a 15.0kg ball is supported

label Physics
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A 15.0 kg ball is supported fromthe ceiling by rope A. Rope B pulls downward and to the side on theball. If the angle of A to the vertical is 22° and if B makesan angle of (= 53°) to the vertical (Fig.12-100), find the tensions in ropes A and B.

 N (rope A)
 N (rope B)
Apr 30th, 2015

Tension in A - T

Tension in B - S

vertical forces equation Tcos22 =mg+S cos 55  (mg = weight of ball)

Horizontal equation Tsin 22=S sin 55

solving: from second equation: T = S sin 55/sin 22

substitute In first S sin55 cos22/sin22=mg + S cos 55

S(sin55 cos 22/sin 22 -cos 55)=mg

S=mg/(sin55 cos 22/sin 22 -cos 55= mg sin 22/(sin55 cos22-cos55 sin22) mg sin 22/sin(55-22)

=mg sin 22/sin 33

S = 15*9.81 sin22/sin33=101.2 N

T= S sin55/sin22= 46.3 N



Apr 30th, 2015

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