CyborgTriceratops

 

You would have serious difficulty using kids as mass ejection to alter the speed and direction of said spaceship. Heck they eat a lot , their mass thus, changes from moment to moment, the also excrete mass, chew mass, drink mass and come in different sizes and shapes?. How do you eject these odd shaped objects at the exact correct angle, at the exact correct velocity, do you have different ejection ports for different size kids?. Only after you have resolved those issues to exactitude, can you think of coming up with the correct mathematical equation.

In a normal spaceship, I would fully agree with you. The one in my equation lasts a combined total of maybe 2 minutes, so there is no additional mass change save for any unwanted gas breaking, and the entirety of the spaceship is kids, nothing else.

a) You write the equation first and then determine the mass(es) to use.

 

b) "Round cows": for the purposes of the OP it is almost certainly accurate enough to approximate an average mass per kid (and the effects of a meal, excretion, etc. are going to be very small, anyway).

That is what I am doing. Swansont is deffinitly helping out a lot, but now I seem to be stuck until I can determine the actual masses and speeds that I need.

Yeah, I know they don't cancel out, not to sure why I said that they did...

My math would of worked out then, had the spaceship not been moving. Since it was, my calculations are in effective and I must return to using F = dp/dt = v dm/dt + m dv/dt?

black holes also radiat mass, though they normally do it at a much smaller rate than they gain mass.

p stands for vector, got it.

p is equal to 0 because there is no increase or decrease of momentum in the begining of the problem, correct? If there was an increase, then it would be a non-zero number.

to get v₁=-(m₂/m1)v₂ I just apply basic math? Divide both sides by m₁? if so, shouldn't the v₂ also be divided by m₁ or no because the m's cancel each other out.

Plugging in the variables I get

1000(3 m/s)=-[100(1 m/s)]

3 m/s=-[(100/1000)(1 m/s)]

3 m/s=-[(.1)(1 m/s)]

3 m/s=-.1 m/s

and this is where I run into problems. They should both equal the same number just one should be a negative. Even if I had used 900 instead of 1000, there difference wouldn't of been -2.9 m/s. Am I doing the p=0 part to late? Should I of started out like this:

900(0 m/s)=-[100(1 m/s)]

0 m/s=-[(100/900)(1 m/s)]

0 m/s=-[(.1)(1 m/s)]

0 m/s=-.111 m/s

or a negative 1/9 m/s in the opposite direction of the push? Since I got your answer, I am guessing it is correct, I just want to make sure I have the math right as I still get 0=.111 which isn't true. Secondly, does the initial mass of the frame count at all? It shouldn't, since the mass being ejected is leaving the spaceship before any of it starts.

Well, I've been trying to find a good clip of the movie to guestimate the mass, trajectory, and speed of both the ship and the ejected mass, but I can't seem to do that. I'll have to wait until I get it on DVD.

Until then, I'll make up some numbers.

Initial mass of ship - 1000kg

Speed of Ship - 3 m/s

Ejected Mass - 100kg
Angle - 45 Degrees of Aft
Speed of Ejected Mass - 1 m/s

Now, according to Swansont, I need to use "F = dp/dt = v dm/dt + m dv/dt" to solve the issue. I am still learning what all of these terms mean, and I am a bit loss. I am learning what I can from Wikipedia and reading forums here, but it is taking some bit. I will go ahead and ask for forgiveness, as my highest level of math so far is College Algebra, so this isn't something I've learned.

F= Force, which I don't know yet as I do not know the acceleration after ejecting the mass.
v=vector at the initial start
d=is determined by the rate of change of time by said object, P, M, and V.
m=mass

Would I plug it in as follows?

F = dp/d(.5 seconds) = (3 m/s) d(900)/dt + (100) d(1 m/s)/d(.5 seconds)

Or am I still off? Is this something that I need to hold off on until I get into calculus and physics?

I think I should clarify my statement. I apologize.

I know that fuel is the largest part of flight in terms of mass. What I meant by

where as in traditional rockets it is a much, much smaller percentage of their mass being used to propel them.

Is that at any one time the percentage is smaller, not that it is smaller overall. Five seconds on a traditional rocket will burn far less of their fuel then the movie does in it's five seconds.

Recently I watched Ender's Game and, with out spoiling it, there is a scene in the movie where mass is ejected out of an object moving through zero-gravity in order to change the object's speed and direction. When I watched it, it struck me as too much change for the mass ejected to mass retained ration and I want to verify it.

SPOILERS: The specific scene I am refering to is the scene in the battle dome where Ender has his army form a 'wedge' of sorts around a main player and then floats their way through the battlefield, ejecting kids at certain angles to make his needed course adjustments. I know some of the work I need to do to verify if the right math was used, such as guestimating the mass of each child, determining how many children there were, the ejected children's speed and angle, and the resulting angle. That is where my knowledge stops though. I am trying to find the formula I need to use but I seemed to have hit a stand still.

NO SPOILERS: I have looked through a few different websites and pulled up my own rusty knowledge, and what I have come up with is using F=MA of the ejected mass, then use the known force into F=MA for the spaceship. We know the mass and we know the force applied to it from a certain angle, we then can determine the acceleration of the ship in that direction. What I do not know though, is how do I calculate the dropping of mass into the equation? In the example it could be around 1/10th or 1/15th of the entire system's mass being ejected, where as in traditional rockets it is a much, much smaller percentage of their mass being used to propel them.

Do I do the second F=MA equation with the lesser mass? Am I on the wrong path completely? Any help in this issue would be greatly appreciated, as it's bugged me since I watched the movie. I do not want to simply be given the answer though. Pointers and tips, maybe say, "research the oberth effect (for example)", or other such help would be appreciated more then, "Use X formula because Y."