Veritasium Falling Ladder Problem
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- Опубликовано: 25 янв 2023
- Here is my solution to the @veritasium falling ladder problem (here's the video - • Falling ladders - why ... .
The demo shows two falling ladders. One hits a table and one doesn't. Which one falls the fastest (greatest acceleration)? The answer is the one that hits the table. Here's why.
Bonus. Here's a python model of a bouncing stick. I'm going to use this to build a full falling ladder model.
• Modeling a Bouncing St...
It would be interesting to repeat the experiment with non-tilted rope ladders. . .
... be good scientific procedure, except this is not an experiment, it is a designed puzzle, to challenge your ability to see the solution/explanation.
How about slinkies?
ruclips.net/video/uiyMuHuCFo4/видео.html
@@you2tooyou2too here it is presented as a puzzle, but it was an experiment. Ruina, Grewal, and Johnson wrote a paper about it in 2011 called "A chain that accelerates, rather than slows, due to collisions: how compression can cause tension".
No tilted rope ladders will fall exactly the same, the whole point is to get the force from the tilt.
ruclips.net/user/shortsn8WxkqMRgS4?si=QHDZZlN8NYEt-vdK
THIS IS SUCH A LOVELY EXPLANATION!
After seing the veritasium short, I instantly understood by looking at your sketches. Good sketches are everything.
Thanks
Very well explained. Didn't understand it before, but You made it clear
Interesting, and it will be fun to see how this works in Python.
I like your explanation. Very well put.
Thanks for your explanation,😊😊
Best wishes from Iran❤
Love the the explanation thank you!
Looking forward to seeing the Python video!
me too
Good explanation. I thought it was because the rungs were falling off the top of the pile which would pull on the strings, but after rewatching the video it looks like you are correct.
Kudos to whoever discovered/invented this puzzle!
BTW: Looking carefully at the strings, you might notice that the strings are more precisely a little spring like, which begs another 'problem' to require recognizing a surprising effect of that subtle characteristic.
THANKS!! :)
great explanation, greetings from Italy
Sounds good to me. After watching your video, I looked at the original video at 0.25 speed, you can see the tension.
Yes. If you look carefully, you can see the tension propagate upward along the string on the non-hitting side of the ladder.
Great content thank you!!
Thank You🏆✔️
the key is conservation of angular momentum - the ladder experiment was created to deterime if a link from a falling chain will interact with the chain when hitting the ground or disconnects from the chain (standard textbook assumption). It is still valid for an ordanary chain, the last link does not pass any energy upwards like in this special angular formed chain.
It's like that stick experiment that the end of the stick exceeds g.
So there has to be multiple pairs of acceleration due to gravity and angle of the rungs of the ladder where the experiment has a differenr eesult, and both ladders fall at the same rate?
E =m x c^2 m = E/c^2
When the ladder contacts the table, the total energy of the ladder increases. Hence, so does the mass. As the mass increases, so does the terminal velocity.
Terminal Velocity = (2 x mass x gravity / density x area x drag coefficient) ^ 1/2
Good video
Thanks
The ladder that is allowed to collapse on itself has less air friction to deal with between each rug.
My first instinct was that there is more surface area on the free-falling ladder for air resistance to act upon. Would/Should this have an effect?
The stopped tabled ladder rungs have much more resistance to falling. ;-)
Does the speed increase exponentially for each rung that hits the table next or will It just reach it’s new max terminal velocity? (Say hypothetically there’s ♾️ number of rungs, string)
It will eventually reach a new terminal velocity. The speed can not increase infinitely.
Wrong is an Important step in reaching right, if you're any good, you'll keep making steps.
Do you think he’s wrong?
Wait, the claim that in free fall the rungs shouldn't pull on each other feels suspect. For that to be true they should maintain a constant distance apart in free fall.
However, the total distance fallen goes like t^2 where t is time from release. Ok so let's look at (t+dt)^2 - t^2 where dt is time between a rung being released and the next one being released.
That's going to be 2t*dt + dt^2 which isn't a constant. So there should be a force exerted!
Very good but the rotation is not just around the center of mass because the other components right from the point of impact still have kinetic energy and thus push down on the lever as well giving even more angular momentum into the effect. Good analysis though
You remind me of Saul Goodman (in a good way)
That stands true only and only if the strings are of unequal lengths. Otherwise the ladders will fall at the same time.
It is one of experiments that is designed to induce thinking in science oriented brains, but for majority people will create confusion as in real life you have no useful ladders with uneven strings, or tilted rungs.
now it makes sense
Assuming the length of the strings holding each rung is the same on both sides, and as you shared one side hits the ground first. However it would then become impossible for the opposing side's string to ever fully extend to exert a force on the rung above. Only in tension would the string exert a force, and it could not be in tension if one side hits the ground. There must be another explanation.
the chains are fixed to the rungs . so they are always fully extended while falling. the rungs can't slide on the chains
You can see the string distance shortening with every successive rung hitting the table. This model is losing that energy every "step" of the way.
We can see the one mass (the ladder on the right) free falling through the curvature of space time longer than the mass of the ladder that hits the table. I think the only "force" at play determining which ladder wins the race is gravity. The ropes and rungs feel like a red herring to distract from the idea that people are simply watching 2 masses in free fall...one falling shorter than the other.
the bottom rungs of one ladder move upward at a speed opposite to free fall, and the table hits the second ladder, removing it.
