Tutorial: Rocket Science! (plus special announcement)
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Tutorial: Rocket Science! (plus special announcement)

August 25, 2019

Hello, and welcome to the Minute Physics tutorial on basic Rocket Science. Before we get started, I’d like to quickly announce that I’m now making these videos at the perimeter institute for theoretical physics So keep your eyes out for plenty of upcoming videos about string theory black holes the Higgs Boson and so on Now, back to Rocket science. Okay, this is gonna be a super simplified version of the basic dynamics of rocket we’re going to start with a Rocket and The rocket we’re going to assume has some fuel in it and the whole rocket together with the fuel is going to have Mass [M] At some point the rockets can ignite its engine start ejecting fuel and hopefully will take off And it will have a velocity “V” in the upward direction and the exhaust will the velocity called “the velocity of the exhaust” going down Now on top of that because we’re on Earth and not in the middle [of] outer space the Whole Rocket and Fuel system, everything together, is going to be affected by the force of gravity. [so] [how] did the dynamics of this system work? Well, you’ve probably all heard of F=Ma Force is equal to mass times acceleration Now in this case what it means is that the force acting on a system causes an acceleration? Or a change of velocity of the system, and you need a bigger Force to move a bigger Mass And that’s why the m is in there So we’re going to start off by looking at the case Before any of the fuel starts ejecting it’ll just be the rocket with Mass M So the total Force is the force of gravity and the force of gravity is equal to the mass of the object times the gravitational acceleration And that’s equal to, of course, Ma which is just the big M again times the acceleration And it’s negative because the force of gravity is in the downward direction. Now in this case the acceleration is negative, the acceleration from Gravity basically if the rockets in [Midair] and it’s not firing it’s going to start falling down at a rate of 9.8 meters per second squared, so after the rocket ignites not all the mass will be in the rocket anymore because some of it will be out here and the exhaust that’s been shot out. In this case the total force stays the same because it’s still minus the total mass times gravity But instead of just writing, Ma on the right side again, we now have two separate masses, the rocket and the exhaust, so we have to add together the mass times acceleration of each Now the mass of the rocket is “m” minus some rate of fuel loss which we’ll call “R” times the amount of time which is passed. Basically “R” times “t” will tell you how many kilograms of fuel have shot out of the rocket is exhaust by time “t” and the whole mass, M minus Rt is multiplied by the acceleration of the rocket. We also have to take into account the mass from the exhaust that came out and we just said that the exhaust comes out of the rate “r” kilograms per second, so it’s mass is just “R” times “t” So now what’s the acceleration of the exhaust, well the definition of acceleration is, “the change of velocity in a given time” and the exhaust goes from moving with the rocket at Velocity “V” before it’s expelled, to Moving with the velocity of the exhaust after it’s expelled. The change or difference between those is negative “Ve.” It’s negative because the exhaust is moving down minus “V” divided by the amount of time that’s passed So the “t’s” cancel and this equation tells us how the whole rocket plus exhaust system moves, where this part is the mass times acceleration of the rocket itself and this part is the mass times acceleration of the exhaust. Now suppose you’re launching a water bottle rocket or trying to levitate by vomiting How much fuel, which in this case is just water or milk, do you have to expel to take off, that is, to just barely beat gravity and begin to hover? Well, if you’re just hovering that means your velocity is zero and your acceleration is zero too. So all the parts of this complicated equation having to do with the rocket go away and we’re left with a much simpler equation describing just the exhaust “m” times “g” equals “R” times “ve” Remember, we’re trying to determine how much water needs to be expelled in order for the rocket to hover but now we have two variables which are trying to tell us that “R” is the rate at which the exhaust water leaves the rocket and “Ve” is the speed it has after leaving; those sound pretty similar. Let’s see if we can figure out a way to relate them to each other. On the bottom of the Rocket there’s probably a circular opening with area “a” or the exhaust comes out and since liquids like milk and water are Incompressible, they’ll take up the same volume when they come out, as when they were inside the rocket. So there will be a stream of water exhaust shooting out of the rocket and in one second, it’ll go a distance “Ve” that’s the velocity of the exhaust This stream is roughly a cylinder with the volume “a” times “ve” measured in cubic meters. How do we relate this volume to the rate “R” of exhaust leaving the rocket? well “R” tells us the number of kilograms of water and a kilogram of water takes up a liter of space and there are a thousand liters in a key meter, so “R” is just 1,000 times the volume. Now that we can relate both “R” and the velocity of the exhaust to the volume of the exhaust, it’s just simple Algebra to plug this into the equation describing the exhaust. Do a little multiplying dividing square rooting and we’ve solved for the volume. All that remains is to plug in numbers for “m” the total mass of Rocket + fuel in Kilograms and “a” the area of the opening at the bottom of the rocket; hint, it’s probably a circle. So what are you waiting for go weigh yourself, measure your throat, and find out how much milk you’d have to vomit in order to levitate and if you want you can share your personalized levitation inducing milk vomiting rate in the comments below. Thanks for watching!

