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Posers and Puzzles

Posers and Puzzles

  1. Subscriber sonhouse
    Fast and Curious
    21 Jul '08 05:11 / 1 edit
    You are on a trip to Alpha Centauri, you have the means to accelerate at 330 G's safely, but it stops short, only accelerates at that rate for 1000 seconds and the engine cuts out. You have the means to go into hibernation for millenia if need be. You make the calculations, find out its going to take a lot longer than the 5 or 6 years you first planned, so you go into hibernation.
    How many years does it take to go the 4 light years (we make it exactly 4 for simplicity) to Alpha Centauri and how much different has time flowed on the ship V time flowing on Earth?
    In other words, you start out on your journey in the year 2200, jan 1.
    You get to AC in what year on your calander, but figured out its not the same on Earth, what year is it on Earth time? Getting it to within one month is fine.
  2. Subscriber AThousandYoung
    It's about respect
    21 Jul '08 06:47
    Originally posted by sonhouse
    You are on a trip to Alpha Centauri, you have the means to accelerate at 330 G's safely, but it stops short, only accelerates at that rate for 1000 seconds and the engine cuts out. You have the means to go into hibernation for millenia if need be. You make the calculations, find out its going to take a lot longer than the 5 or 6 years you first planned, so ...[text shortened]... s not the same on Earth, what year is it on Earth time? Getting it to within one month is fine.
    First step:

    d = di + vi*t +(1/2)at^2, di = vi = 0
    d = (1/2)at^2
    d = (1/2)330*32(ft/s^2)(1000s)^2
    d = 2.38 * 10^9 ft

    By the time the engines cut out, the ship has travelled 2.38*10^9 ft.
  3. Subscriber AThousandYoung
    It's about respect
    21 Jul '08 06:50
    Originally posted by sonhouse
    You are on a trip to Alpha Centauri, you have the means to accelerate at 330 G's safely, but it stops short, only accelerates at that rate for 1000 seconds and the engine cuts out. You have the means to go into hibernation for millenia if need be. You make the calculations, find out its going to take a lot longer than the 5 or 6 years you first planned, so ...[text shortened]... s not the same on Earth, what year is it on Earth time? Getting it to within one month is fine.
    v = vi + at
    v = 330(ft/s^2)(1000 s)
    v = 3.3*10^5 ft/s

    The ship after 1000 seconds is moving at 3.3*10^5 ft/s.
  4. Subscriber AThousandYoung
    It's about respect
    21 Jul '08 06:59 / 1 edit
    Alpha Centauri is 4 LY away. One LY is 9,460,730,472,580.8 km. I will use 9.5 * 10^12 km for simplicity. 4 * 9.5 * 10^12 is

    d = 3.8 *10^13 km
    d = di + vt + at^2
    3.8 * 10^13 km = 2.38*10^9 ft + (3.3*10^5 ft/s)t + 0
    (3.8 * 10^13 km - 2.38*10^9 ft)/(3.3*10^5 ft/s) = t

    That will be the amount of time the trip takes from the perspective of the people in the ship.
  5. Subscriber AThousandYoung
    It's about respect
    21 Jul '08 07:00 / 1 edit
    Originally posted by AThousandYoung
    Alpha Centauri is 4 LY away. One LY is 9,460,730,472,580.8 km. I will use 9.5 * 10^12 km for simplicity. 4 * 9.5 * 10^12 is

    d = 3.8 *10^13 km
    d = di + vt + at^2
    3.8 * 10^13 km = 2.38*10^9 ft + (3.3*10^5 ft/s)t + 0
    (3.8 * 10^13 km - 2.38*10^9 ft)/(3.3*10^5 ft/) = t

    That will be the amount of time the trip takes from the perspective of the people in the ship.
    t = (3.8*10^13 km - 2.38*10^9 ft)/(3.3*10^5 ft/s)
    t = (3.8*10^13 km - 2.38*10^9 ft*[km/3281 ft])/(3.3*10^5 ft/s*[km/3281 ft]
    t = (3.8*10^13 km - 7.25*10^5 km)/100 km/s

    We can see the distance covered while accelerating is negligable.

    t = 3.8*10^11 s

    That's how long the trip takes.

    t = 3.8*10^11 s * (year/3.15*10^7 s)
    t = 1.2*10^4 years.

    It's a good thing we can hibernate! We're going to experience 12,000 years of travel!
  6. Subscriber AThousandYoung
    It's about respect
    21 Jul '08 07:32 / 1 edit
    Originally posted by AThousandYoung
    v = vi + at
    v = 330(ft/s^2)(1000 s)
    v = 3.3*10^5 ft/s

    The ship after 1000 seconds is moving at 3.3*10^5 ft/s.
    vf = (3.3*10^5 ft/s)(m/3.3 ft)
    vf = 10^5 m/s

    is the final velocity. The speed of light is three orders of magnitude higher. The ship is not going at relativistic speeds and there will be no appreciable time dilation.

    This is not consistent with the statement

    "but figured out its not the same on Earth"

    Is this an SAT prep problem?
  7. Subscriber sonhouse
    Fast and Curious
    21 Jul '08 08:29 / 2 edits
    I see where you went wrong. Do you want me to say it or do you want to look over your work again?
    It's not an SAT test, it's a DNJ test.
    (Donald Neal Jennings
    BTW, the relativistic effect is small but will be measurable on this trip.
  8. Subscriber AThousandYoung
    It's about respect
    21 Jul '08 12:24
    Originally posted by sonhouse
    I see where you went wrong. Do you want me to say it or do you want to look over your work again?
    It's not an SAT test, it's a DNJ test.
    (Donald Neal Jennings
    BTW, the relativistic effect is small but will be measurable on this trip.
    I'll find it.
  9. Subscriber AThousandYoung
    It's about respect
    23 Jul '08 02:38
    Originally posted by AThousandYoung
    I'll find it.
    No I won't. Too lazy. What did I do wrong?
  10. Subscriber AThousandYoung
    It's about respect
    23 Jul '08 02:41 / 4 edits
    Originally posted by AThousandYoung
    v = vi + at
    v = 330*32*(ft/s^2)(1000 s)
    Forgot the factor of 32. Still, is that enough?

    3.3x10^5 x 32 is...1.1x10^7. Ahh...
  11. Subscriber sonhouse
    Fast and Curious
    23 Jul '08 06:02
    Originally posted by AThousandYoung
    Forgot the factor of 32. Still, is that enough?

    3.3x10^5 x 32 is...1.1x10^7. Ahh...
    There you go.
    But I also wanted to show there was a bit of time shift too, see if you can figure out what it is, relativistic effects show up even at 0.01C.
    So what is the trip time now you spotted your error?
  12. Subscriber AThousandYoung
    It's about respect
    25 Jul '08 15:45
    Originally posted by sonhouse
    There you go.
    But I also wanted to show there was a bit of time shift too, see if you can figure out what it is, relativistic effects show up even at 0.01C.
    So what is the trip time now you spotted your error?
    You multiply the speed I calculated by the Lorenz factor, but I've been too lazy and busy to do that and give you the answer. Maybe later.
  13. Subscriber sonhouse
    Fast and Curious
    26 Jul '08 21:14
    Originally posted by AThousandYoung
    You multiply the speed I calculated by the Lorenz factor, but I've been too lazy and busy to do that and give you the answer. Maybe later.
    Well its a lot more than just a few microseconds.