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Homework Help: 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

    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
    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:

    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 :)
    its been a long day i was counting 10^2 as 1000 o0)

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


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    You mean, like one of these?
    Or, one of these?

    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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