A basketball scoreboard that weighs 9 kN is to be hung from the roof frame of an indoor stadium using a cable ABC. The ends of the cable are attached to hinges at points A and C. Before the scoreboard is attached at B, the midpoint, cable ABC is slightly slack (i.e. it is longer than 3 metres). The weight of the scoreboard is to be applied slowly at B until equilibrium is reached. At equilibrium, point B on the cable is at a distance d below the line AC as the cable becomes taut (its length does not change, however). The cable can safely carry a maximum tension of 20 kN. Design limitations require that point B drop not more than 30 cm below the horizontal dashed line AC as the scoreboard is attached.
As a consulting engineer, you are asked to design the system. Analyze the given data to see whether you can satisfy the requirements. If requirements are met, specify the precise length of the cable and the value of θ to use. If not, you are required to, design an alternate hanging configuration (shown below) such that all requirements are met.
The question belongs to Physics and it discusses about calculation of cable tension required to hold a scoreboard in an indoor stadium.
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