Byrd Pope
05/31/2023 · Primary School

Exercise 4: A light string ABCDE whose extremity A is fixed, has weights \( \mathrm{W}_{1} \) and \( \mathrm{W}_{2} \) attached to it at B and C . it passes round a small smooth peg at D carrying a weight of 300 N at the free end E as shown. If in the equilibrium position, BC is horizontal and AB and CD make \( 150^{\circ} \) and \( 120^{\circ} \) with BC . Find (a) tensions \( \mathrm{AB}, \mathrm{BC} \) and CD for the string and (b) magnitudes of \( \mathrm{W}_{1} \) and \( \mathrm{W}_{2} \)

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(a) The tensions in the string are \( T_{AB} = 150 \, \text{N} \), \( T_{BC} = 150 \, \text{N} \), and \( T_{CD} = 150\sqrt{3} \approx 259.81 \, \text{N} \). (b) The magnitudes of the weights are \( W_1 = 150 \, \text{N} \) and \( W_2 \approx 259.81 \, \text{N} \).

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