Therefore, it falls faster, it has less stress from the steps moving up
"But what happens adfter the other side hits."
"It's too late ..."
This is a key point. In an undamped system, the rungs recoil, and then bounce off the table. This is a damped system, and the rungs do not recoil. So it actually does matter what happens after. In an undamped system, with elastic collisions, and a zero-mass rope, the strike of the left side will cause the left side to recoil, and it will bounce back, not at the same initial speed, but with the whole ladder having the same kinetic energy, since the earth can absorb momentum but due to its infinite mass cannot accumulate kinetic energy (E = p^2/2m).
What we know is the net acceleration of the whole latter, with the bounce, must continue to be g (or -g, depending on coordinates), the acceleration of gravity. So when the upper rungs are accelerating at a greater acceleration, then the bottom rung is accelerating at something other than g. This is due to the tension on the rope: the rope is supporting the lower rung.
If the ladder were infinitely long there would be no effect. As the remaining ladder gets shorter, the effect grows inversely proportional to the remaining ladder.
It is Andy ruina experiment not veritasium channel’s
Here is the solution:
Let the distance which hit the table be S1 and other one be S2
And time taken by both respectively be x and y
To prove XS1
can u clarify s1 and s2
@@omurice8534 s1 and s2 are distance between initial and final position as you can see s1 is smaller as compared with s2
If you drop a single stick at an angle does the free end speed up more when the lower end strikes the table than a second similar stick that misses the table? Long winded way of claiming that you just need to model a single wrung and not the whole ladder.
Yes. The part that hits first rebounds faster
@@DotPhysics In your experience, you know this is true, since as you will remember, such a solitary rod (or fork or knife ...) dropped that way clatters at least several times, as the ends alternately bounce, before it finally comes to rest.
This more than any other confounding problem, initially blew my brain (not that difficult)
the weight pulling down is more ?constant on the right. the left ladder has less mass pulling it down as the rungs hit. The no table ladder has constant downforce of ALL the rungs. no interruption.
But the table ladder falls faster.
correct
This is my intuition as well. My only issue is that when the side of the rung hits the ground it should also apply an upwards force to the other side that hasn't hit yet. But if that force is less than the rotating force it works out. And maybe this ratio depends on something like the length of the rungs.
Looking forward to your model. It would be interesting to see what varying the lengths do.
The explanation seems logical and correct. (With reference to the diagram in video) when one end of the rung will hit the table, then by considering the end as pivot if we apply torque balance, then there will be a net unbalanced torque due to weight acting at centroid. Thus, there will be an angular acceleration in clockwise direction, which will pull the string downward.
Edit: Did the math, the angular acceleration is coming out to be 3g/2L. Thus, the linear acceleration of the free end will be 3g/2 (>g).
The upward force on the left, however, is not affecting the upper parts of the ladder, since it is connected only by ropes that will simply fold up...
@@m.rieger8856 exactly
The ratio depends on the angle of the rungs and acceleration due to gravity, I think. And also the elastic coefficient or collision coefficient (I don't remember what it's called.) Like, if the end of the rung that hits first has a perfectly elastic collision then it'll tend to exert a force promoting higher angular momentum. So imo, there must be pairs, or rather triads of data points, like, for a value of the collision coefficient, a value of the acceleration due to gravity and a value of the angle of rungs with horizontal the ladders could fall at the same rate irrespective of which lands on the table.
I can't see how the rung hitting the table would rotate faster than gravity is pulling the rung above down? It has to be due to vibration of the rungs caused by hitting a hard surface.
As soon as he said remember the ladder rungs are tilted I figured it all out just drop a pencil and watch it when it hits the ground at an angle the part of the pencil that in the air travels faster than the following speed of the pencil
i epxlained it to myself the same way.
I propose that he's wrong, because it happens because the air friction is reduced each time a rung hits the table.
That is kind of similar to the chain fountain phenomenon.
Putting this here before I watch it to see if im stupid: Is it just because the slats are wonky and as one hits the table and takes the chain out of tension, the other chain is placed under tension, creating a moment on the next slat that works to pull the whole ladder down???
Yooooo I was right, seriously wasn’t expecting that
Shit - I was right if you were right**
If you think yout explanation is correct, you should verify it with 2 all horizontal rungs ladders.
Good, but the fairly random string positions might still cause one end of some of the rungs to stop/bounce first. (Silk or some vanishingly flexible line would reduce this complication.)
In short: Newtons 3rd law… Actio=Reactio
air resistance: the ladder hitting the table has less (actually decreasing) contact with the air.
I suspect that the mass of the ladder (and the speed that it moves) means that any air resistance force would be negligible
@@DotPhysics it is not… negligible
@@DotPhysics Have you tried a setup with thinnest flexible fish‑cord to attach the elements? The resistance of the cord from Veritasium's setup is in favour of the slower fall though, so it can not e a reason.
To accelerate something faster with the same amount of energy seems unintuitive
Rotation is Slower than gravitational acceleration
As the rung hits the table it vibrates. As the rung vibrates it's exerting energy up and down, because it's connected via rope to the rungs above, it's almost entirely the downward energy that transferred increasing the ladders decent. This is why they make hammers with wooden handles.
Good try
💤🥱💤