Shooting an arrow out the back of a moving train - Page 1
Forum section: electronics / general

author: Circlotron
author_rank: Super Contributor
timestamp: January 14, 2025, 12:29:50 pm
content: 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.

author: thephil
author_rank: Regular Contributor
timestamp: January 14, 2025, 12:36:16 pm
content: 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.

author: Circlotron
author_rank: Super Contributor
timestamp: January 14, 2025, 12:43:16 pm
content: 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.

author: krish2487
author_rank: Frequent Contributor
timestamp: January 14, 2025, 12:59:48 pm
content: In one direction... vertically, it still has potential energy by virtue of its height from the ground...

author: NE666
author_rank: Frequent Contributor
timestamp: January 14, 2025, 01:01:04 pm
content: 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.

author: Nominal Animal
author_rank: Super Contributor
timestamp: January 14, 2025, 02:57:20 pm
content: Quote from: Circlotron on January 14, 2025, 12:29:50 pmIf 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.

author: themadhippy
author_rank: Super Contributor
timestamp: January 14, 2025, 03:05:05 pm
content: 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

author: Stray Electron
author_rank: Super Contributor
timestamp: January 14, 2025, 03:29:58 pm
content: Quote from: Circlotron on January 14, 2025, 12:29:50 pm

author: magic
author_rank: Super Contributor
timestamp: January 14, 2025, 03:33:50 pm
content: You have accelerated the train by stopping a moving arrow and dropping it on the ground.

author: bw2341
author_rank: Regular Contributor
timestamp: January 14, 2025, 03:42:09 pm
content: 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.

author: armandine2
author_rank: Frequent Contributor
timestamp: January 14, 2025, 03:43:08 pm
content: I might be wrong, I think it is in this one

author: RoGeorge
author_rank: Super Contributor
timestamp: January 14, 2025, 04:03:56 pm
content: 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?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?

author: m k
author_rank: Super Contributor
timestamp: January 14, 2025, 06:38:21 pm
content: Quote from: Circlotron on January 14, 2025, 12:43:16 pmBy 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.

author: Analog Kid
author_rank: Super Contributor
timestamp: January 14, 2025, 09:53:51 pm
content: Quote from: RoGeorge on January 14, 2025, 04:03:56 pmIf 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?

author: Circlotron
author_rank: Super Contributor
timestamp: January 14, 2025, 11:00:59 pm
content: 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.

author: jonovid
author_rank: Super Contributor
timestamp: January 14, 2025, 11:02:05 pm
content: 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

author: RoGeorge
author_rank: Super Contributor
timestamp: January 15, 2025, 05:21:05 am
content: Quote from: Analog Kid on January 14, 2025, 09:53:51 pmFirst 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_paradoxhttp://kirkmcd.princeton.edu/examples/twocaps.pdfThird 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.And, to be honest, because I like rambling about things like these.Helps me sorting out my own thoughts, so thanks for the question.

author: IanB
author_rank: Super Contributor
timestamp: January 15, 2025, 05:37:45 am
content: Quote from: Circlotron on January 14, 2025, 12:29:50 pmAn 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.

author: IanB
author_rank: Super Contributor
timestamp: January 15, 2025, 05:44:16 am
content: 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.

author: NE666
author_rank: Frequent Contributor
timestamp: January 15, 2025, 10:18:21 am
content: Quote from: IanB on January 15, 2025, 05:44:16 amI think it does. It's accelerating under gravity towards the ground, hence it has velocity in that reference frame.

author: jonovid
author_rank: Super Contributor
timestamp: January 15, 2025, 11:10:28 am
content: 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 thenthe 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.

author: tom66
author_rank: Super Contributor
timestamp: January 15, 2025, 11:19:07 am
content: Quote from: jonovid on January 15, 2025, 11:10:28 amYou 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.)

author: IanB
author_rank: Super Contributor
timestamp: January 15, 2025, 05:20:26 pm
content: Quote from: NE666 on January 15, 2025, 10:18:21 amYou 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.

author: Ranayna
author_rank: Super Contributor
timestamp: January 16, 2025, 08:10:31 am
content: 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.

author: mikerj
author_rank: Super Contributor
timestamp: January 16, 2025, 10:52:06 am
content: Mythbusters S07E09 "Vector Vengeance"https://youtu.be/ZMO9T5x7_-I?si=X6JJZiZT8YRYbO9P

author: EPAIII
author_rank: Super Contributor
timestamp: January 17, 2025, 05:41:16 am
content: Bingo!Before shooting the arrow both the train and the arrow have kinetic energy because both are moving at 100 MPH with respect to the ground.Now, every action has an equal and opposite reaction. So when the arrow is shot it loses it's kinetic energy with respect to the ground. And, due to that equal and opposite reaction, the train's kinetic energy is increased by exactly the same amount.The arrow then drops to the ground because it has no horizontal velocity with respect to the ground. And the train is going faster. The total kinetic energy of the overall system remains exactly the same, neglecting the inevitable losses to heat due to friction of course.Please spare me the nit picking. This is not intended to be a complete explanation of what happens but it does cover the broad strokes.Quote from: magic on January 14, 2025, 03:33:50 pm

author: coppercone2
author_rank: Super Contributor
timestamp: January 17, 2025, 07:26:50 am
content: you shoot a neutronium tipped arrow from the back of a train car

author: Andy Chee
author_rank: Super Contributor
timestamp: January 17, 2025, 09:43:57 am
content: Another relevant Mythbusters experiment is the elevator drop, and whether jumping before impact would soften the blow.

