Answer to Question #122808 in Physics for Susan Williams

Question

A body of weight 150 N is supported by a thin cord attached to a point in the ceiling. Another cord is attached to the weight and pulled horizontally until the supporting cord makes an angle of 300 with the vertical. Draw the diagram of the arrangement and calculate the tension in each string

Answer 1

According to Newton's second law, forces in vertical and horizontal directions are in equilibrium because the mass does not move. Assume that positive y is upward and positive x is to the right:

$$Ox: T_1-T_2\text{ sin}30°=0,\\ Oy: T_2\text{ cos}30°-mg=0.$$

The solution is

$$T_1=86.60\text{ N},\\T_2=173.2\text{ N}.$$