Theory question 117
StaticsA body of mass 20kg is suspended at point A by two inextensible strings to points X and Y, where |AX| = 1.7m, |AY| = 2.1m and |XY| = 2.9m. If the body remains in equilibrium, calculate, correct to three significant figures, the tension in each string. [Take g = 10ms−2]
Show the model answer
Model answer
Assume X and Y are at the same level. Weight = 200 N
Cosine rule in triangle AXY: angle X = cos⁻¹[(1.7² + 2.9² − 2.1²)/(2 × 1.7 × 2.9)] ≈ 45.67°; angle Y ≈ 35.39°; angle A ≈ 98.94°
Horizontally: TX cos 45.67° = TY cos 35.39°
Vertically: TX sin 45.67° + TY sin 35.39° = 200
TX = 200 cos 35.39°/sin 81.06° ≈ 165 N (string AX)
TY = 200 cos 45.67°/sin 81.06° ≈ 141 N (string AY)
Explanation
Find the angles of the triangle with the cosine rule, then resolve forces horizontally and vertically.