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Applying Newton's laws

  1. Mar 13, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider the system shown in the figure (Figure 1) . Block A weighs 46.1 N and block B weighs 28.7 N . Once block B is set into downward motion, it descends at a constant speed.

    http://session.masteringphysics.com/problemAsset/1038576/6/YF-05-54.jpg
    upload_2016-3-13_22-18-20.png
    A

    Calculate the coefficient of kinetic friction between block A and the tabletop
    μ= 0.623

    B
    A cat, also of weight 46.1 N , falls asleep on top of block A. If block B is now set into downward motion, what is its acceleration magnitude

    2. Relevant equations
    F=ma


    3. The attempt at a solution

    ∑F in x direction of A: -F+T = ma
    -μ92.1+T = 92.2/ 9.8 a
    -.623(92.1)+T=9.4 a

    ∑F in y of A N-w = ma
    92.2-9.4(9.8) = 0

    ∑F in Y of B T-w
    T-2.93 (9.8) = 2.93 a
    T= 28.7+2.93a

    plug T into first equation: -.623(92.1)+28.7+2.93a = 9.4a
    -.623(92.1)+28.7= (9.4-2.93) a
    divide both sides
    ( -.623(92.1)+28.7) /9.4-2.93 = a

    gives me wrong answer, where did I go wrong?
     
  2. jcsd
  3. Mar 13, 2016 #2
    I think that the easiest way to solve is to do a free body diagram including the forces of friction, gravity, and tension then proceed to fill in the known values for the forces which should lead to tension canceling out algebraically then you can solve for acceleration

    Remember that for each side of the pulley the sum of the forces should equal the mass of the block times the acceleration
     
  4. Mar 13, 2016 #3

    PhanthomJay

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    What is the direction of the acceleration of each block?
     
  5. Mar 13, 2016 #4
    I do not understand why you are calculating 'a ' the acceleration of masses as it should be zero as per your problem.
     
  6. Mar 13, 2016 #5
    So i have looked through your original post and i have found some problems. Like -μ"92.1"+T = 92.2/ 9.8 a => "92,2"
    But i suggest you using this formula : a = ΣF / ΣM, more faster and i think that you should start again rather than try figuring the mistake
     
  7. Mar 13, 2016 #6
    In the above case is it possible that the accelerated motion take place?
     
  8. Mar 13, 2016 #7
    I think that the friction force is greater than gravity so the system won't move
     
  9. Mar 13, 2016 #8

    PhanthomJay

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    it is zero in part a but non zero in part b. The error is in part b.
     
  10. Mar 14, 2016 #9
    That is what I did, or at least tried
     
  11. Mar 14, 2016 #10
    A is left
    B is up
     
  12. Mar 14, 2016 #11
    which force is moving the body A towards the left?
     
  13. Mar 14, 2016 #12
    What is wrong with what I posted?
    The friction force u92.2 is pulling left and Tension pulling right
    Friction
     
  14. Mar 14, 2016 #13
    Got it, I was missing a negative sign, thanks
     
    Last edited: Mar 14, 2016
  15. Mar 14, 2016 #14
    friction can not move -it can only provide resistance to motion-
    if your body is pulled left it will oppose it

    again if your body gets pulled towards right it will oppose it - so will there be motion towards right if it opposes the motion?
     
  16. Mar 14, 2016 #15
    Yes the motion is to the right but the acceleration is to the left so the object is slowing down due to the friction force which acts towards the left. I figured out the answer, my mistake was not putting a negative sign in front of the acceleration
     
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