Icarus Aquanaut Acoustic show: 7:00 PM on Monday, July 27 (beside Osaka's in Tallahassee)
Icarus Aquanaut is playing an acoustic show at a grand opening for a new pilates center in Tallahassee. That's right--we're not just rocking your face off, we're going to help you control the muscles that control your face. Keep your face on just a little bit longer with Icarus! We'll be playing outdoors near Osaka's in Tallahassee (the center is right beside it) at 7:00 PM on Monday, July 27th. Feel free to drop by--it's a free show, and Penelope will be there!
(Penelope is the bass.)
Doctorus Iquanaut answers your questions
Last week, we asked for questions from our fans to pass on to Doctorus Iquanaut. Here's the first one, from someone who likely expected to stump Doctorus Iquanaut:
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Question:
A bullet is fired through a board 5.0 cm thick in such a way that the bullet's line of motion is perpendicular to the face of the board. The initial speed of the bullet is 350 m/s and it emerges from the other side of the board with a speed of 250 m/s.
(a) Find the acceleration of the bullet as it passes through the board. in meters/ second squared
(b) Find the total time the bullet is in contact with the board.
in seconds
thanks for your help!
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I was told there would be no math. However, we always have a backup plan.
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Answer (courtesy of Chall and Dr. Dan Warren, Ph.D)
This is kind of a tough problem, unless I'm missing an easy way to do
it. I'm guessing by the first question that you can assume the
acceleration is constant. That's a big assumption, but you'll need to
make an assumption about the nature of the acceleration to answer this
question, so it may as well be that one. It's probably reasonable to
do so; it's equivalent to assuming that friction is a constant force.
Now, acceleration is change in speed over time, so if the acceleration
is constant, then it must be the difference in the two speeds given,
over the time. You'll notice, however, that the time it takes to get
through the board is not given. So let's do some calculus.
If acceleration is constant, then velocity must be linear, as velocity
is the antiderivative of acceleration, and the antiderivative of a
constant function is a linear function. That is, v(t) = at + b, where
a and b are constants. We don't know what time it is when the bullet
leaves the board, so call it T. If we assume that the clock is at
zero when the bullet starts going through the board, we have
350 = a(0) + b,
so b = 350, and
250 = aT + b.
To find a we'll have to go up another step. The antiderivative of
velocity is position, i.e. the distance the bullet has traveled
through the board at time t, which is
x(t) = 1/2 a t^2 + bt + c
We assume the clock starts when the bullet hits the board, so c=0. We
already know b= 350, so
x(t) = 1/2 a t^2 + 350 t.
We know also that x(T) = .05, because the bullet goes .05 meters in T
seconds, that is,
.05 = 1/2 a T^2 + 350 T.
To find a and T, we now have two equations and two unknowns:
250 = aT + 350
.05 = 1/2 a T^2 + 350 T
Even this system is a pain to solve, because it's not linear in T, but
I get T = 1/6000 and a = -600000. So the acceleration is -600,000
m/s^2 (negative because it's slowing down, not speeding up), and it
takes 1/6000th of a second to get through the board.
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Next question: Which is better for time travel, Quantum Tunelling or Gravitational Time Dilation?
Answer (courtesy of Gingerbread):
Quantum tunneling.
It is easier to produce results with gravitational time dilation, but the results (at least with current technology) cannot achieve much in the way of real time travel. To go off on a slight tangent from this into the expansion of Einstein's general theory of relativity (in which gravitational time dilation is predicted): in hypothetical scenarios, the closer one travels to the speed of light, the slower time will pass for that individual. This is Einstein's theory of special relativity, and it has been proven. To the individual, this seems like time travel, and to the rest of the universe, this likely seems like time travel as well. However, this method cannot send any individual into the past (at least not any farther back than the point that they leave), and technically, it only preserves the individual in a state until they emerge into normal time. If you're a stickler for definitions, this may as well be time travel since it looks like time travel and feels like time travel, but it is not the ideal method--and neither is gravitational time dilation.
Quantum tunneling is the ideal method to pursue this, but technology is not at any position to make it happen. Until then, we will have to rely on the trusty DeLorean DMC-12, a flux capacitor, and McFly.
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We've had more discussions about recording this summer/fall, so stay tuned for more. The Icarus music will be up on facebook as soon as facebook verifies our account.
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