Lever Launcher and Angular Momentum - Testing Physics
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- Опубликовано: 16 июл 2024
- In this video, we demonstrate the principle of conservation of angular momentum for a series of lever launcher experiments, where a mass m1 collides with a horizontal lever in such a way that it launches a second mass m2 on the other side of the lever. We do 26 different trials covering 13 different physical scenarios, using a variety of different masses hitting at different distances, using different bumpers for the masses (spring bumpers or clay), and using both rigid and flexible bars.
We find a strong agreement between the standard physics model based on conservation of angular momentum and our data, with a strong match between the initial and final angular momenta (22 of 26 trials matching within 5% and half of the trials matching within 2.5%). We do not find a single case where the final velocities of the carts are outside of the range of what was predicted for the elastic and completely inelastic cases (as predicted by standard physics models). We do not find a single case where the energy of the system increases (no free energy).
Full Series Playlist: • Testing Physics
0:00 Introduction
0:54 Overview of relevant physics
3:36 Key importance of angular momentum
4:12 Models for completely inelastic and perfectly elastic cases
5:25 Using Excel for calculations
10:36 Verifying Excel Calculations match predicted equations
13:03 Measuring properties of rigid and flexible bars
18:46 Track setup
21:16 Types of collisions
22:40 Equal Mass Equal Distance Data Collection (Trials 1-4)
28:01 Analysis Preamble
31:36 Measuring angular velocity
35:27 Equal Mass Equal Distance Analysis (Trials 1-4)
41:07 It’s not linear momentum
42:53 Double Mass Half Distance Data Collection (Trials 5-8)
48:24 Double Mass Half Distance Analysis (Trials 5-8)
55:03 Triple Mass Third Distance Data Collection (Trials 9-12)
1:00:20 Triple Mass Third Distance Analysis (Trials 9-12)
1:06:20 Equal Mass Half Distance Data Collection (Trials 13-16)
1:11:46 Equal Mass Half Distance Analysis (Trials 13-16)
1:15:57 Double Mass Equal Distance Data Collection (Trials 17-20)
1:20:06 Double Mass Equal Distance Analysis (Trials 17-20)
1:22:58 Wood Lever Double Mass Half Distance Data Collection (Trials 21-22)
1:26:43 Wood Lever Double Mass Half Distance Analysis (Trials 21-22)
1:29:12 Wood Lever Triple Mass Third Distance Data Collection (Trials 23-24)
1:31:33 Wood Lever Triple Mass Third Distance Analysis (Trials 23-24)
1:33:05 Wood Lever Equal Mass Half Distance Data Collection (Trials 25-26)
1:35:46 Wood Lever Equal Mass Half Distance Analysis (Trials 25-26)
1:37:37 Concluding Remarks
Opening Image Credit: NASA, ESA, CSA, Janice Lee (NSF's NOIRLab) webbtelescope.org/contents/me...
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Thank you so much for the enormous pile of work you did, Michael. 👍
Physics works!
There is NO free energy.
#TetherIncident
A Herculean effort, Michael. Thank you.
Thank you Michael.
Amazing amount of time and effort put in here, especially after losing the first runs on the crashed laptop.
I don't think this will be a convincer for a certain someone, but that is no detriment to your good self, no experiment would do that, for obvious reasons.
Great work though Michael, I enjoyed it.👍😊
I can't imagine the amount of hours that went into the making of this video. Thanks a lot for doing this!
Thanks Michael for the video. Gives me something interesting to listen to at work! 🙇
"You are diverting your attention.
Get back to work!" - Boss 👺
Thank you. Would you kindly consider a video about the Higgs Mechanism, please? Thank you.
3:34 I am I right in saying this?
_|L|/ℓ(bar) is the magnitude of the distance weighted average of all the linear momenta components of the system relative the pivot point that are normal to the_
_rod's length._
Hello PhysicistMichael, i just wanted to let you know that i also have done a (small scale) lever experiment with a very light weighted carbon tube (2.75g). I did some tests with a one mass at twice the distance from the fulcrum and a 2 mass at half the distance from the fulcrum. The results that i got was that the one mass went 1.51x faster than the two mass on average.
Link: ruclips.net/video/mzoA2aV0FWg/видео.html
Would it be possible for you to do the 3:1 mass ratio newtons cradle experiment? I think that's the only experiment DS will accept.
I'm looking into making a large Newton's cradle experiment. I'm not sure if I'll have the equipment for the exact 3:1 mass ratio, but it will be large:small and we can calculate the predicted vs measured accordingly. However, at this point I doubt anything would ever be accepted (I hope I'm wrong)
@@PhysicistMichael
Sweet!
I recently saw DS mock your voice, but I quite like it because it reminds me of _Brian Griffin_ from _Family Guy._ 😁
Have to admit, when I read this, Peter Griffin was the image that jumped in my head and I didn't see the resemblance until I remember which one Brian was.
