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)
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 :)