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Question for sliding object

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  1. Jan 30, 2016 #1
    1. The problem statement, all variables and given/known data
    Object B with mass m is sliding on an object A with mass M. Object A is being pulled by a string with acceleration A. There is no friction. (Picture Uploaded)

    1) Find the maximum value of A that allows m to stay on M (sliding)
    2) Find the x and y value of the acceleration of object B
    3) In this case, what is the value of the force T (the force that is pulling Object A)
    4) Find the value of the normal force F that is acting on object A.
    5) As an alternate version of this question, suppose that force T was given instead of acceleration A.

    2. Relevant equations

    Newton's Law; F=ma

    3. The attempt at a solution

    1) In the case of object B, there are three forces; the normal force N, mg and inertia mA
    setting a new coordinate with X and Y where Y is perpendicular to the hypotenuse and X perpendicular to Y, I showed that acceleration in Y direction must equal 0 and the A in this case is the A for 1). The answer I got was (mgcosθ-N)/msinθ

    2) Using the coordinate and the forces from 1), I figured out that X direction of the acceleration equals mAcosθ+mgcosθ. The angle between X and x is θ, so x direction would be -(mAcosθ+mgsinθ)cosθ, and y direction would be -(mAcosθ+mgsinθ)sinθ

    3) Because there is only one force given from the outside, which is T, T=∑ma for a in the x direction.
    T=-(mAcosθ+mgsinθ)cosθ+MA

    4) Normal force equals the force acting on the surface which is object B's force in the y direction
    F=(mAcosθ+mgsinθ)sinθ
    5) This would be a simple change, just writing the answer from 3) like A= f(T)

    Overall I have tried to solve all these and came up with answers. But I'm not sure if they are correct.
    If someone could check them I would be grateful.
     

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  3. Jan 30, 2016 #2

    CWatters

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    You can simplify that further.

    Hint: If object B is "only just" in contact with A (eg it's just about to leave the surface) what is the value of N ?
     
  4. Jan 30, 2016 #3

    haruspex

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    This is rather confusing because A is being used both as the label on an object and as an acceleration. I assume you mean an inertial force ma, where a is the acceleration of A.
    Looks like you are using a noninertial frame here. It would help if you were to state that at the start.
     
  5. Jan 30, 2016 #4

    CWatters

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    Once simplified the answer just looks more obviously correct :-)
     
  6. Jan 31, 2016 #5
    Then N=0 so A=g/tanθ?
     
  7. Jan 31, 2016 #6

    haruspex

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    Looks right to me.
     
  8. Jan 31, 2016 #7

    CWatters

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    and me.
     
  9. Feb 1, 2016 #8
    How about the rest? Are they correct as well?
     
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