6 A shelf consists of a horizontal uniform plank AB of length 0.8 m and mass 5 kg with light inextensible vertical strings attached at each end. A stack of bricks each of mass 2.3 kg is placed on the plank as shown in the diagram.
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- Explain the meaning of each of the following modelling assumptions.
- The stack of bricks is modelled as a particle.
- The plank is modelled as uniform.
Either of the strings will break if the tension exceeds 75 N. - Find the greatest number of bricks that can be placed at the centre of the plank without breaking the strings.
- Find an expression for the moment about A of the weight of a stack of \(n\) bricks when the stack is at a distance of \(x \mathrm {~m}\) from A . State the units for your answer.
- Calculate the greatest distance from A that the largest stack of bricks can be placed without a string breaking.