A light string has its ends tied to two walls separated by a distance equal to five-eighths the length of the string. A 53 kg mass is suspended from the center of the string, applying a tension in the string.

Question

What is the tension in the two strings of length L/2 tied to the wall? The acceleration of gravity is 9.8 m/s^2.
Answer in units of N.

Answer 1

Let L be the total string length.

Use geometry/trig to determine the angle that the string makes with the horizontal, on both sides. That angle is
A = cos^-1 (5L/16)/(L/2)
= cos^-1(5/8) = 51.32 degrees

Then apply a static force balance. Both strings have the same tension force T because of symmetry.

2 T sin 51.32 = M g

Solve for T