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Understanding an equation in a dynamics spring problem

  1. Apr 30, 2017 #1
    1. The problem statement, all variables and given/known data
    A block of mass [itex]M = 0.5kg[/itex], attached to a spring of elastic constant [itex]k = 3N/m[/itex] on a vertical wall, slides without friction through an horizontal air table. A disk of mass [itex]m = 0.05kg[/itex] is placed on the block, whose surface has a coefficient of static friction [itex]\mu _e = 0.8[/itex]. What is the maximum oscillation amplitude of the block so the disk won't slide off of it?

    2. Relevant equations
    [itex]\vec F = m\vec a \\ \vec F = -kx \\ F_{\mu e}^{max} = \mu _emg[/itex]
    3. The attempt at a solution
    I have already solved this problem, and then I've checked part of a solution on the web containing an insight on the theory behind it:

    1c7011bead14427b87f743c4a160802d.png
    I don't really understand the second part where the author talks about the non-inertial frame reference, and about the forces involving it, and ends up with the equation
    0b68a8320cdf4b95900429b9740468a3.png
    Even though I was able to solve the exercise, I reached the last equation through a more direct way, without thinking too much about it, so this explanation made me a bit confused. Am I being clear enough?

    I hope someone can help!
     
  2. jcsd
  3. May 1, 2017 #2

    haruspex

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    There are cases where noninertial frames make life simpler, but this is not one of them. The sign of a is irrelevant since reversing it just leads to the other extreme of x, so it matters not whether you write a=μeg or a=-μeg. This same equation arises whether you think in terms of an inertial frame or a noninertial one.
     
  4. May 1, 2017 #3
    Hmm. I think I get it. So this is why in these equations we don't really take into account the negative signs? Because we're just interested in the value?
     
  5. May 1, 2017 #4

    haruspex

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    No, I'm saying that both signs are correct for maximum displacement; but the question asks for amplitude, which is by definition the magnitude of the maximum displacement, so non-negative.
     
  6. May 1, 2017 #5
    OK. I see. Thank you.
     
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