R х W2 Question 9 (20 marks) (a) The figure shows a uniform plank of weight w pivoted so that it remains in equilibrium

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R х W2 Question 9 (20 marks) (a) The figure shows a uniform plank of weight w pivoted so that it remains in equilibrium when weights W1 and X2 W2 are placed on it at distances Xi and xa from the pivot as shown. R represents the normal reaction at the pivot. (i) Applying the principle of moments about the pivot, complete the expression for wixi. (ii) Write down an expression for R. (b) An experiment is carried out to find the weight of a boy. A uniform plank of wood PQ, 3.0 m long, weighing 80 N is pivoted about a point 0.5 m from P. The boy stands 0.3 m from P. A 20 N weight is placed 0.5 m from Q in order to balance the plank horizontally. Draw a diagram of the plank representing each force on it by an arrow. Indicate distances in your diagram. (ii) Calculate the weight of the boy. (iii) Determine the value of the force exerted by the pivot on the plank.