- #36
168918791999
- 23
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F=m*Δv
3.8=0.1*Δv
Δv=38m/s2
3.8=0.1*Δv
Δv=38m/s2
I don't know which post this is a reply to, but it makes no sense.168918791999 said:F=m*Δv
3.8=0.1*Δv
Δv=38m/s2
P=mgvg. vg is unknown.168918791999 said:KE=2,7x106*mg
mg = Mass of the gunpowder
P=mg*v
P=mg*38
Bystander said:Efficiency. There is an upper limit to the efficiency of about 1/3.
That kinetic energy is irrelevant now. We used it to calculate the launch velocity of the rocket. We used the launch velocity of the rocket to calculate the launch momentum of the rocket. We used the launch momentum of the rocket to calculate the downward momentum of the exhaust gasses.168918791999 said:However can you say the momentum (p) is 3.8 Ns?
And that the kinetic energy is
KE=0.5*mg*V2
KE=0.5*mg*38.362
Ke=735.7448*mg
Yes.168918791999 said:However can you say the momentum (p) is 3.8 Ns?
KEg=0.5*mg*Vg2, and Vg is UNKNOWN.168918791999 said:KE=0.5*mg*V2
The way I described in the last paragraph of post #37: if the mass of gunpowder is mg, you can write down an expression for the energy in the gunpowder. If its exhaust speed is vg, you can write down an expression for the KE of the exhaust. Finally, total KE equals total available energy (though in practice a bit less). This will leave you with two equations, an energy equation and a momentum equation, involving two unknowns, mg and vg. Solve.168918791999 said:P=Mg*Vg
3.8=Mg*Vg
But how to calculate any of the unknowns?
Yes. It is a reasonable assumption that essentially all of the original chemical energy (Eg) in the gunpowder turns into kinetic energy (KEg) of the exhaust gasses.168918791999 said:KEg=P2/2mg
KEg=3.82/2mg
KEg=14.44/2mg
Can you say KEg=Eg
It is in the right ballpark. Liquid oxygen/liquid hydrogen manages 4462 m/s. Nitrogen tetroxide/hydrazine manages 3369.168918791999 said:Vg = 2323.79 m/s = 8365.644 km/h
Would this not be too fast?
What is the temperature of the exhaust gases? How much chemical energy goes into heating the exhaust gases?jbriggs444 said:It is a reasonable assumption that essentially all of the original chemical energy (Eg) in the gunpowder turns into kinetic energy (KEg) of the exhaust gasses.
A figure of 10% for rocket efficiency is unfounded. Before such a figure could even make sense, one would need to come up with a measure of efficiency. One such measure is the fraction of chemical energy which goes into accelerating the payload. That measure depends on how fast the rocket is going already. When rocket velocity is equal to exhaust velocity, 100% efficiency can be approached. When rocket velocity is zero, 0% efficiency always results.168918791999 said:mg=1.63525964 gr
Do you still have to multiply it by 10 because a rocket is on average only 10% efficient?
For a suitably ideal nozzle operating in vacuum, the exhaust gas temperature can become negligible. Adopting realistic assumptions for this seems to be out of scope for the problem at hand.insightful said:What is the temperature of the exhaust gases? How much chemical energy goes into heating the exhaust gases?
Using your method from your original post and an efficiency of 0.6% will give you a reasonable answer.168918791999 said:However thank you for your help!
No, that would mean we needed:insightful said:Using your method from your original post and an efficiency of 0.6% will give you a reasonable answer.
This efficiency is derived from data on Estes model rocket performance.
What is 1.63... and why multiply 0.6 times 100?168918791999 said:No, that would mean we needed:
1.63525964 / 0.6 *100 = 272.543273333 grams of gunpowder
That would mean that we needed more gunpowder than the rocket itself is
Do you mean "at 100% efficiency"? If so, redo your calculations.168918791999 said:1.6 is the mass of the gunpowder
First, define 100% efficiency.insightful said:Do you mean "at 100% efficiency"? If so, redo your calculations.
That is an incorrect definition of rocket efficiency.insightful said:100% efficiency = all gunpowder energy ends up as mgh energy.
I believe this is the OP's definition and a useful one here if defined as such.jbriggs444 said:That is an incorrect definition of rocket efficiency.
Given the numbers we have come up with for exhaust velocity and rocket velocity at burnout, a figure of 10% as given in the problem statement cannot possibly be compatible with the definition that you propose.insightful said:I believe this is the OP's definition and a useful one here if defined as such.
Where did I say a figure of 10% is compatible? I said 0.6%.jbriggs444 said:Given the numbers we have come up with for exhaust velocity and rocket velocity at burnout, a figure of 10% as given in the problem statement cannot possibly be compatible with the definition that you propose.
168918791999 said:Keg = Eg
KEg = 0.5*Mg*Vg2
Eg = 2.7x106*mg
0.5*Vg2 * mg= 2.7x106*mg
0.5*Vg2 = 2.7x106
Vg2 = 5.4x106
Vg = 2323.79 m/s = 8365.644 km/h
Would this not be too fast?
jbriggs444 said:It is in the right ballpark. Liquid oxygen/liquid hydrogen manages 4462 m/s. Nitrogen tetroxide/hydrazine manages 3369.