Question

An automobile engine has weight(w) whose magnitude is W= 3150 N. This engine is being positioned above an engine compartment. To position the engine , a worker is using a rope. Find the tension (T), in the supporting cable and the tension (T²), in the positioning rope.

Answer 1

We know that for the engine to be in equilibrium, the sum of forces in horizontal and vertical directions must be zero, so:

$$y: -W+T_1\text{ cos}10°-T_2\text{ sin}10°=0,\\ x: -T_1\text{ sin}10°+T_2\text{ cos}10°=0.$$

Two equations with two variables - easy! The solution is

$$T_1=3301.2\text{ N},\\ T_2=582.1\text{ N}.$$