The Nature of Gravity, Part 2: Projectile Motion in Constant Gravity

This is the second video in The Nature of Gravity, a series which explores the nature and essence of gravity. In this video, we analyze the motion of objects which are thrown, or in freefall, in constant gravity near the surface of Earth. We see how the height of an object will decrease over time, then vectorize that situation into a general equation for parabolic motion in constant gravity, then we apply that equation to solve the range problem.
If you haven't seen the previous video yet, you can find it here:
• The Nature of Gravity,...
Wikipedia article on Projectile Motion:
en.wikipedia.org/wiki/Project...
Thanks to fesliyanstudios.com for the background music! :)
#math #science #physics #gravity #philosophy #projectilemotion #calculus

[@Baron._]

Hey do you know anything about tungsten it would be cool to learn about that

[@RichBehiel]

😂

[@guslackner9270]

"Uncle Tungsten" is a fun autobiography/science book on the subject

[@davidmurphy563]

This is the best video I've watched in ages. My son was starting his a-levels and doing projectile motion and I made a gravity solar system sim in a games engine as well as a cannon ball range thingy in python. Anyway, best video I've watched in ages. Hope you continue with the series.

[@RichBehiel]

Thanks, I’m glad to hear that! :) Someday I’d like to get back to the gravity series, but lately I’ve become addicted to quantum physics.

[@davidmurphy563]

@@RichBehiel For sure, quantum is mesmerising and everyone wants to know about the raggedy edge of science with its mind bending experimental results. Just there's arguably more value in settled science which we know is true and determines the world around us. Not that quantum mechanics isn't science, consequential or true - of course it is - but you did such a fantastic job of showing the deeper beauty and elegance of everyday things we take for granted. I'd urge you to continue with the series.

[@RichBehiel]

@davidmurphy563 that’s a very good point!

[@michaelblankenau6598]

Beautiful work . Clear explanations and wonderful animations. Deserves to have orders of magnitude more views .

[@RichBehiel]

Thanks, I’m glad you enjoyed the video! :)

[@Gigano]

Loving these videos so far, and looking foward to see more!

[@padraiggluck2980]

Feynman sounds like a smart Ed Norton.

[@mathusalen1]

Hope you continue with this series, it's wonderful stuff

[@RichBehiel]

Thanks! :) I’ve gotten sidetracked with quantum stuff lately, but one of these days I’d like to get back to gravity.

[@mikip3242]

I would love to see the code of the bouncing ball animation. Is it in Python? That's a beautiful and satisfying thing to see

[@tissuepaper9962]

bouncing ball is a classic VFX demo, you should be able to find thousands upon thousands of code examples online at all levels of conplexity from raw shader language all the way down to visual block programs in kiddie languages.

[@daniellewilson8527]

What do you mean by kiddie language and shader language?

[@krishnagopalsrivastava2084]

So you are the immortal being who serenaded about the qualities of tungsten cube. Loved the review. Just wanted to say hi .

[@RichBehiel]

Hi! 😂

[@TimDrogin]

beautiful explanation and video quality! I am surprised with only 80 views.. You did a greate job making this not intuitive topic at first really logic at the and. Keep going!

[@RichBehiel]

Спасибо Тимофей! I’m glad you enjoyed the video. More views might come eventually. If not that’s fine too, it was fun to make the video, and I’m looking forward to Part 3! :)

[@DanielSilva-cq6vz]

Hey Richard, great videos! I'm just wondering since this was posted 1 year ago, do you plan on continuing this series on the future? I reckon you said we would dive into general relativity later on the series...

[@JamieHorsburgh1]

"..that's a bit of a tangent.." 😂😂😂

[@brendawilliams8062]

Thankyou

[@thorkelson]

The visualization with sound is fantastic! What software did you use to make it?

[@RichBehiel]

Thanks! :) I used python, with matplotlib.

[@thorkelson]

@@RichBehiel Thanks! I have been using outdated tools to make the visualizations for the courses I teach, I have to teach myself these.

[@omega82718]

Will you do a video on symplectic geometry and how it's the best formalism for classical mechanics?

[@RichBehiel]

I’d like to do a video on symplectic geometry someday. Not sure it’s the best formalism for classical mechanics, but I see the appeal. We’ll be working with a Hamiltonian in the upcoming hydrogen video, so maybe that’ll provide a segue into symplectic geometry. In the near future though I’d like to dive more into quantum electrodynamics, in pursuit of the nature of the electron.

[@amanbajracharya7403]

❤❤❤

[@asaliphon351]

Is the formula for the distance traveled on the x axis by the cannonball on the raised ground example d=2v^2/g *sin(theta)cos(theta)+v*sqr(2h/g)

[@ShantRising]

Legendary

[@RichBehiel]

Thanks Shant, I’m glad you liked it! :)

[@unrelentingawesomeness7501]

how do you get the initial values from the integrals like the initial position and velocity?

