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Vector component problem

  1. Jan 13, 2016 #1
    1. The problem statement, all variables and given/known data
    An air-conditioning unit is fastened to a roof that slopes at an angle of 35° above the horizontal (Fig. 1.33). Its weight is a force on the air conditioner that is directed vertically downward. In order that the unit not crush the roof tiles, the component of the unit’s weight per- pendicular to the roof cannot exceed 425 N. (One newton, or 1 N, is the SI unit of force. It is equal to 0.2248 lb.) (a) What is the maxi- mum allowed weight of the unit? (b) If the fasteners fail, the unit slides 1.50 m along the roof before it comes to a halt against a ledge. How much work does the weight force do on the unit during its slide if the unit has the weight calculated in part (a)

    2. Relevant equations
    Fy=Fsinθ
    W=FS

    3. The attempt at a solution
    I created x / y axes with x being on the slope of the roof
    then try to find F as I know the Fy and the angle so:
    Fy=Fsinθ or F=Fy/sinθ
    F=425N / sin125 = 425N / 0.82 = 518.3 N

    and then for (b)
    First find Fx = Fcosθ = 518.3N x cos55 = 518.3N x 0.574 = 297.5N
    then
    W=FS = 297.5N x 1.50m = 446.25Nm

    Does this sound about right??
    the results in the answers are: (a)5.2 x 10^2 N
    (b) 4.5 x 10^2 Nm

    which look similar but i think im missing one zero somewhere?
    link to the page of the book:
    http://s9.postimg.org/nhklria4f/Screen_Shot_2016_01_13_at_16_02_15.png

    Thanks in advance! Hope its ok to post things like this :)
     
  2. jcsd
  3. Jan 13, 2016 #2
    Don't your answers agree with the textbook answers, or am I missing something?
     
  4. Jan 13, 2016 #3
    oh crap they do :)
    lol
    sorry!!!!
    its been a long day i was counting 10^2 as 1000 o0)

    time for a brake i think :)
     
  5. Jan 13, 2016 #4

    SteamKing

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    Staff Emeritus
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    You mean, like one of these?
    Or, one of these?
    Outside-Brain-Break-Tools.jpg

     
    Last edited by a moderator: Apr 18, 2017
  6. Jan 13, 2016 #5
    love the break joke !
    i always spell it wrong :)
     
  7. Jul 19, 2017 #6
    I know this is an old thread and I'm really sorry for resurrecting it, but this is quite related to my question:
    I did the same thing as OP on the x/y axis. Using basic geometry, I got that the angle between the x-axis and the vector is 55°. Since it goes from x to y, it's either -25° or 325°. Thus, I fail to understand how OP got 125° there. Can someone explain it to me?
     
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