Author Topic: Shooting an arrow out the back of a moving train  (Read 3615 times)

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Offline CirclotronTopic starter

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Shooting an arrow out the back of a moving train
« on: January 14, 2025, 12:29:50 pm »
Say you are on a train doing 100 kph and you shoot an arrow out the back of the train at 100 kph opposite to the direction you are moving. The arrow is therefore stationary with respect to the ground, so it falls straight down to the ground. If the back door of the train was closed the arrow would have pierced the door, so it definitely had kinetic energy. But it is not moving with respect to the ground, so as far as the ground is concerned it does not have kinetic energy. What is going on here? This must be an old problem, but I only just thought of it.
 

Offline thephil

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Re: Shooting an arrow out the back of a moving train
« Reply #1 on: January 14, 2025, 12:36:16 pm »
From the perspective of the ground, the arrow is stationary and the train slammed into it piercing the door. The relative velocity between train and arrow is the same => same energy.
« Last Edit: January 14, 2025, 12:41:01 pm by thephil »
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Offline CirclotronTopic starter

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Re: Shooting an arrow out the back of a moving train
« Reply #2 on: January 14, 2025, 12:43:16 pm »
What about when it reaches the ground though? That is the main question. It appears to have no kinetic energy because it is not moving with respect to the the ground.
 

Online krish2487

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Re: Shooting an arrow out the back of a moving train
« Reply #3 on: January 14, 2025, 12:59:48 pm »
In one direction... vertically, it still has potential energy by virtue of its height from the ground...  :)
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Offline NE666

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Re: Shooting an arrow out the back of a moving train
« Reply #4 on: January 14, 2025, 01:01:04 pm »
Newton's third law, perhaps? i.e. reaction force, to accelerate the arrow relative to the train.

Sounds the same class of problem as 'how do rockets work'. Momentum is conserved as the mass of the arrow is lost from the train, causing it to accelerate relative to the ground.
« Last Edit: January 14, 2025, 01:12:18 pm by NE666 »
 

Offline Nominal Animal

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Re: Shooting an arrow out the back of a moving train
« Reply #5 on: January 14, 2025, 02:57:20 pm »
Say you are on a train doing 100 kph and you shoot an arrow out the back of the train at 100 kph opposite to the direction you are moving.
If you were in vacuum, then to an observer looking at the train whizzing past, the arrow just drops to the ground, vertically.

It is the fluid medium (air) and its movement with respect to the shooting position and arrow during flight that makes reality behave differently.  We humans take it instinctively into account when thinking of the situation: when we see a rotating ball flying towards us, we can often instinctively "see"/"tell" how the trajectory will curve.

If we included the fluid medium into the model, all the weirdness and unintuivity would drop away, into the air turbulence following the train.  Even the difference to when shooting the arrow inside the cabin would become obvious: now the medium is in standstill with respect to the shooter, whereas before there was a turbulent transfer from still with respect to shooter to still with respect to ground.
« Last Edit: January 14, 2025, 02:59:09 pm by Nominal Animal »
 

Offline themadhippy

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Re: Shooting an arrow out the back of a moving train
« Reply #6 on: January 14, 2025, 03:05:05 pm »
If youd watched enough spaghetti westerns  youd know the answer,the arrow hits the  cowboy chasing down the train and at the same time the cowboy shots the injun on the train,killing em both- roll credits
 
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Offline Stray Electron

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Re: Shooting an arrow out the back of a moving train
« Reply #7 on: January 14, 2025, 03:29:58 pm »
Say you are on a train doing 100 kph and you shoot an arrow out the back of the train at 100 kph opposite to the direction you are moving. The arrow is therefore stationary with respect to the ground, so it falls straight down to the ground. If the back door of the train was closed the arrow would have pierced the door, so it definitely had kinetic energy. But it is not moving with respect to the ground, so as far as the ground is concerned it does not have kinetic energy. What is going on here?

  <\quote>

  With respect to the ground the arrow has no horizontal velocity but the door of the train does (100 MPH) so in effect the door of the train runs into the stationary arrow.  The arrow has no kinetic energy with respect to ground but the train does. It's exactly the same situation as if you were to hit a stationary baseball with a bat.

    In addition as you point out, neglecting any energy imparted by the possible impact of the door the arrow is effected by gravity so it does drop only vertically with respect to ground. 


 

Offline magic

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Re: Shooting an arrow out the back of a moving train
« Reply #8 on: January 14, 2025, 03:33:50 pm »
You have accelerated the train by stopping a moving arrow and dropping it on the ground.
 

