Question

Find the tension in cables B and C if w1 = 73.0 N and w2 = 170 N.

60°у 60°

Answer 1

60° 60° TB Tc TA

Applying Newton’s 2^nd law horizontally at the knot,

F_net = ma

T_Cx -T_Bx = 0

T_Cx =T_Bx

T_Ccos60=T_Bcos60

T_C =T_B--------------(1)

Applying Newton’s 2^nd law vertically at the knot,

F_net = ma

T_Cy +T_By –T_Ay = 0

T_Csin60+T_Bsin60 = T_Ay ……………(2)

Plug (1) in (2)

T_Bsin60+T_Bsin60 = T_Ay

2T_Bsin60 = T_Ay……………(3)

Applying Newton’s 2^nd law vertically at the knot,

F_net = ma

T_Ay-W₁-W₂ = 0

T_Ay=W₁+W₂---------------(4)

Plug (4) in (3),

2T_Bsin60 = W₁+W₂

T_B = (W₁+W₂)/(2sin60)

Plug values,

T_B =(73.0+170)/(2sin60)

T_B = 140.3 N

From (1),

T_C =T_B = 140.3 N