A car is made to move by applying resultant force R = 2000 N along the x-axis. This resultant is developed due to two pulling forces \(F_1\) and \(F_2\) on two ropes as shown in figure. Determine the tension in individual ropes.[Figure: car with fron…

Method: \(F_1\), \(F_2\) and R form a force triangle (triangle law); apply the sine rule. The angle opposite R = 180° − 35° − 25° = 120°, so \(\sin 120^\circ = \sin 60^\circ\).

\(\dfrac{F_1}{\sin25^\circ} = \dfrac{F_2}{\sin35^\circ} = \dfrac{R}{\sin(180^\circ - 60^\circ)} = \dfrac{2000}{0.8660} = 2309.4\)

\(F_1 = 2309.4 \times 0.4226 = 976.0\) N, \(F_2 = 2309.4 \times 0.5736 = 1324.6\) N

Check: \(\sum F_y = 976.0\sin35^\circ - 1324.6\sin25^\circ = 559.8 - 559.8 = 0\); \(\sum F_x = 976.0\cos35^\circ + 1324.6\cos25^\circ = 799.5 + 1200.5 = 2000\) N ✔

Answer: \(F_1 = 976.0\) N, \(F_2 = 1324.6\) N.