Question

A crazed armadillo with a mass of 60kg stands at the center of a rope which was initially strung horizontally between two poles 50m apart. Its weight causes the rope to sag 1.20m. What is the tension in the rope

Solution:

2Tsin(angle) - mg = 0

Tan-1() = 1.2/25 = 2.75°

2Tsin(2.75°) - mg = 0

T = mg/2Sin(2.75°)
T = 6200 N

My questions is regarding the first part of the solution and how would I know I have to set 2Tsin(angle) - mg equal to 0.
Please help me understand this problem.

Answer 1

the rope is evidently mass less.

total force up = total force down because nothing is accelerating.

Total force down = m g

Tension in rope is T on each side of mass
horizontal component of T = T cos angle above horizontal right and left

vertical component of T = T sin angle, twice because from both sides of mass

so
total up force = 2 T sin angle
so 2 T sin angle = m g

to get angle simple geometry
tan angle = 1.2/(.5*50)