author: Circlotron
author_rank: Super Contributor
timestamp: January 17, 2025, 11:34:35 am
content: Quote from: EPAIII on January 17, 2025, 05:41:16 amThat's the same conclusion I came to.Quote from: Circlotron on January 14, 2025, 11:00:59 pm

author: EPAIII
author_rank: Super Contributor
timestamp: January 21, 2025, 08:37:00 pm
content: Evil minds think alike!My apology, I didn't read all the responses before answering.Seriously, it is the first year mechanics class in physics explanation. It leaves out all the absurd factors like the speed of light and the curvature nature of the gravitational field, relativity, etc. and probably still predicts the results to at least 10 places, probably 12 or more.Did I say first year mechanics class? Probably in the first few weeks, before the first pop-quiz. Elementary my dear Watson, elementary!Quote from: Circlotron on January 17, 2025, 11:34:35 am

author: BrianHG
author_rank: Super Contributor
timestamp: January 21, 2025, 09:52:56 pm
content: These 2 videos seem to hit the point:Shooting a Nerf Gun Backwards While Driving At The Bullet's Speed ForwardRunning Off A Vehicle Backwards At The Same Speed That It Is Driving Forward!

author: IanB
author_rank: Super Contributor
timestamp: January 21, 2025, 11:18:51 pm
content: Quote from: EPAIII on January 17, 2025, 05:41:16 amAn important message to really take home from all the discussion above, is that kinetic energy is not a "property" of an object. You cannot know the kinetic energy of an object. You can only measure the kinetic energy of an object (strictly speaking the change in kinetic energy) relative to some external frame of reference.For example, if you are inside the moving train, with all doors and windows blacked out, radio signals blocked, on a perfectly smooth track with no noise and vibration, and no acceleration, then there is no way to tell whether the train is moving or not. In that case, your frame of reference is the floor you are standing on, and the arrow in the bow has zero kinetic energy in your frame of reference. If you shoot the arrow from the bow, then it gains kinetic energy according to its new speed, and that is all you can say about it.As a further illustration, consider that everyone reading this is currently traveling at a speed of at least 67,000 mph, and yet we don't think we have a kinetic energy corresponding to that speed. (Although, relative to something not moving at 67,000 mph, that is a LOT of kinetic energy.)

author: Analog Kid
author_rank: Super Contributor
timestamp: January 21, 2025, 11:26:36 pm
content: Heh; in my younger days when I'd get high (420) and take a walk, I'd sometimes imagine that, instead of me moving along my path, I was stationary and my footsteps were revolving the entire Earth beneath me. Amazing how effortless that was!Pretty kewl illusion if you can manage it ...

author: Andy Chee
author_rank: Super Contributor
timestamp: January 22, 2025, 12:53:02 am
content: Quote from: Analog Kid on January 21, 2025, 11:26:36 pmSomething like this?

author: Analog Kid
author_rank: Super Contributor
timestamp: January 22, 2025, 01:07:38 am
content: Something like that.Never had a totally natty hat like that, though.

author: SiliconWizard
author_rank: Super Contributor
timestamp: January 22, 2025, 01:30:30 am
content: It's all relative.For a bit more elaboration, you can refer to this discussion:https://physics.stackexchange.com/questions/51220/kinetic-energy-with-respect-to-different-reference-frames

author: IanB
author_rank: Super Contributor
timestamp: January 22, 2025, 03:41:25 am
content: Unfortunately, that StackExchange discussion only deals with elastic collisions. An arrow hitting wood is an inelastic collision. But the theory still works if we consider conservation of momentum, and that thechangein kinetic energy is what matters, before and after, rather than the absolute value of kinetic energy.For example, let's suppose two lumps of dough, each weighing 1 kg, collide, and after the collision they stick together. Not sure how or why this might happen, but whatever. To an outside observer, each lump of dough is travelling at 5 m/s.Case 1: From the outside observer's frame of reference, each lump of dough has a kinetic energy of 0.5 x (1 kg) x (5 m/s)² = 12.5 J, for a total of 25 J. After the collision, the combined lump of dough is stationary, so it has a kinetic energy of 0 J. The change in kinetic energy during the collision was 25 J − 0 J = 50 J.Case 2: From the perspective of a fly sitting on one dough ball, it is stationary, but the other dough ball is approaching at -10 m/s. So the total kinetic energy before the collision is 0 J plus 0.5 x (1 kg) x (-10 m/s)² = 50 J. Assuming the fly didn't get squashed, it will find the combined lump of dough after the collision is now moving backwards* at -5 m/s. So the new kinetic energy is 0.5 x (2 kg) x (-5 m/s)² = 25 J. Therefore the change in kinetic energy is 50 J − 25 J = 25 J. The change in kinetic energy is 25 J, the same as before.*Why it's moving backwards at 5 m/s is conservation of momentum: We have (1 kg) x (0 m/s) + (1 kg) x (-10 m/s) = (2 kg) x (? m/s), therefore the new velocity = -5 m/s to balance the equation.