@@PhysicistMichael I'd never refer to you as a fat dumb slob like that. Brian is probably the best character on that show, so it is a complement ‼️
Brian is voiced by Seth MacFarlane with his own voice, so I guess you are from Boston as well..?
I do take it as a compliment, just mentioning my own initially mistaken attribution. I laughed after I corrected the character.
@wotteo702 I don't know what you're talking aboot.
@@wotteo702The german dissident physicist _Alexander Unzicker_ backs him up on that.
He recently plugged a book aboot it on his channel. _Liquid Sun_ 🌞 💦, _Cold Sun_ 🥶..
-Who'da thunk it, eh? Ya think I need a _toque_ for the walk to _Timmies?_
I'm interested in trial 13. You have equal masses, m.
Before: velocities to the left of 0.554 and 0
After: velocities to the left of -0.282 and -0.408
That means the linear momentum went from 0.554m to -0.690m, a loss of over 224%.
I understand that linear momentum won't be conserved, because a bunch of it goes into the earth via the fulcrum. But isn't it surprising that over 200% of it can go into the fulcrum? When you get a perfect elastic bounce (like a steel ball off an anvil, say), only 200% of the linear momentum goes into the anvil. How is it possible for over 200% to go into the fulcrum? Does this result surprise you too?
DS states that this is creating "free KE", but that's obviously not the case. KE before is (0.554^2)m/2 = 0.307m/2 and KE after is (0.282^2 + 0.408^2)m/2 = 0.246m/2 - a clear loss of KE.
See also trials 14 (222% linear momentum loss), 25 (207% loss), and 26 (211% loss)
This is a great question and the full response might warrant its own video, but let me give a quick (not very quick) rundown.
The case of a single object bouncing off a very massive object (steel ball off anvil) and this lever launch (with the lever fixed to a massive object like the Earth) is different in that the lever is launching back more mass than was originally incoming (both m1 and m2), and because of this, we can arrange scenarios where there can be MUCH more momentum transferred to the large object.
In both cases, the original incoming object has a certain amount of KE (1/2 x m1 x v0^2). In order to transfer more momentum to the large mass, we want to use that KE to get as much motion being launched in the opposite direction. If the target object is MUCH more massive, then even if there is a large momentum transfer, it'll barely use up any of the KE.
In the steel ball off anvil case, there's only one object, so if it uses essentially all the available KE to go back in the original direction, at the original speed, so that reversal of the direction of the momentum gives that 200% transfer to the massive object.
In the lever case, _we launch more mass backwards than was originally incoming_ , that being both m1 and m2. If the mass launched backwards is larger, we can get more backwards momentum for those pieces using the same total KE.
I've been playing around with how to optimize this, and the best cases are when m2 is much larger than m1 and closer (but not too close) to the fulcrum point, such that after impact, both m1 and m2 bounce backwards with the same speed (the needed r distances can be calculated). The amount of change in momentum you can get for the mass attached to the fulcrum maxes out at (1+sqrt((m1+m2)/m1))
In terms of the mechanics, when m1 hits at a further distance, even though the force of the impact might be small, it generates much larger forces at m2's location closer to the fulcrum (and even larger forces at the fulcrum itself). That large force at the fulcrum acting over the impact time results in an increased change in momentum. But there's a balancing act... if m2 is too far from the fulcrum, there's too much leverage during the hit, and m1 will just reflect backwards with most of the original velocity, and we'll be back to the anvil case. If m2 it too close to the fulcrum, there's not enough leverage and m1 will just knock through the lever, barely even being affected by the lever.
Like I said, there's enough in here that I might make a separate video on it, and some of the methods for calculating the optimal conditions. I'll try to make time for this in the next few weeks. Hopefully this gives some of the key points.
@@PhysicistMichael Thank you so much for the detailed analysis. I don't know why it didn't occur to me that the >200% change was due to the amount of moving mass increasing.
I guess to put an upper bound on the maximum change in linear momentum we could look at the case where a mass 1 with velocity V exchanges all its KE with a mass M. Before the exchange it has KE VV/2, so after the exchange it also has KE VV/2 = MV'V'/2, so V' = -V/sqrt(M).
The momentum changes from V to -V.sqrt(M), a change of V(1+sqrt(M)).
So if the object mass is only 4x the starting mass, we can't get more than a 300% decrease in linear momentum, for example.
I found 3 small transcription errors in your data:
in trial 9, for v0 you measured 0.536 at 56:52 but logged 0.531 at 1:00:36
in trial 10, for v1 you measured -0.229 at 58:05 but logged -0.227 at 1:01:48
in trial 21, for v1 you measured -0.111 at 1:25:23 but logged -0.110 at 1:27:26
All 3 are roughly 1% errors so aren't significant.
