Answer to Question #160304 in Physics for Nana

Question

A a body of mass of 65 kg is supported by two strings one of the strings is inclined at an angle of 30° and the other 40 degrees to The downward vertical find the tension in each string if the system is in equilibrium

Answer 1

If the strings are inclined 30 and 40° to the horizontal with T₁ at 30° and T₂ at 40°, the equilibrium would mathematically look like this (by each axis):

$$x: -T_1\text{ cos}30°+T_2\text{ cos}40°=0,\\ y: T_1\text{ sin}30°+T_2\text{ sin}40°-mg=0.$$

So, we have a system of two equations with two undefined forces. Find them:

$$T_1=519\text{ N},\\ T_2=587\text{ N}.$$