Offline bw2341

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Re: Shooting an arrow out the back of a moving train
« Reply #9 on: January 14, 2025, 03:42:09 pm »
When you calculate kinetic energy, you are using the relative velocity of the object to something else. This number does not become an intrinsic property of the object.

When you switch to the arrow’s velocity relative to the ground, the old value of kinetic energy is meaningless. You have to measure the horizontal velocity of the arrow relative to the ground which would be zero. You can’t compare the two values for kinetic energy because they are not in the same frame of reference.
« Last Edit: January 14, 2025, 03:55:14 pm by bw2341 »
 
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Offline armandine2

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Re: Shooting an arrow out the back of a moving train
« Reply #10 on: January 14, 2025, 03:43:08 pm »
I might be wrong, I think it is in this one  :palm:

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Offline RoGeorge

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Re: Shooting an arrow out the back of a moving train
« Reply #11 on: January 14, 2025, 04:03:56 pm »
If same speed for train and shooting arrow, then yes, if you are a tree, then for you the arrow will just fall like a drop of rain.

The arrow already has kinetic energy before you shoot, because of the moving train.  Then when the arrow is shoot with a bow, all the extra energy from the bow is used to defeat the speed of the train.



But if you want to break physics, take a voltage source, and charge a capacitor through a resistor.  Then disconnect all, and calculate how much energy is left in the capacitor, how much energy was spent by the resistor, and how much energy was taken in total from the voltage source.

You'll discover that half of the energy apparently is missing.  Where energy?  :o



The internet might tell you that the missing energy went into outer space, dissipated as electromagnetic fields.

Now, do the same, charge a capacitor to a certain voltage then disconnect all, except this time, use a current source instead of a voltage source.  If you count the energy again, you'll probably expect half of the energy is missing again, dissipated as electromagnetic fields, just as before when you charged from the voltage source.

Well, no.  When you charge the capacitor from a constant current source, no energy will be missing.  Why?  ;D
« Last Edit: January 14, 2025, 04:07:23 pm by RoGeorge »
 

Offline m k

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Re: Shooting an arrow out the back of a moving train
« Reply #12 on: January 14, 2025, 06:38:21 pm »
What about when it reaches the ground though? That is the main question. It appears to have no kinetic energy because it is not moving with respect to the the ground.

By shooting the arrow you're decreasing its kinetic energy, from the perspective of the ground.
From the perspective of the train the result is negative.
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Online Analog Kid

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Re: Shooting an arrow out the back of a moving train
« Reply #13 on: January 14, 2025, 09:53:51 pm »
If same speed for train and shooting arrow, then yes, if you are a tree, then for you the arrow will just fall like a drop of rain.

The arrow already has kinetic energy before you shoot, because of the moving train.  Then when the arrow is shoot with a bow, all the extra energy from the bow is used to defeat the speed of the train.


But if you want to break physics, take a voltage source, and charge a capacitor through a resistor.  Then disconnect all, and calculate how much energy is left in the capacitor, how much energy was spent by the resistor, and how much energy was taken in total from the voltage source.

You'll discover that half of the energy apparently is missing.  Where energy?  :o


The internet might tell you that the missing energy went into outer space, dissipated as electromagnetic fields.

Now, do the same, charge a capacitor to a certain voltage then disconnect all, except this time, use a current source instead of a voltage source.  If you count the energy again, you'll probably expect half of the energy is missing again, dissipated as electromagnetic fields, just as before when you charged from the voltage source.

Well, no.  When you charge the capacitor from a constant current source, no energy will be missing.  Why?  ;D

If I could possibly understand all of what you wrote, I'd be a fucking genius and would have an innate understanding of electronics. This is Important Stuff to Know.

Unfortunately, neither is true. Scratching my head here.

Care to give us some answers here, Teach?
 

Offline CirclotronTopic starter

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Re: Shooting an arrow out the back of a moving train
« Reply #14 on: January 14, 2025, 11:00:59 pm »
Okay, so now I understand it is like this - before the arrow is fired it is moving at the speed of the train so it has kinetic energy. As it leaves the bow it slows down to zero speed with respect to the ground so it’s kinetic energy also falls to zero. This kinetic energy is transferred into the RECOIL of the bow, then into you, then into the train. So the train and everything in it gets accelerated by the kinetic energy that was in the arrow while it was moving with the train.

What a difference a sleep makes.
 

