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Force to stop a space ship

  1. Mar 21, 2014 #1
    1. The problem statement, all variables and given/known data
    A spaceship is accelerating at ##1000# m/(sec per sec). How much force is required from the backthrusters to completely stop the spaceship?


    2. Relevant equations



    3. The attempt at a solution
    Let's assume the spaceship has mass ##m## and no mass is lost when firing the backthrusters.
    Using Newtons second, we have
    $$
    \sum F = 1000m.
    $$
    The only force would be the velocity from the backthrusters correct?
    So we have
    $$
    -v_0x = 1000m.
    $$
    Is this correct? How do I find the force needed to stop the ship?
     
  2. jcsd
  3. Mar 21, 2014 #2
    I'd like to point out that an object in motion will remain in motion unless a constant acceleration is applied to it. That being said,

    No, velocity would not be the force you're looking. Here's two tips:
    1. Check your units, as they do help verify you're doing something right if your calculations look funny
    2. Newton's Laws of Motion.
     
  4. Mar 21, 2014 #3
    So the force on the LHS needs to be acceleration then?
     
  5. Mar 21, 2014 #4
    Force has units of kg * m/s2. Acceleration has units of m/s2.
    You're almost there. :)
     
  6. Mar 21, 2014 #5
    The question doesn't make complete sense since if it is accelerating then it must be moving as well. And therefore the stopping force would need to be slightly larger than the force causing it to accelerate in which case you would also need to know the time required to bring it to a an instantaneous stop.

    And 1000 m/s^2 is 100g's which is a huge acceleration. I doubt any practical rocket ship could withstand this amount of acceleration. It would just crumple or tear apart.

    Otherwise I thought the mass assumption by the OP was very insightful.
     
  7. Mar 22, 2014 #6
    What other information do we need to assume to solve the problem then?
     
  8. Mar 22, 2014 #7

    NascentOxygen

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    Staff: Mentor

    The question fails to specify the time span in which you are required to competely stop the ship. (Whatever 'stop' means in space, anyway.)

    It would seem better to have been asked for the force needed to exactly cancel the gravitational acceleration.

    Do you have the answer yet?
     
  9. Mar 22, 2014 #8
    No I don't have an answer. So we can make our own assumptions.
     
  10. Mar 22, 2014 #9

    NascentOxygen

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    Staff: Mentor

    :smile: No, I don't think you should decide on an arbitrary time to halt the ship.

    For starters, you are not told its current speed....

    Probably the best you can do is to state that any force exceeding xxx Newtons will eventually bring the ship's speed to zero if it remains in the grip of that field. So, find xxx.
     
  11. Mar 22, 2014 #10
    How do I find xxx? This problem comes from the Nuclear Propulsion Study Guide for the Navy.
     
  12. Mar 22, 2014 #11
    I think you kind of stated the answer already in your first try. Your trying to find the force Fstop to stop the ship.

    Fstop = ?
     
  13. Mar 22, 2014 #12
    So that is just a 1000 then?
     
  14. Mar 22, 2014 #13
    No, not quite, that is the acceleration remember. Again you actually already stated the answer in the OP.
     
  15. Mar 22, 2014 #14
    1000m
     
  16. Mar 22, 2014 #15
    You got it.

    My suggestion in any problem you do is to always include the units. Even if none are given you should assume some appropriate unit. This a good way to make sure you have understood the problem correctly and also catch any mistakes you make in the arithmetic.
     
  17. Mar 22, 2014 #16
    Would the answer change if we assumed the current speed is ##v_0##?
     
  18. Mar 22, 2014 #17
    Yes, as now you need a larger force with enough time to slow the ship from v0 to zero.
     
  19. Mar 22, 2014 #18

    NascentOxygen

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    Staff: Mentor

    +1

    I read your answer "1000m" as 1000 metres, and puzzled how you managed to express a force in metres. :frown:

    Had you written "1000m newtons" I would have recognized it without hesitation.
     
  20. Mar 22, 2014 #19

    NascentOxygen

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    Staff: Mentor

    No problem if you wish to do that, but you'll also need to nominate a time, ##t_s##, or a distance, ##d_s##, in which to bring the ship to a standstill.
     
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