Відео

Thank you. I might grow my hair out again someday.

You are correct that we treat projectile motion as two separate motions, but that only works when horizontal and vertical are clearly defined. The point is that once you bring the curvature of the planet into it, what would be a purely horizontal motion would end up appearing to have a vertical component from the frame of reference of the Earth's surface. That is, the horizontal projectile motion would appear to move the object father from the surface of the Earth, because the Earth is curving away from it. Kepler's Third Law doesn't really have much to do with this situation, other than being the result of the same law of gravity. It compares the period and radii of different orbits. However, Kepler's First Law, that planets orbit the Sun in elliptical orbits, is entirely in keeping with the laws governing projectile motion. Newton showed how the same law of gravity that causes a projectile to follow a parabolic path if the launch speed is too low to achieve orbit, will follow an elliptical orbit if the launch speed is fast enough to achieve orbit, and a hyperbolic path if the launch speed exceeds escape velocity. The parabola, ellipse and hyperbola are all just different conic sections.

@@marklesmeister Do you think it's possible for an object to be both falling and increasing its distance from the gravitational center of the object it is falling toward?

@@numbynumb Absolutely. Happens all the time. Take a tennis ball. Throw it up in the air. While the tennis ball is rising, it is falling towards the Earth. It is also falling towards the earth when it is getting closer to the Earth. It is even falling towards the Earth at the instant the ball comes to rest at the top of its motion. In physics we learn to be specific about what mean by terms like falling. So let me clarify that when I say it is falling, I mean it is accelerating towards the Earth. We say it is in free fall. You have referred to projectile motion, so you understand that in projectile motion, at the same time as an object is moving horizontally with constant velocity, vertically it is accelerating toward the Earth. If the object's initial velocity was in the upwards direction, then the object will move away vertically from the Earth initially, but eventually it will come to rest then start moving toward the Earth, all the while keeping its horizontal velocity. If that initial velocity is horizontal, it will start to move toward the Earth right away. But if the velocity is fast enough, then the whole time it is accelerating toward the Earth, the Earth is curving away underneath it at just the right rate so that it never gets any closer to the Earth. Now, how can an object accelerate toward something, yet never get any closer? Again, that happens all the time. Take that tennis ball and poke holes through it at opposite ends of a diameter. Now push a string through the tennis ball and tie it off so that you have a string with a tennis ball attached to one end. Whirl that tennis ball on a string in a horizontal circle around your head. The string is constantly pulling on the tennis ball, accelerating it towards your head. And yet the tennis ball doesn't get any closer. That's just what happens to an object in orbit in Newton's cannon analogy, except the string force is replaced by the force of gravity. I have heard that every equation in a science explanation causes one's audience to diminish by half. But, if you want to know how fast something moving with a certain speed has to be accelerated toward the center of a circular path of a certain radius, so that it never gets any closer, the equation is acceleration = (speed squared)/radius. Since gravity accelerates things near the surface of the Earth at a rate of about 10 meters/second/second, or 32 feet/second/second, you could use those numbers to figure out how fast something has to be moving to stay in a circular orbit. The Earth has a radius of about 6,400,000 meters. Multiplying that by 10 and then taking the square root gives an orbital speed of about 8000 m/s, or about 18000 miles per hour.

You are in good company on this one. No less an authority than the New York Times claimed (in 1920) that rockets with gas exhaust wouldn't work in space because in the vacuum of space they would lack "something against which to react." Unfortunately for you, the NYT retracted their absurd claim, the day after the Apollo 11 launch in 1969. No doubt the Gray Lady realized their sophomoric mistake long before that time, but they found it humorous to "retract" an error on that auspicious occasion.

@@marklesmeister Do you know the equation used to calculate the work done by a gas?