Only registered users can comment.

  1. if you ejected the fluid at a higher speed you would need less fluid. E.g. if you can vomit at near the speed of light you wont need much milk to hover.

  2. Hello!

    could anyone here explain me how to calculate the v in the mg=(m-rt)a + r(-ve-v)?

    Nice vid btw helped me out alot!

  3. +minutephysics
    Wouldn't the gravitational force get smaller as further as your rocket flies away from earth?
    And how would it affect the equation?
    Thanks a lot and I hope you'll answer my question

  4. What this video taught me (unless my math is off which it very well could be) is that I would need to expel about 14.5L (or about 3.8 gallons for all you US dwelling folk) of water from my mouth per second in order to levitate… I think I'm gonna just stay on the ground.

  5. Just learned this to say "Um actually rocket science is easy." To just assert myself as the alpha nerd.

  6. wait, there is this one thing confusing me, everybody talks about how the speed of the rocket and such is proportional to the exhaust velocity, and I can see why, you push something twice as fast away from you, you get twice the thrust, but wouldn't the fuel you are using be important too? since the force coming out of one side is mass times acceleration, the other side has the same force (that is also mass times acceleration) and exhaust velocity just tells you the acceleration of what you're pushing away from you, not its mass, or am I missing something?

  7. I did not know what F=ma was, never heard of it untell this video, I am only a 13 year that just wants to learn about science, and I have been watching your videos minutescience to learn

  8. Awesome! Check also this Rocket equation calculator:

  9. I wonder if we could do a propulsion by vomit easier if we/person vomiting were in water vomiting something less dense than water so we could use the buoyancy force to propel us too????

  10. could you work an equation? one in which the rocket is moving? is there a time limit, you seem to have moved threw it very fast!

  11. But Volume which is m^3 is not the same as A x Ve (Area x Velocity) m^3/s. I know that you said that this happens in one second, which would cancel off the s, but you dont show this in the equation. Shouldnt the equation be Vol = A x Ve x T (the amount of time that passes)?

  12. So a 200# person through a 1” opening (converter to 90.71874, and 0.07976453 meters)
    I got 0.26635 liters per second??) doesn’t seem so bad?!!

  13. most of the equations are hilariously wrong
    chect out 4:03
    v_e is a distance, but also a velocity?? this doesn't help explain anything

  14. Well, atleast there was no calculus in this video, I pretty much understood everything there. But if calculus showed his ugly face, I would be by the door

  15. I need to vomit approximately 29839293849203848293481636y7583294&nvei8537vu31*t229384494944r444444949L of milk.

  16. 4:15 incorrect. It's not cubic meters. Area times velocity is meter cubed PER second(check the units for yourself). So he had to write vol/time= A * v

  17. Instructions unclear. Currently stuck in the ceiling fan.
    Update: i managed to turn off the fan.
    Update2: obtained basic knowledge about vomiting

  18. Ok so, quick question : (I'm a CS guy, I'm not that good at physics so please don't judge)

    Considering a payload be of 0.5 KGs , how big would a rocket have to be to justify using it over a helium balloon ?

    Like, I know Helium balloons burst at a certain altitude, and I'm just wondering how big (how much fuel) would the rocket need in order so surpass the maximum height reached by a He Balloon ?
    Neglecting the mass of the rocket frame,
    flight path straight up
    And rocket fuel : standard solid KNO3 based hobby rocket fuel

  19. 5:06 NEVER!!!!😫😫😫😦😦😦😦😦😦😧😧😧😧😧😥😥😥😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱😱

  20. 65 kilogram man.
    with a lets say 5 cm radius of mouth.
    with gravity at about 9.8 ms.
    i would need to be spewing 3.185 liters of milk per second.

  21. Ha! Found a mistake. In a system there must be at least 2 object. The rocket is affected by the EARTH gravity which must be shown. OwO

  22. Nice video. Heres a question though. Do you have the time to make a good video on the pendulum rocket fallacy?

  23. But g is decreasing with increasing altitude (as the rocket gains height), so how do I calculate the energy needed WITH the changing value of g?

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