Offline jonovid

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Re: Shooting an arrow out the back of a moving train
« Reply #15 on: January 14, 2025, 11:02:05 pm »
kinetic energy in the moving train would cancel out the kinetic energy of the arrow with respect to the ground.   
just as kinetic energy of the solar system does not rip us apart.   differential gear if you like.

put section of railway track on top of a flatbed train carriage on a moving train with a small train carriage piggybacking the train.
that small carriage will try to say stationery with respect to the ground.  see- pulling the tablecloth trick
Hobbyist with a basic knowledge of electronics
 

Offline RoGeorge

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Re: Shooting an arrow out the back of a moving train
« Reply #16 on: January 15, 2025, 05:21:05 am »
Care to give us some answers

First paragraph is my understanding about why when looking from the train, the arrow seems to go normally, while when looking from the ground, the arrow falls like dropping a rock.

Second paragraph is a about the "capacitor paradox"
https://en.wikipedia.org/wiki/Two_capacitor_paradox
http://kirkmcd.princeton.edu/examples/twocaps.pdf

Third paragraph is something that I've accidentally "discovered" by myself while trying to come up with a more intuitive explanation for the capacitor paradox.  I still don't understand why the capacitor paradox doesn't happen any more when charging from a constant current source instead of a constant voltage source.



While in the 2nd paragraph the question was rhetorical, like in the "where banana" meme, in the 3rd paragraph my question is genuine.  I don't understand why the difference when replacing a voltage source with a current source.  It was yet another example of a "What is going on here?", as the OP asked, except this time the "What is going on here?" was about electricity, not mechanic.

As for why jumping from an apparent physics paradox about mechanic to another about electricity, it was because of the OP question "What is going on here?".  The question is not about a formula, is about understanding.

Now, what does it means to "understand" something?  That's a tough question.  Usually it means to be able to deconstruct something into components one is familiar with.  There is a saying the we can never "learn something", we can only "get used with something".  The last one is a hint about how a mind works:
- there is an outside reality, that is there independent of us
- there is an inner reality, which is a draft representation of the outside reality
- the outside world is too complex to fit all in one's mind, so we decompose the world into simpler parts, and remember only those main ideas instead of all the details.

Well, how you decompose something?  Imagine you have a continuous datastream coming from your sensory inputs, say you are a newborn hearing others talking for the first time.  You don't know any words yet, the sounds are no different then a noise or a music, the audio datastream from your newborn ears has no meaning.  So what does the brain do?  It classifies.

The most frequent sounds are grouped by their similarities, and by their proximity to each other.  At first, the grouping is fuzzy, but the more often a sequence of sounds occurs, like for example a word, the more that neural path is reinforced, and eventually the brain will auto-learn words.  Won't know yet what the meaning of those words, but will know the sounds. 

But hey, a neuron doesn't know that datastream is coming from a sound, an image, or maybe just from another inner thought.  So it continues to fire and thus to reinforce certain neuro-paths and thus making new categories, this time between the words and the images, and so on.

Eventually, we get an inner representation of the most frequent "categories" out there.  Those categories are the foundation.  We feel we "understand" something when we manage to decompose that something into categories we already formed.



Why the long rambling about understanding, and about how a mind learn to make sense of a stream of sensory inputs and turns it into meaning?  Because the "categories" by which a mind understands, the basic bricks are different from one person to another.  A physicist will try to decompose by using categories like the laws or physics, a programmer will tend to see the world through the perspective of a different set of "categories" like algorithms or data, a mathematician will see the world as math, and so on.

"When all you have is a hammer, everything looks like a nail".  All a mind has is its inner categories.

These basic "groups", in terms of which a brain makes an inner representation of the outside world, are keep morphing over our entire life.  New categories may form (simply by repeated exposure), they can merge and consolidate, or they can refine by splitting into smaller groups, and so on.

That is why the inner representation of a same "something" will always be more or less different from one person to another.  Each brain has its own neuro-pathways for a same datastream, its own "categories".

Another interesting aspect of a mind is about awareness, but this is already too long.



Why the wall of text, you may think.  Sorry man, you asked for it.  ;D

And, to be honest, because I like rambling about things like these.
Helps me sorting out my own thoughts, so thanks for the question.

