Answer :
Answer:
T = 104.2 N
Explanation:
For this exercise we must define a coordinate system, the x axis is horizontal and the y axis is vertical, let's write the equilibrium equations on each axis
X axis
T₁ₓ-T₂ₓ = 0
T₁ₓ = T₂ₓ (1)
y axis
[tex]T_{1y}[/tex] + T_{2y} - W = 0
T_{1y} + T_{21y} = W (2)
Let's use trigonometry to find the decomposition of the stresses, they indicate that the angle between the two forces is 140º, but each force has an angle of 70º
cos 70 = T₁ₓ / T₁
T₁ₓ = T₁ cos 70
sin 70 = [tex]T_{1y}[/tex] / T₁
T_{1y} = T₁ sin 70
for tension 2 we have a similar equation
T₂ₓ = T₂ cos 70
T_{2y} = T₂ sin 70
From equation 1
T₁ cos 70 = T₂ cos 70
T₁ = T₂
therefore the two children apply the same force
From equation 2
T sin 70 + T sin 70 = W
2 T sin 70 = W
T = W / 2sin 70
T = 196 / (2 sin 70)
T = 104.2 N
the two children have the same strength