author: .RC.
author_rank: Frequent Contributor
timestamp: January 22, 2025, 11:00:54 am
content: This is an easy one to experiment with yourself and someone reliable. Just use a slow moving vehicle say under 10kph and jump from it preferably from the rear so you do not get run over. It you just slowly step off onto the ground you will fall in the direction the vehicle is travelling. If you jump off in the opposite direction the vehicle is travelling you will cancel out your momentum with respect to the ground.Another one that catches people out is say you have two tractors joined by a piece of rope pulling against each other, each tractor can pull five tonnes. How much strain is on the rope?A: 0 tonnesB: 5 tonnesC: 10 tonnesD: 12.75 tonnesE: There is no rope.

author: EggertEnjoyer123
author_rank: Frequent Contributor
timestamp: January 23, 2025, 02:31:16 am
content: Quote from: RoGeorge on January 14, 2025, 04:03:56 pmYou could theoretically have a current source connected to a capacitor with no resistance, and no rules are broken. There is no infinite voltage or current in this scenario. The capacitor voltage would just increase linearly. With the voltage source, infinite current would flow through the capacitor if there were no resistance, which is impossible, so there must be some kind of loss in the circuit. If we assume the voltage source is 1V and the capacitor is at 0V, then charging the capacitor from 0V to 0.1V forces you to waste at least 90% of the power from the voltage source (the remaining 0.9V is dissipated or radiated across something). With the current source, charging the capacitor from 0V to 0.1V costs pretty much no power, because power is I * V and V is almost zero. If the current source is 1A, then at the beginning no power is supplied by the current source because 1A * 0V = 0. At the end, the current source is only providing 0.1W (1A * 0.1V). If the voltage source provides 1A, then it must produce 1W, which is a lot higher than what the current source provides.

author: Andy Chee
author_rank: Super Contributor
timestamp: January 23, 2025, 02:44:05 am
content: Quote from: .RC. on January 22, 2025, 11:00:54 amMythbusters also has a similar episode, testing the statement that two cars crashing head-on at 50mph is the same as a single car crashing into a stationary brick wall at 100mph.

author: electrodacus
author_rank: Super Contributor
timestamp: February 03, 2025, 04:50:23 am
content: Quote from: RoGeorge on January 15, 2025, 05:21:05 amI think the original problem was answered.Regarding the capacitor paradox (there is no paradox).In your example charging a capacitor trough a series resistor from a constant voltage source half of energy is found in capacitor and the other half was dissipated by the series resistor.There is nothing missing. That half you think is missing had just increased the temperature in the room you performed the experiment.

author: coppercone2
author_rank: Super Contributor
timestamp: February 03, 2025, 05:40:17 am
content: this is why a educational lab needs a 50 amp power supply, super caps and smoke

author: SiliconWizard
author_rank: Super Contributor
timestamp: February 03, 2025, 05:50:36 am
content: Or you need to destroy vehicles just to illustrate basic laws of physics.

author: coppercone2
author_rank: Super Contributor
timestamp: February 03, 2025, 04:53:34 pm
content: you wont hear someone going 'well uh... lemme try to remember what that guy wrote on a chalk board 20 years ago..."

author: vidarr
author_rank: Frequent Contributor
timestamp: February 08, 2025, 09:14:10 pm
content: If you were on a high speed train and you fired a round from a pistol/rifle at another train behind it by the correct distance, which you are standing at the front of, you could catch the bullet in the air.

author: benseno
author_rank: Regular Contributor
timestamp: February 08, 2025, 09:28:15 pm
content: What is the difference between the car hitting the wall and the wall hitting the car?

author: Circlotron
author_rank: Super Contributor
timestamp: February 08, 2025, 10:33:13 pm
content: Quote from: benseno on February 08, 2025, 09:28:15 pmThe difference is who is liable and has to pay the cost of damages.

author: SiliconWizard
author_rank: Super Contributor
timestamp: February 08, 2025, 10:45:06 pm
content: Quote from: benseno on February 08, 2025, 09:28:15 pmThis question is more interesting than it may look at first sight. Assuming the same acceleration functions, it appears to be the same thing.While this is a matter of reference, we're tempted to think that causality is only a one-way direction though, and thus that causality is not (quite) relative to the frame of reference.Feel free to elaborate on that though: from the reference frame of the car, it's the wall that is moving towards it. But is the wall the cause of the collision?

author: benseno
author_rank: Regular Contributor
timestamp: February 08, 2025, 11:04:39 pm
content: Quote from: SiliconWizard on February 08, 2025, 10:45:06 pmOne hand can never applaud alone. So the collision. It is a party of two.