Pendulums (and measuring g again) - Testing Physics
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- Опубликовано: 16 июл 2024
- We use dimensional analysis to predict how the period of motion for a pendulum will depend on the length of the pendulum and the gravitational acceleration. We put these predictions to the test and find agreement to within 2%. We also use the individual pendulum trials to measure the value of g and match the expected 9.8m/s^2 (including units) to within a few percent for every trial.
Full Series Playlist: • Testing Physics
0:00 Introduction
1:49 Dimensional Analysis for Simple Pendulums
7:55 Predictions for Simple Pendulum Motion
12:31 First Pendulum Test - Period Independent of Amplitude
17:55 Second Pendulum Test - Period Independent of Mass
21:07 Third Pendulum Test - How Period is affected by Length
30:02 Analyzing the Data
32:56 Predictions Match Experimental Data
35:20 Calculating g from individual pendulum trials (including units)
39:43 Closing comments
Opening Image Credit: NASA, ESA, CSA, Janice Lee (NSF's NOIRLab) webbtelescope.org/contents/me...
Your curve fit found g to within 1.2% and the coefficient to within 1.3%.
How could it be so accurate when your individual data points were all off in the same direction (overestimating g) by an average of 3.43%?
If the errors were random, in different directions, I understand that the curve fit would average them out and get a more accurate result (similar to the effect that caused you to time 10 oscillations and divide the time by 10 rather than just timing 1) - but when they're all off in the same direction (presumably because of some systematic error) I don't understand how the curve fit isn't also off by around 3.4%
Two things that I think would contribute to this result. First, when we calculate g for the individual trials, we divide by period^2, and when you square a value, any errors are going to increase (I'll eventually get to a video on propagation of errors). If I compare 5 and 5.1, those are only two percent off, but if I compare 5^2=25 and 5.1^2=26.01, that's about four percent off.
Second, when you use the graphing method, different sources of error could affect the different fit parameters in different ways. For example, in my Newton's 2nd Law video ruclips.net/video/TMlMrpztGGI/видео.html I apply different forces to a cart and measure the acceleration, graph applied force vs acceleration, and find that the slope gives the mass of the cart to very high accuracy (matching the predictions of Newton's 2nd law). But if you just take a single trial and calculate force/acceleration, the mass that you get is significantly off. I then show in the video that the presence of friction in this system _would only affect the value of the y-intercept from the graph, and not the slope of the graph_ . So where the errors show up in the graph fitting method can be different than using the single trial calculations, and my guess is that some of those sources of error might have slightly cancelled in the graphing method.
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No need to be a _martyr_ ‼️
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Gary will not pay the money he has promised to you and others. He quickly moves the goalpost soyyou can NEVER get the sum he has promised. He is like a creationist in that way.
Hi Michael, thanks for the nice video.
I like this kind of experiments and their equations.
I entered a few numbers into a spreadsheet, and did some calculations.
For two runs I calculated the period from the measured length, and the length from the measured period.
I found that the period is very close to the measurement, but the length differs somewhat more.
I guess that someone can try to find the center of mass by laying the bob on its side, and putting a toothpick under it, while drawing a small line on the bob with a marker when it more or less ballances on the toothpick.
I also think that the parallax plays a role when you measure from the center of mass to the pivot.
I found 1.7 cm difference for run #1, and 1.2 cm for run #3.
Probably not realistic, but a strong indication if you ask me.
Thanks again and take care, Michael.
For anyone else reading this, THIS is what it looks like to provide some criticism for an experiment. Not just saying "I don't like your data/conclusions so _something_ must be wrong because I just can't accept the results", but instead identifying specific potential sources of error and then doing the work to determine how much error would have to be present to explain the data, and then seeing if that amount of error is plausible given the experimental setup.
I think it's very plausible that I could have been off by a cm in measuring those distances (since I was trying to do it quickly for the camera), but I also think there was probably some small errors with the timing, because when you calculate g using the individual runs, you divide by T^2, and that causes small errors to become a bit larger (from squaring the time). This would explain why we got consistently larger errors when calculating g from each run (which are always overestimates, see @WhiteHenny comment) but smaller errors when looking at the fit values from the graph.
