The forces acting on a bucket suspended by three cables are analyzed. Cable A experiences an upward tension force of 8.01 kN to balance the downward gravitational force on the 817 kg bucket. Using trigonometry and the fact that the system is in equilibrium, the tensions in cables B and C are calculated to be 3.65 kN and 5.66 kN, respectively, based on their angles relative to the x- and y-axes.

1. 15. (a) The forces acting on bucket are the force of gravity, down, and the tension force of cable A, up.
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Since the bucket is in equilibrium and its weight is WB = mB g = (817 kg)(9.8 m/s ) = 8.01 × 103 N,
the tension force of cable A is TA = 8.01 × 10 N.
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(b) We use the coordinates axes defined in the diagram. Cable A makes an angle of 66◦ with the
negative y axis, cable B makes an angle of 27◦ with the positive y axis, and cable C is along the
x axis. The y components of the forces must sum to zero since the knot is in equilibrium. This
means TB cos 27◦ − TA cos 66◦ = 0 and
cos 66◦ cos 66◦
TB = TA = (8.01 × 103 N) = 3.65 × 103 N .
cos 27◦ cos 27◦
(c) The x components must also sum to zero. This means TC + TB sin 27◦ − TA sin 66◦ = 0 and
TC = TA sin 66◦ − TB sin 27◦ = (8.01 × 103 N) sin 66◦ − (3.65 × 103 N) sin 27◦ = 5.66 × 103 N .