1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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)

    2. Relevant equations

    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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

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

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

  5. Mar 11, 2016 #4


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    (I get -3.88 m/s2, but close enough).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted