6 A small box B of weight 400 N is held in equilibrium by two light strings AB and BC . The string \(B C\) is fixed at \(C\). The end \(A\) of string \(A B\) is fixed so that \(A B\) is at an angle \(\alpha\) to the vertical where \(\alpha < 60 ^ { \circ }\). String BC is at \(60 ^ { \circ }\) to the vertical. This information is shown in Fig. 5.
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\caption{Fig. 5}
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- Draw a labelled diagram showing all the forces acting on the box.
- In one situation string AB is fixed so that \(\alpha = 30 ^ { \circ }\).
By drawing a triangle of forces, or otherwise, calculate the tension in the string BC and the tension in the string AB .
- Show carefully, but briefly, that the box cannot be in equilibrium if \(\alpha = 60 ^ { \circ }\) and BC remains at \(60 ^ { \circ }\) to the vertical.