@@numbynumb I know the equation we derive when we do the kinetic theory of gases, W = PdV, where P is the pressure and dV is the differential change in volume. However, that only works for a closed system. Moreover, using energy methods would require us to know something about the internal energy of the system. For a system such as a rocket, where the mass of the rocket is changing as it ejects exhaust, and where details of the conversion of chemical energy to kinetic energy might be quite complex, it is far easier to analyze it in terms of Newton's 2nd Law or the Impulse-Momentum Theorem. If we treat the rocket and the exhaust as a system, with no external force acting on the system, then the total momentum of the system is constant. The derivation of the rocket equation is quite straightforward from there. Numerous places on the INTERNET give the details if you are interested.

@@marklesmeister You are incorrect. The equation is w=-PdV. -P stands for external pressure. Gas cannot do work without an external pressure, in other words. And the idea that this equation only applies to closed systems is illogical non-sense. The reason kinetic molecular theory exists is because the basic Newtonian equations of motion can't explain or predict the behavior of gases.

@@numbynumb Dear me, where to begin. First, your equation is identical to mine save the negative sign. The presence or absence of a negative sign depends on whether one is writing the equation for work done on the gas or by the gas. You asked for work done by a gas, so I wrote the correct equation, without the negative sign, indicating that when the system does positive work on the environment the differential of volume increases, hence must be positive. I actually teach the equation with the negative sign when I teach it, because I find it more natural to think in terms of work done *on* the system, and heat added to the system, to be the positive quantities. But you asked for work done by the system. And I'm also correct that the equation only works for closed systems, that is those that are not losing matter to the outside. If one allows that, the volume can easily change with no work being done. But the system isn't isolated. Energy can cross the system boundary in the form of work and the form of heat. Also, the kinetic theory of gases is based on applying the "basic Newtonian equations of motion" to the random motion of gases. When I do it in class, I used Newtonian mechanics in the form of the impulse-momentum theorem. One can only get so far with that, but for example with a few simplifying assumptions we derive the ideal gas law from Newtonian mechanics. I have the distinct impression that you're "having me on." The modern phrase would be "trolling me" I suppose. I will continue to reply as long as it amuses me to do so, but I can see that coming to an end soon.

para su seguridad permanesca sentado manos brazos pies y piernas dentro del vehiculo.

@@roughbridge290 para su seguridad permanesca sentado manos brazos pies y piernas dentro del vehiculo also you're stupid

@@DonaldDuck225 19 dollar fortnite card WHO WANTS IT

Just a teacher who loves what he does. Thanks for the comments.

@@marklesmeister Would you be willing to fund a burger king party for anyone that gets a 5 on their ap exam? I believe a certain someone gets a discount.

Too bad the wonderful in-person demonstrations were at 1 frame per second on Microsoft Teams! We missed out!

Prove it name every woman thats been underpaid

@@neerajanantha6743 as a fellow hindu i must say i am disappointed

yes it is

@@neerajanantha6743 you're just mad cause bad

shut up i dont wanna hear it

stfu stop playing brawlstars kid

@@DonaldDuck225 i dont appreciate your toxicity

@@neerajanantha6743 i dont appreciate you replying back to me

go play another game stupid

@@DonaldDuck225 what else he gonna play. amogus???? sussy??

you gonna reply or are you just bad?

Bad will stay bad just like poor stay poor #Democracy

@@DonaldDuck225 people now tie their suffering to superficial things like upvotes, likes, retweets in contrast to back in the state of nature where suffering was defined as getting sick, not finding a mate, not finding enough food, getting banished by your tribe, or getting eaten

@@figgioso9039 shut up Conservative #Democracy

@UCe18AcYO6EjJQgceBK6eZ3w get help even jesus christ cant save you.

Thank you 😁

Thanks 👍

I have learned a lot of orbital mechanics playing Kerbal Space Program the last few months.

@@marklesmeister KSP is my favorite game of all time.

Thanks for the comments. I agree the F-1 was special. I never got to see a Saturn V launch in person. I was a kid at the time. I've already told my colleagues that I plan to watch an SLS launch in person, and if that means I need to quit my job, so be it! (I'm only half kidding.)