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How is there no net force in this situation

  1. Sep 20, 2016 #1
    1. The problem statement, all variables and given/known data

    A man pushes on a piano with mass 190 kg ; it slides at constant velocity down a ramp that is inclined at 17.0 ∘ above the horizontal floor. Neglect any friction acting on the piano.

    A. Calculate the magnitude of the force applied by the man if he pushes parallel to the incline.


    2. Relevant equations
    Sum of forces = ma


    My question is not regarding the solution. I'm aware that the solution is mgsin(theta) but my question is how come there is no acceleration, yet there is only one force in the positive x direction since it says there is no friction. And why does the man push exactly as hard as the component of gravity in the x direction? I can see where the answer comes from, just not why.
     
  2. jcsd
  3. Sep 20, 2016 #2

    Orodruin

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    There is a normal force from the ramp even if there is no friction.
     
  4. Sep 20, 2016 #3
    I also can not figure out why the man has to push with a force equal to the component of weight. One insight though is that they have asked to neglect friction which does not mean friction is not present. If a net force is acting then it can not move with constant velocity.
     
  5. Sep 20, 2016 #4

    gneill

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    What in the question statement tells you the direction of the applied force? I see no direction given other than that it's parallel to the incline...
     
  6. Sep 20, 2016 #5

    Orodruin

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    It means you are supposed to treat the problem as if it was not present.

    Exactly. So you need to figure out how hard the man has to push in order for there to be no net force. You have two unknowns, the magnitude of the normal force and the magnitude of the applied force. You need to make sure that all of the force components are zero and so you have two equations to determine your two unknowns.

    Hint: It is easier if you consider the force equations in the direction parallel and perpendicular to the plane, respectively.
     
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