Thanks for pointing these out (keeps me honest!) I'm probably going to post a summary video (one that just rapid fires through the trials and then shows results) so I'll make sure to correct these values.
@@PhysicistMichael No problem. I was mostly interested in the >200% change in linear momentum, and wanted to double check that that wasn't a result of mis-reading the velocities. Did you see my other comment, starting "I'm interested in trial 13"? I'm curious whether you have any intuitive understanding of how the linear momentum could have changed by more than 200% in 4 of the cases.
@@WhiteHenny I'm checking a couple of things about that (it's not an error, and I'm trying to find the max theoretical change in linear momentum). Hopefully get to a full response by tomorrow.
37:17 How did you get 2572.6% ?
You have me flummoxed... 😕
Values:
(v1/v0)_elastic= -0.0125
(v1/v0)_measured= 0.01461
These are the equations I thought 🤔 you'd use for the difference and the percentage version:
Diff= (v1/v0)_measured - (v1/v0)_elastic
Either: %Diff= 100×Diff÷(v1/v0)_elastic
or: %Diff= 100×Diff÷(v1/v0)_measured
Either should get around 200% in magnitude, so Idk where the 2572% came from...
35:55
Update: I see that the equation for C14 is ABS((c10-c12)/AVERAGE (C10, C12))
This is the equivalent of what you
have in cell c14 at 35:55 :
|−2×0.0625÷(.05−.0125)|×100%
= 333.33_ %
You are nearly dividing by zero‼️
This is a _very_ bad way of comparing your experiment to your prediction because it is not what your equation is saying.
What your equation is saying is to take the difference with respect to the average of a hypothetical and a real measurement.
This makes no sense whatsoever.
You need to find the difference wrt either experiment or reality, not BOTH at the _same time!_
Update 2:
I had:
Diff= (v1/v0)_measured - (v1/v0)_elastic
Either: %Diff= 100×Diff÷(v1/v0)_elastic
or: %Diff= 100×Diff÷(v1/v0)_measured
If the elastic measurement is negative,
the top in both cases is :
|(v1/v0)_measured| + |(v1/v0)_elastic|
This may make the comparison worse in some cases, and we need consistency.
Here is my proposal:
Diff=|(v1/v0)_measured| - |(v1/v0)_elastic|
Of course, this means that you have to forget about the direction information.
Try this in your %diff cells and add another 2 rows so you can compare wrt either measured or hypothetical:
ABS((ABS(C10)-ABS(C12))/C10)
ABS((ABS(C10)-ABS(C12))/C12)
The problem with your proposed calculations above is that let's say that one value is 0.5 and the second is decreasing to the point of becoming negative. When the second value hits zero, you'll be at 100% error, but when it becomes negative (say -0.1) the % error will actually decrease (back to 80%) even though we're even further off from what we were expecting (velocity has direction, it's part of the quantity). I wanted to avoid that causing an underestimate of the error when one of the major points I've been needing to make about linear momentum is that direction does matter.
Since I mention in the video that the % differences for cart 1 are not expected to be small (because we don't have either a perfectly elastic or completely inelastic case, it's something in between and those two values often straddle zero, it's going to cause the issues you've pointed out) I though this was the best of a bad set of ways to calculate the errors. I also point out that in every single trial our results for the motions of each cart is between the values for the elastic and inelastic cases (those are the extreme cases).
@@PhysicistMichael I think you should ask a mathematician like that aussie on "Stand Up Maths" channel.
Trying to find errors with vectors is finicky.
Also bear in mind that you cannot divide by a vector, but you can divide by its magnitude.
Here you are dividing by the sum of two vectors, one hypothetical and one real.
What's worse is that they arithmetically nearly cancel sometimes.
This situation reminds me of quantum mechanics... Very confusing. 😵
I think you should check out the normalisation procedure they use in QM. It might help.
@@PhysicistMichael
"pinecone io learn vector similarity"
- Look this up.
@@The_Green_Man_OAPYou don't half talk some shit boy! Telling Michael what he should do and how to do it.
The main issue isn't directly that we're dealing with vectors (because this is one dimensional, so the vector part isn't all that big a deal) it's whether we use % error or % difference, and each one has its drawbacks in this case. Usually you use % error when you have an independent measurement of a quantity and you have a high confidence in that independent measurement, and you want to see how close your experimental results are to this "true" measurement. That would be the abs(difference)/true, but I'm not saying that I was expecting a perfectly elastic or completely inelastic collisions. I was hoping to get closer to the elastic in the spring bumper case and closer to inelastic in clay bumper case, but I had no illusions that these were going to be super close matches.
Also, there are some trials where the expected final velocities or the measured final velocities were very close to zero, so if we used abs(difference)/one of those velocities, we'd also get giant % values for those trials anyways. I was going back and forth on this before doing the test and settled on % difference = abs(difference)/average. If I did it again I'd probably do something different, but that's part of the iterative nature of science.