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Dynamics of a Box attached to a pully

  1. Mar 11, 2016 #1
    1. The problem statement, all variables and given/known data
    Body A in Fig. 6-33 weighs 102 N, and body B weighs 32 N. The coefficients of friction between A and the incline are μs 0.56 and μk 0.25. Angle θ is 40. Let the positive direction of an x axis be up the incline. In unit-vector notation, what is the acceleration of A if A is initially (a) at rest, (b) moving up the incline, and (c) moving down
    the incline?

    Free body diagram: http://postimg.org/image/fh6livrer/

    See attached picture (problem 27)
    http://postimg.org/image/5svunp27z/

    2. Relevant equations
    Fnet=ma

    3. The attempt at a solution

    Clearly the answer to part a is 0-- I'm stuck on part b.

    For B, [tex] F_{Net, y}= -m_B a_y = F_T -m_B g \rightarrow F_T = m_B g - m a_y[/tex]

    For A, [tex] F_{Net, x}=ma_x = - \mu _k m_A g cos(40) +F_T - m_A g sin(40)[/tex]

    Plugging in the information,

    [tex] 102 a= -0.25*102*cos(40)+32-32a -102sin(40) \rightarrow a=-.39[/tex]

    However, the book lists the correct answer as -3.9, so I'm off by a power of ten. Where did I go wrong?
     
  2. jcsd
  3. Mar 11, 2016 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Be sure to distinguish between mass and weight.
     
  4. Mar 11, 2016 #3
    D'oh! It should be

    [tex]
    \frac {102}{9.8} a= -0.25*102*cos(40)+32- \frac {32}{9.8}a -102sin(40) \rightarrow a=-3.82 [/tex]

    Thanks!
     
  5. Mar 11, 2016 #4

    TSny

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    Homework Helper
    Gold Member

    Good.
    (I get -3.88 m/s2, but close enough).
     
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