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How do I find the normal force?

  1. Feb 25, 2013 #1
    1. The problem statement, all variables and given/known data

    Let's say I'm holding a crate up against the ceiling with a force of 'P', and the crate is stationary.
    What is the normal force?


    2. Relevant equations

    Newton's 1st law: ƩF=0

    3. The attempt at a solution

    I have three forces acting on the crate - The normal force, the gravitational force, and the applied force.

    According to Newton's first law, Fg+Fn+Fa=0

    Thus, Fn=-Fg-Fa

    Since Fg pulls down Fg=-mg
    Since Fa pushes up, Fa=P

    Thus, Fn=mg-P

    However, my book says Fn=P-mg. What am I doing wrong?
     
  2. jcsd
  3. Feb 25, 2013 #2
    Fn is pushing downward, so its sign in your force balance equation should be negative.
     
  4. Feb 25, 2013 #3
    Why is it I only apply this negative to the normal force? If a downward force is negative, then Fg should be negative too, and

    -Fg-Fn+Fa=0

    Fn=Fa-Fg=P+mg

    Which still isn't the right answer :/
     
  5. Feb 25, 2013 #4
    I made a force table that I can use to analyze the component of each force and the net force that results.

    Force - y-component
    Fg:____-mg
    Fa:____+P
    Fn:____mg-P?
    __________________
    ma:____0

    Adding the entries in this table, it seems obvious that the normal force must equal mg-P. Otherwise, the sum of this table wouldn't be zero.
     
  6. Feb 25, 2013 #5
    OK. Here's my version of it, where the positive direction of force is in the upward direction:

    Fa-mg-Fn=0

    This gives Fn=P-mg

    In these equations Fn stands only for the magnitude of the normal force. The direction of the normal force is downward.
     
  7. Feb 25, 2013 #6

    tms

    User Avatar

    It will be easier to set up the forces so that they are all positive, and you deal with direction explicitly with the signs. Since [itex]F_n[/itex] and [itex]F_g[/itex] are both down, and [itex]F_a[/itex] is up, you should write
    [tex]-F_g - F_n + F_a = 0.[/tex]
    From which the book's answer comes. Your answer is correct, too, but the value of [itex]F_n[/itex] is then negative.

    Edit: Oops, someone beat me to it.
     
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