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Free body diagram problem

  1. Feb 27, 2013 #1
    1. The problem statement, all variables and given/known data

    An 82 kg couch is being pushed with a force of 56 N at an angle of 40 above horizontal. If the coefficient of friction between the couch and the floor is 0.051, what is the acceleration of the couch?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 27, 2013 #2

    SammyS

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    Hello gullyb. Welcome to PF !

    What have you tried?

    Where are you stuck?

    Before we can help you, you need to show some effort at solving this problem.
     
  4. Feb 27, 2013 #3

    SteamKing

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    Merely stating a problem is not enough effort to obtain help.

    Please follow the homework template.
     
  5. Feb 27, 2013 #4
    ooh sorry,

    okay i broke down the fa into its components which i get
    fapph=56cos40
    fapph=42.9

    fappv=56sin40
    fappv=36.0

    then i found the fg to be 804.42
    fg=mg
    fg=(82)(9.81)
    fg= 804.42

    then i solved for fn by making fnet = 0 because the forces cancel out because there is no movement in the verticle direction.
    fn=fnet-fg-fappv
    fn=0-804.42-36.0
    fn=840.42

    then i find the force of friction which turns out to be the same as fapph this is where im stuck, because i dont think they should be the same
    ff=uk*fn
    =(0.051)(840.42)
    =42.9

    so if i try to find the acceleration it wont make sense
    fnet=ff-faaph
    fnet=0
    fnet=ma
    a=fnet/m

    idk what i did wrong please help ?
     
  6. Feb 27, 2013 #5

    PhanthomJay

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    Looks good, keep going, solve for a. What does that imply?
     
  7. Feb 27, 2013 #6
    well this would mean that the acceleration is 0 so there is no acceleration? but i dont think that is right
     
  8. Feb 27, 2013 #7

    haruspex

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    I would have interpreted that as pushing upwards. Am I wrong?
     
  9. Feb 27, 2013 #8

    PhanthomJay

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    Why not? What does it mean if the couch is moving but not accelerating?
     
  10. Feb 27, 2013 #9
    hmmm it means that its moving at a constant velocity. ooh okay yes that makes sense thank you! :D
     
  11. Feb 27, 2013 #10

    haruspex

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    Did you see my comment, post #7?
     
  12. Feb 27, 2013 #11
    oooh sorry no, hmm that could be right because they didnt really give any direction to where the couch is going, but i kinda assumed that its moving forward so there wont be any displacement in the verticle direction?
     
  13. Feb 27, 2013 #12

    haruspex

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    There won't be any vertical displacement provided the upward component is insufficient overcome gravity. But it will reduce the normal force, and hence the friction.
     
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