@@PhysicistMichael oh, interesting. If the measured period is off by x%, the period squared will be off by 2x%. Errors compound like that. Having 1.2% error in the period gives 2.4% error when squared. Coupled with a 1% error in the measured length would give a 3.4% total error which is what we observed.
Specific numbers on how much error is from which source might be a bit different, and whether the errors happen to add or cancel could be different in different cases (they seemed to add in this experiment), but that's the general idea.
@@DraftScience I'm sorry that you can't seem to address the topics of any videos (this one's about pendulums and measuring g) and instead deflect to other topics and evade. I'm sorry you can't demonstrate _any_ of your ridiculous claims, even for things as basic as the units of acceleration. I'm sorry you can't remember that I have multiple videos already demonstrating that direction matters for momentum (using collisions with repelling magnets, springs, velcro, and all of them demonstrate that direction matters), and that you can't remember that you just reacted to the Leska video where he showed the video _you brought up_ and demonstrated your model failed.
I'm sorry that your so dishonest that you would resort to ad hominem attacks, including claiming that I "support malicious doxing" when, for the comment you refer to, the first thing I did was to ask the general location mentioned to be removed (which it immediately was), and that I have previously removed comments mentioning your last name and put that on the banned words list when we had the livestream. I'm sorry your position is so weak and your understanding of science, math, logic, and the concept of needing evidence to defend your claims is so utterly broken that throwing insults is all you're capable of doing. I'm sorry that you think you can continue to act in this repugnant way and think the rest of us are going to keep doing your homework for you.
@@DraftScience Lmfao "anti-momentum" is your latest parlor trick. That's genuinely funny. Maybe you should try stand up comedy. Your physics is the equivalent of someone who can't read music telling musicians that music notation is wrong and they have no basis for believing that what they play matches the charts.
Looking back, what do you think is your greatest accomplishment in your almost 20 years of pretending to be someone with something useful to say?
Again, I'm glad to see the _Laws of Physics_ still work, despite any particular pet theory.
Excellent video Michael. 👍💯%.
Now, I was thinking about the
string tension "force": F=μc²,
with c=speed of sound in string,
μ=string mass/string length=m/ℓ
... and I thought:
_How about combining this equation with that of the period: (T/2π)²=ℓ/g ...?_
Well, then I thought to just decompose the gravity force Mg↓ into trig components,
then take the cos component
and equate to the tension, thus: F=Mg.cosθ=μc²,
and then substitute
for g in the period equation:
(T/2π)²=ℓ/(μc²/M.cosθ)
=Mℓ.cosθ/μc²=(M/m)(cosθ)(ℓ/c)²
So, finally we have:
T=2π(ℓ/c)√{cosθ}.√{M/m}
Here, g is given by g= mc²/Mℓ.cosθ
Any chance you can check this out with your data or is there another experiment that can take this into account?
You'll need c though.. _BUT_ it actually varies as the tension changes (with cosθ)!
- For small θ, cosθ≈1, so maybe analysing this will be more achievable:
T≈2π(ℓ/c)√{M/m}, g≈ mc²/Mℓ
Sanity check by substituting for M:
T≈2π(ℓ/c)√{mc²/mℓg}
=2π√{ℓ/g} ✅
So, again my question is:
_Can you analyse the validity of the physics of this equation_ : T≈2π(ℓ/c)√{M/m} ..❓
What I see here is that c _mostly depends on_ M, rather than cos(θ) for a _tense string, oscillating through small θ._
Can you please respond to draft sciences 5 minute videos, it’s not only him that wants to see a response out of you.
It's time for you guys to admit that gary has been answered and answered. When he doesn't like an answer (always) you guys have an agreement to call that "not getting an answer".
its time for you guy to stop being dishonest doxxers @@pyrrho314
@@pyrrho314 You've known DS for longer than any of us. Do you think he is aware of his deception, or is he deceiving himself? I get the sense that he believes what he says, and is so invested in it that he cannot accept being wrong despite all the evidence. Anything that suggests he is wrong cannot be evidence because he's not wrong. It's almost a religious position - exactly what he accuses everyone else of.
@@pyrrho314 can i ask you why you stopped making videos? I looked at some of your stuff and thought it was good