone rockhounding we often wear knee pads depending on the site, because of the sharp rocks, loose and solid, so I absolutely think the obsidian ground is very painful. Especially, because obsidian is volcanic glass so it breaks unevenly with pointy edges and unless they took a grinder to the floor (which even then) it’d be very course not unlike how it’d feel to kneel on beans like you describe, though potentially actually sharp to the point of breaking skin. (If you buy obsidian at a store lots of times the corners are rounded off because they’ve been tumbled (basically sanded down) a little to smooth it out.)

And not to get too engineery, but additionally, obsidian is very hard and not very shock absorbent, meaning it does not absorb much of the energy of your weight leaving the energy and force to essentially rebound back into you. If you’ve ever walked around all day on concrete floors and your legs and feet are sore afterwards this is part of the reason why. The floor isn’t taking a lot of the pressure off your feet like wood does when it bends under your weight. Hence, one of the reasons why we wear padded shoes, especially if you work on hard floors all day, to help absorb some of that energy.

So even without Quackity’s visits and the resulting injuries, Dream’s body would still be in bad condition as a result of the floor alone, not just because of all the cuts from the jagged surface, but the lack of shock absorption. He would likely develop calluses over time to deal with the floor, but there is also only so much you can do if it’s super uneven and sharp. And the result of the forces on his body from a lack of shock absorption would lead him to face a lot of joint strain and likely chronic pain in his knees, hips and lower back as well as muscle pain, posture deterioration and fatigue making it strenuous to stand for long periods of time… in other words, even if the cell wasn’t surrounded by lava, even if he wasn’t starved, even if he wasn’t in isolation, and even if he wasn’t tortured, Pandora’s Vault was still hell and he’d leave that cell in poor physical condition with chronic pain just from the obsidian…

[aurosoulart]

[ID: tags via @lanixigay that read "#BUGS IN LOVE #THEYRE LOVEBUGS YEW #HOW COULD YEW NOT" /end ID]

dragons in love is winning but Yew puns are my secret weakness. this is too stupid to be an official video so it's literally just for tumblr, enjoy ghskgh

[hookhausen]

no one understands him like i do

[quietbatperson]

[hexameterwrench]

running warlord’s yesterday my friend and i were talking about enhanced weapon perks and in a fit of inspiration i was like

“what if enhanced hatchling just spawned a giant hatchling”

and now we need this to be real. bungie pls. you gave us the mini screeb, now give us giant hatchling

[m0e-ru]

bye girl

[entryn17]

these damn things have been bothering me for MONTHS i finally fixed them. peace and love on planet jawbreaker rage

[fuckyeahfluiddynamics]

Tracking Break-Up

In fluid dynamics, researchers are often challenged with complicated, messy flows. With so much going on at once, it's hard to work out a way to keep track of it all. Here, researchers are looking at the break-up of two colliding liquid jets.  (Video and image credit: E. Pruitt et al.) Read the full article

[ducktales-four-years]

Got attached to my Robotica design so i made a 3D model, still needs some tweaks!

[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.

[movies-tv-more]

Home Video Releases for April 2, 2024

[sableeira]

when you think about it, Tanizaki’s ability is basically creating a irl real-time rendering engine