Not getting right answer in force problem

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Homework Statement


A 100 kg object is accelerated by a force of 10,000 N. What is the acceleration of the object caused by the force?

Homework Equations


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

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.
 
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Answers and Replies

  • #2
Nidum
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This problem does not need any complicated analysis .

What well known formula links Force , Mass and Acceleration ?
 
  • #3
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Milgrom's law?

I am using the simplest interpolating function and the generally agreed upon acceleration constant.
 
  • #4
Nidum
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Newton's Law's ?

Which one is relevant to this problem ?
 
  • #5
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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.
 
  • #6
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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.
 
  • #7
Nidum
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There is nothing to interpolate .

What is the common formula definition of Newton's second Law ?
 
  • #8
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Force = the derivative of momentum with respect to time

Which of course as any school child knows, falls apart completely due to dark matter.
 
  • #9
Nidum
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You obviously know more than me . I give up .
 
  • #10
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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.
 
  • #11
Drakkith
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I'm using u(a / a_0) = 1 / (1 + a_0 / a) as my interpolating function.
Just use the equation: F=MA. Simple algebra will give you the correct answer very quickly. No need for interpolating.
 
  • #12
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Isn't that idealized...? I think that would only work in a universe that did not have a dark matter component.
 
  • #13
Drakkith
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Dark matter has absolutely nothing to do with this problem. Forget about it.
 
  • #14
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What do you mean?
 
  • #15
CWatters
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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.
 
  • #16
Drakkith
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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.
 
  • #17
CWatters
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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.
 
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  • #18
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Milgrom's law?
Don't use Milgroms law. This is a question about Newton's 2nd law, not Modified Newtonian Dynamics.

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