1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Not getting right answer in force problem

  1. Aug 21, 2016 #1
    1. The problem statement, all variables and given/known data
    A 100 kg object is accelerated by a force of 10,000 N. What is the acceleration of the object caused by the force?

    2. Relevant equations
    F_N = m * u(a / a_0) * a
    a_0 = 1.2 * 10^-8 cm / s^2

    3. The attempt at a solution
    I'm using u(a / a_0) = 1 / (1 + a_0 / a) as my interpolating function.

    This gives F_N = m * a / (1 + a_0 / a)

    10,000 N = (100 kg) * a / (1 + (1.2 * 10^-8 cm/s^2) / a)

    10,000 N / 100 kg = a^2 / (a + (1.2 * 10^-8 cm/s^2))

    a^2 - (10,000 N / 100 kg) * a - (10,000 N / 100 kg) * (1.2 * 10^-8 cm/s^2) = 0

    Applying quadratic formula:

    a = ((10,000 N / 100 kg) +/- sqrt((10,000 N / 100 kg)^2 + 4*(10,000 N / 100 kg)*((10,000 N / 100 kg) * (1.2 * 10^-8 cm/s^2)))) / 2

    Which comes out (cleanly I might add) to a number slightly smaller than 100 m/s^2: 99.999999988 m/s^2
    This was the query I gave Google for calculating this: "(100 + sqrt(10000 - 4 * (1.2 * 10^-6))) / 2"

    The answer in the book is 100 m /s^2.
     
    Last edited: Aug 21, 2016
  2. jcsd
  3. Aug 21, 2016 #2

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    This problem does not need any complicated analysis .

    What well known formula links Force , Mass and Acceleration ?
     
  4. Aug 21, 2016 #3
    Milgrom's law?

    I am using the simplest interpolating function and the generally agreed upon acceleration constant.
     
  5. Aug 21, 2016 #4

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    Newton's Law's ?

    Which one is relevant to this problem ?
     
  6. Aug 21, 2016 #5
    I would assume his law about force which is incorrect but was corrected in 1983.

    The teacher (10th grade) hasn't done a very good job of teaching. His method is to give us problems and ask us to research how to find the answer. I researched force and read about the correct model for Newtonian dynamics.

    It bugs me that the answer I'm getting is so close to the one in the book.
     
  7. Aug 21, 2016 #6
    I also tried it with the standard interpolating function: (1 + x^2) ^ (-1/2) and still got an answer that is slightly different from the book's.
     
  8. Aug 21, 2016 #7

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    There is nothing to interpolate .

    What is the common formula definition of Newton's second Law ?
     
  9. Aug 21, 2016 #8
    Force = the derivative of momentum with respect to time

    Which of course as any school child knows, falls apart completely due to dark matter.
     
  10. Aug 21, 2016 #9

    Nidum

    User Avatar
    Science Advisor
    Gold Member

    You obviously know more than me . I give up .
     
  11. Aug 21, 2016 #10
    I highly doubt that. I'm just a kid and I'm not that into science and definitely not very good at it. But thank you anyway, Nidum.
     
  12. Aug 21, 2016 #11

    Drakkith

    User Avatar

    Staff: Mentor

    Just use the equation: F=MA. Simple algebra will give you the correct answer very quickly. No need for interpolating.
     
  13. Aug 21, 2016 #12
    Isn't that idealized...? I think that would only work in a universe that did not have a dark matter component.
     
  14. Aug 21, 2016 #13

    Drakkith

    User Avatar

    Staff: Mentor

    Dark matter has absolutely nothing to do with this problem. Forget about it.
     
  15. Aug 21, 2016 #14
    What do you mean?
     
  16. Aug 21, 2016 #15

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    It took a long time for us to realise that Newton's laws arent perfect because other effects are small - so safe to ignore in many cases.

    In this case it really is as simple as using F=ma.
     
  17. Aug 21, 2016 #16

    Drakkith

    User Avatar

    Staff: Mentor

    I mean that you need to completely forget about dark matter when learning physics at this level. No one on Earth takes dark matter into account when building bridges, planes, or anything else. The only possible time you would need to consider it is if you were an astrophysicist or some other scientist working directly in a field investigating dark matter.
     
  18. Aug 21, 2016 #17

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    PS It's a long time since I was at school but Newton's laws were good enough to solve all the problems I was set until I was over 18 years old.
     
  19. Aug 21, 2016 #18

    Dale

    Staff: Mentor

    Don't use Milgroms law. This is a question about Newton's 2nd law, not Modified Newtonian Dynamics.

    Thread closed
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook