Formula of tension in string

Consider a hanging pot rack. There are two ropes holding up a 30-kg rack, each at an angle of 15 degrees from the corners of the rack.

To find the tension in either rope, the ​net force​ in both the x- and y-directions must be balanced.

Start with the free-body diagram for the pot rack.

Of the three forces on the rack, the force of gravity is known, and it must be balanced equally in the vertical direction by both of the vertical components of the forces of tension.

\(F_g=mg=F_{T1,y}+F_{T2,y}\)

and because ​_F_T1,y= F_T2,y_​ :

\(30\times 9.8 = 2 F_{T1,y}\implies F_{T1,y}=147\text{ N}\)

In other words, each rope exerts a force of 147 N upwards on the hanging pot rack.

To get from here to the total force of tension in each rope, use trigonometry.

The trigonometric relationship of sine relates the y-component, the angle and the unknown diagonal force of tension along the rope on either side.

Solving for the tension on the left:

\(\sin{15}=\frac{147}{F_{T1}}\implies F_{T1}=\frac{147}

how to calculate tension in physics grade 11

how to determine tension in physics