Hello, I'm 16 years old and aspiring to be an aerospace engineer, primarily astronautical. Just wanted to thank you on your thorough explanation on this topic. I'm preparing for a summer university course and you have brought me that much closer to my dreams! Thank You
+Mark Somerville I would've appreciated if you integrated your final expression to derive the Tsiolkovsky equation. I was able to figure it out anyway, but otherwise, your video is very good and clear and consistent in notation unlike in many other such videos and on wikipedia.
Well, when I was taking calculus the derivitive always had dx/dt or something similar at the end. What that means is "as x changes relative to time" or something similar. The whole thing made more sense when I made that connection between the math and the reality. I mean, I understood that was what was going on, but not that that's how it was expressed in the math.
Frank Harr There in lies the difference between physicists, and mathematicians. A physicist is not bothered by mathematical notation. d for all physicists purpose means "change in". We don't care about precise definitions in cases like this.
This video has really widened my vision of applying mathematics to science. Though I’m studying biology in a university, it kinda helps me in being prepared
I'm 14 and hoping to become a rocket engineer and this helped me very much, I'm starting by designing my own rockets, and testing them, this helped me explain them better.
Momentum is vectorial in nature and it is described as mass x speed. It is preserved for as long as 7there is no other force acting upon the object. It just makes sense under the thrust equation and it's environmental factor or atmospheric pressure.
@@-danR you are correct. Speed doesn't (theoretically) imply a vectorial traslation. But that's only in paper. In real life there is always a vector. Basically, velocity is speed in a given direction. ... In physics, velocity is more important than speed because it tells you more about the object's motion. Always, the more you know, the better.
@8:55 the change in momentum of the system is d(Mr.Vr). So if I take the derivative with respect to time, I get the force experienced by the rocket right? Which would be equal to -dMr/dt.(Ve+Vr) but it should be constant and not depending on Vr isn't it?! Shouldn't it be thrust=-dMr/dt.Ve instead?
How fast do I have to poop to propel myself in the air and touch the ceiling with my head? I assume I poop 1kg and my weight is 80kg. All of this happens on the earth with a gravitational acceleration of 9.81 m/s/s.
At 9:43 you treated the left hand side Vr as a function and you used the derivation rule for the multipication of two functions, however on the right hand side you derived as if Vr where a constant. why?
I think the velocity of the exhaust relative to the rocket is constant because once it leaves the rocket there’s no more forces and f=ma so no acceleration. So each chunk of fuel going out has a constant exit velocity relative to the rocket. Every force has an equal and opposite reaction so the only way the velocity relative to the rocket would increase is if the force the rocket were putting on it was increasing to send it out at a higher velocity (more impulse) and the rocket would experience constantly increasing thrust
ALEX L it's just a notation that's showing a different point in time. Let's say t=1 second and dt=2 seconds. X_t= distance after 1 second. X_(t+dt)=distance after 3 seconds. If I'm correct, it's referred to as an "index".
Thank you for your effort in explaining and preparing the video. Um..., you known..., computers can also print some very neat and ordered printed equations. Very clarified for the eye, that a badly handwritten text.
In ideal rocket equation, the velocity of the rocket is derived from multiplying the rocket's exhaust velocity to the natural log of the rocket's initial mass divided by its mass when propellant is subtracted. ”ve • ln(m0/mf)”
I'm in 6th grade watching this and it's really easy I love rocket science and astronomy my dad works at NASA so he is always on my case about things like this
Infinity 1 (and foobar42). Right! It sets up the vector direction (force, velocity, momentum, acceleration, etc.) to account for all rocket and exhaust component motion.
I am building a class 2 rocket. I really do not find this math helpful. Is this video designed for someone taking a test? I am trying to get an impulse to mass ratio to make sure I have enough thrust. Or to cut weight.
Scott Hickle in mathematics the definition of a change in f(t) per. t is given by f'(t) = (f(t+dt)-f(t)) / dt where dt goes to zero In physics we use this all the time, so as you see, everytime we can rewrite an equation into for example (p(t+dt) - p(t))/dt this is really just the dirivative of p(t) also called p'(t) change in momentum per time. Or be it (m(t+dt)-m(t)) / dt = m'(t) the change in mass per time.
I am e^5i years old, and I am growing older at a rate of 24 faster than average. Currently my growth rate dA/dt is 86s/0.007s. My growth rate is unitless because A is also measured in seconds, and its derivative is the rate at which I grow in dt that an average person takes to grow.
I think there might me some inaccuracies in the way you do the calculus. I mean, first they should be partial differential equations and when you convert the d(x) in a the total derivative in time.
Right off the bat, instead of this guy either A) Bringing up the propulsion element of the need for an atmosphere to push off of (which is tabu because it would debunk the possibility of rocketry in space) OR B) Just ignoring this factual rocketry need and pretending only the "motion movement" of gas out the back of the rocket can push it (which is proven non-sense), Instead of choosing teams, this guy actually says BOTH viewpoints are Valid? WTF?
I think you're confused. Assumptions are made all the time physics. All models are wrong at some level. What we do as physicist and engineers is constantly update models to try achieve the best one's we can.
Bleh Newtonian crap. Do at least the special relativistically correct v=ctanhθ Δθ=(vex/c)ln(mi/m) Yeah I know you're too slow to even be able to type such things into the text so much as understand it, so much as to derive it.
What the hell is wrong with you? Was that the goal video? I think not. We're talking about the speed of a rocket, as of right now engineers don't need to worry about the small margin of error that comes from not using special relativity.
