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I'm having trouble figuring out what this thread is about.
So far it looks like a menagerie of different thoughts.
Rauber, Joel wrote:
A firearm w/ out a bullet is a rocket.
I don't understand what point this is trying to make.
-- A firearm (with propellant charge) *with or without* a bullet
satisfies the dictionary definition of rocket, and has the same
physics as a rocket.
-- A firearm (with propellant charge) without a bullet is a rather
inefficient rocket.
-- A firearm (with the same propellant charge) with a bullet is a
more powerful rocket.
On 10/06/2006 06:57 PM, Bernard Cleyet wrote:
I [initially guessed] that w/ o the bullet the low mass POR (products of reaction) left w/ high speed. W/ the bullet much lower speed, but high mass, so the p was the same, therefore, the kick the same. [A]
However, using maths instead of qualitative reasoning ....
Doing the math is fine, but qualitative reasoning works too, if done
right. Jeffrey Schnick got it right.
At an intermediate level of detail, you can do the following argument in
your head:
1) KE is *quadratic* in the momentum; it's not a proportional tradeoff
as assumed in [A].
2) The *reduced mass* (denoted M) plays a dominant role in all such
two-body interactions. It is far more relevant than either mass
separately. 1/M = 1/m + 1/m'.
3) The reduced mass is dominated by the lesser of the two masses, if
they are significantly unequal. This should be (a) a familiar result
and (b) obvious from the definition of reduced mass: resistors in
parallel.
4) Therefore the equation that defines the impulse (aka kick) (denoted p)
must be something like p^2/2M = E. So the smaller the bullet, the smaller
the kick, with a square root involved.
I don't have Dan's or Jim's experience with weapons, but I do have lots of
experience helping kids launch water rockets.
http://users.hubwest.com/gordo/waterrocket.html
I've had kids as young as 8 ask the key physics question: Why does the
rocket need both air *and* water? I answer that the air is needed for
energy, and the water is needed for momentum. I then explain what that
means.....
This is AFAICT nearly the same physics as the classic "what makes the
car go" question. The answer involves energy *and* momentum.
http://www.av8n.com/physics/car-go.htm
suggests rocket engineers prefer denser fuels (w/ the same specific energy),
It's more complicated than that. The most obvious complication is that
you have to *lift* the fuel, so in many cases, making the fuel heavier
creates more problems than it solves. A glance at the rocket equation
http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
tells the tale. Making all the fuel heavier (at constant energy) will
reduce the exhaust velocity, which is disadvantageous. On the other
hand, increasing the fuel mass (at constant non-fuel mass) makes an
advantageous contribution via the logarithmic term, especially when
the non-fuel mass is relatively large.
What are the chances that a rocket would use heavy propellants for
takeoff, and light propellants for later stages?
Maybe aluminum + perchlorate versus hydrogen + oxygen???
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