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Nov 2012 p43 q4
3663
A particle P of weight 21 N is attached to one end of each of two light inextensible strings, S1 and S2, of lengths 0.52 m and 0.25 m respectively. The other end of S1 is attached to a fixed point A, and the other end of S2 is attached to a fixed point B at the same horizontal level as A. The particle P hangs in equilibrium at a point 0.2 m below the level of AB with both strings taut (see diagram). Find the tension in S1 and the tension in S2.
Solution
To solve for the tensions in the strings, we can use the equilibrium conditions for the forces acting on the particle P. The forces involved are the tensions in the strings S1 and S2, and the weight of the particle.
Let the tension in S1 be T1 and in S2 be T2. The weight of the particle is 21 N acting vertically downward.
Using trigonometry, we can resolve the tensions into horizontal and vertical components. The horizontal components must balance each other, and the sum of the vertical components must balance the weight of the particle.
From the diagram, we can determine the angles using the given lengths:
