Answer:
42 N
Explanation:
Draw a free body diagram of the sign. There are three forces: two tension forces at 45° from the horizontal, and weight force mg straight down.
The vertical component of the tension forces can be found with trigonometry:
sine = opposite / hypotenuse
sin 45° = Tᵧ / T
Tᵧ = T sin 45°
Sum of forces in the y direction:
∑F = ma
2Tᵧ − mg = 0
Tᵧ = mg/2
T sin 45° = mg/2
T = mg / (2 sin 45°)
T = mg / √2
Given that m = 6 kg:
T = (6 kg) (9.8 m/s²) / √2
T ≈ 42 N