[@RichBehiel]

Those initial conditions are degrees of freedom. In different scenarios, they might take on different values. For example, a ball dropped from height at rest would have an initial position of that height, and initial velocity of zero. A thrown ball would have some initial velocity. Depends on the initial condition relative to your coordinate system.

[@unrelentingawesomeness7501]

@@RichBehiel thank you but how do you derive them mathematically like where do they come from when you do the integral of the acceleration vector or velocity

[@RichBehiel]

In essence they’re integration constants, like the +C you put after doing an indefinite integral. To be more precise, they’re initial conditions since it’s a definite integral over some time period.

[@1mizzouman2004]

I've been having a conversation with a friend regarding what general relativity states about the acceleration bodies on the surface of the earth feel that we call the force of gravity. While my understanding is that the mass of the Earth literally, physically accelerates us outward into spacetime, opposite the direction of the center of Earth's mass (i.e. the earth literally 'pushes up' on our feet), my friend says this language is misleading at best, if not simply incorrect and that the earth is not literally moving or expending energy 'pushing' on our bodies standing on the ground. It seems as if your first two videos on the nature of gravity is heading in the direction of providing insight to that issue. There are plenty of credible physists that use the language of "the apple in free fall is not being accelerated or pulled towards the earth, but rather it is more appropriate to consider the earth and everything attached to it as accelerationg upwards into the apple" (Gabe Perez, Brian Cox, Sabine Hossenfelder, and more). While I understand these physists to be choosing their words intentionally to bring clarity to a physical reality that is difficult to picture, my friend says the language is rather metaphorical (ultimatley misleading) and that the earth is not literally, physically pushing up on our feet. He states the equivalence principle is not directly applicable to what gravity on the surface of the earth is as while the box in space has a rocket physically accelerating it, causing a sense of a downward to the floor force/pull to the person inside, the earth's surface on the other hand does not have a rocket under pushing the person on the ground upwards - and therefore its not an actual, physical equivalence. This is contrary to my understanding of what GR states - that the mass of the earth is in fact accelerating our bodies upward/outward from the center of its mass - and that the equivalence in the equivalence principle was a real, physical equivalence in regards to the feeling of a downward pull on our bodies to the surface of the earth is caused by a real, physical upward push/acceleration away from the center of the Earth's mass. Could you please share your understanding of this issue as it relates to what GR states about the acceleration we feel standing on the surface of the earth that causes objects to be stuck to the ground? I would immensly appreciate your thoughts - and really looking forward to the next video in this series on the nature of gravity. Thanks!

[@DanielSilva-cq6vz]

Physicists are not being metaphorical. According to GR space itself falls into earth, so for you to be standing on earth's surface, you need to be accelerating up through the space falling on earth. Space falling into earth is tighly connected to the equivelence principle.

[@guslackner9270]

Isn't projectile motion technically an ellipse? How large is the (small) error from that approximation?

[@RichBehiel]

Yes, you’re correct! :) If we make the approximation that the gravitational field near the surface of the earth is constant, then trajectories are parabolic. But when you factor in that tiny amount of variation in the field’s direction near the surface of the earth, trajectories are technically part of an ellipse. It’s so similar to a parabola though that the difference is negligible, and much smaller than the effect of air resistance.

[@georgemasiuk1582]

Is there a "The Nature of Gravity, PART 3" on youtube?

[@RichBehiel]

There will be someday! :) I’ve gone off on a bit of a quantum tangent lately, but I’ll come back to gravity eventually. Part 3 is in the works, got about half the animations done but haven’t worked on it in a while.

[@wdobni]

suggest you start the video from the 8 minute mark and just state your definitions and refrain from trying to teach math at the same time as you are trying to teach physics.....nothing is lost by assuming your viewers already have high school level knowledge.

[@RichBehiel]

This is good feedback, thanks. The upcoming videos in this series will be more advanced, eventually much more advanced as we get into GR. My intention was to start from scratch, building up the ideas from first principles to meditate on where all this structure arises from, but I can see how that’s suboptimal for someone who already knows the material. That’s been a balance I’ve had to think about when making these videos, trying to figure out what people will already know vs what they will want to learn. I don’t always get that balance right, but I hope to improve over time, so I really appreciate your perspective.

[@islaymmm]

@@RichBehiel I did appreciate the rudimentary bits on the contrary. It's all up to you to decide who you wanna cater to most, but to me (never gone to uni, not so much of a hobbyist, just wanna learn about science when I have enough time and energy) it was a good refresher on the basics and it's always fun to learn about different perspectives and spins on what is otherwise supposed to be common knowledge. P.S. I was delighted to hear the Wittgenstein quote! What can be said can be said clearly (and scientifically).