An air-conditioning unit is fastened to a roof that slopes at an angle of 35° ab

ID: 1330060 • Letter: A

Question

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 perpendicular

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 maximum

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)?

maximum the weight allowed perpendicular to the surface = 425 N

let W be the weight of the unit

component of weight directed vertically down ward to roof = W*costheta

W*cos35 = 425

W = 425/cos35 = 518.8 N <<-----answer

(b)

component of weight of the unit parallel to roof = W*sin35

work done = W*sin35*l

W = 518.8*sin35*1.5 = 446.3 J <<-----answer

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