Online IanB

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Re: Shooting an arrow out the back of a moving train
« Reply #17 on: January 15, 2025, 05:37:45 am »
Say you are on a train doing 100 kph and you shoot an arrow out the back of the train at 100 kph opposite to the direction you are moving. The arrow is therefore stationary with respect to the ground, so it falls straight down to the ground. If the back door of the train was closed the arrow would have pierced the door, so it definitely had kinetic energy. But it is not moving with respect to the ground, so as far as the ground is concerned it does not have kinetic energy. What is going on here? This must be an old problem, but I only just thought of it.

An object does not "have" kinetic energy of itself. Kinetic energy is relative between two reference frames (this is Newtonian relativity).

The arrow has a certain kinetic energy relative to the train. It has a different kinetic energy relative to the ground. It would have no kinetic energy by itself in empty space, regardless of how fast it "might" or "might not" be moving. If there is no reference frame to measure against, you cannot assign a speed, nor a kinetic energy, to it. Relativity says that an object moving at a constant speed cannot be distinguished from an object at rest.

Therefore, when measured against the train, the arrow has a speed and a kinetic energy. When the arrow hits the (back door) of the train, the arrow undergoes a change in speed until it matches the speed of the train. That change in speed of the arrow (the delta-v) causes a dissipation of kinetic energy in the form of sound, vibration and heat.
 
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Online IanB

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Re: Shooting an arrow out the back of a moving train
« Reply #18 on: January 15, 2025, 05:44:16 am »
Another way to see this. Suppose we drop a rock from a bridge in front of a moving train (hypothetically, not a suggestion).

Relative to the ground, the rock has no speed and no kinetic energy. But if the train is travelling at 100 km/h, then as far as the train is concerned, the rock has a kinetic energy corresponding to 100 km/h, because as far as the train is concerned, that is how fast the rock is travelling towards the train. If you are in the train, a rock is flying towards you at 100 km/h, and that is how much kinetic energy it has.
 

Offline NE666

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Re: Shooting an arrow out the back of a moving train
« Reply #19 on: January 15, 2025, 10:18:21 am »
Relative to the ground, the rock has no speed and no kinetic energy.

I think it does. It's accelerating under gravity towards the ground, hence it has velocity in that reference frame.
 

Offline jonovid

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Re: Shooting an arrow out the back of a moving train
« Reply #20 on: January 15, 2025, 11:10:28 am »
mass , acceleration & space-
in the 90s I had a job at a business that made motorized roller doors were I would test 4amp 24volt brushed DC motors on a work bench.
upon applying power, the DC motor would jump & roll across the bench until the armature reached maximin RPM speed then
the motor would just sit still running at top speed. 
there was No mechanical connection between the motor's armature and the work bench. just a change in velocity of the spinning mass inside the motor.

Hobbyist with a basic knowledge of electronics
 
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Offline tom66

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Re: Shooting an arrow out the back of a moving train
« Reply #21 on: January 15, 2025, 11:19:07 am »
mass , acceleration & space-
in the 90s I had a job at a business that made motorized roller doors were I would test 4amp 24volt brushed DC motors on a work bench.
upon applying power, the DC motor would jump & roll across the bench until the armature reached maximin RPM speed then
the motor would just sit still running at top speed. 
there was No mechanical connection between the motor's armature and the work bench. just a change in velocity of the spinning mass inside the motor.

You have indirectly discovered why we have accelerometers, but not velocimeters. (We can use a sensor to measure velocity, but only with respect to an external reference frame, like GPS satellites or computer vision, or a speedometer measuring wheel speeds.)
 

Online IanB

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Re: Shooting an arrow out the back of a moving train
« Reply #22 on: January 15, 2025, 05:20:26 pm »
Relative to the ground, the rock has no speed and no kinetic energy.

I think it does. It's accelerating under gravity towards the ground, hence it has velocity in that reference frame.

You are correct, but I excluded this in the interests of brevity. The rock has downward velocity, but no horizontal component of velocity in the direction of motion of the train. Therefore the downward velocity has no influence on the outcome of the impact between rock and train.
 
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Offline Ranayna

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Re: Shooting an arrow out the back of a moving train
« Reply #23 on: January 16, 2025, 08:10:31 am »
This reminds me of the Mythbusters skit, where they shot a ball from a moving car, to show that the velocities cancel each other out. They managed to get it impressively close.
It's on Youtube, i can try to find the link tonight.
 

Offline mikerj

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Re: Shooting an arrow out the back of a moving train
« Reply #24 on: January 16, 2025, 10:52:06 am »
Mythbusters S07E09  "Vector Vengeance" https://youtu.be/ZMO9T5x7_-I?si=X6JJZiZT8YRYbO9P
 


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