Answer:
T₁ = 19.39N with an angle of 52° with the horizontal.
T₂ = 15.64N with an angle of 40° with the horizontal.
Step-by-step explanation:
1)We calculate the weight of holiday decoration
W = m×g
W: holiday decoration weight in Newtons (N)
m: holiday decoration weight = 3 kg
g: acceleration due to gravity = 9.8 m/s²
W = m×g = 3 kg × 9.8 m/s² = 29.4 N
2)We apply Newton's first law to the system in equilibrium:
ΣFx = 0
T₁Cos52° - T₂Cos40°=0
T₁Cos52° = T₂Cos40°
T₁ = T₂(Cos40° / T₁Cos52°)
T₁ = 1,24×T₂ Equation (1)
ΣFy = 0
T₁Sin52° + T₂Sin40° - 29.4 = 0 Equation (2)
We replace T₁ of Equation (1) in the Equation (2)
1.24×T₂×Sin52° + T₂Sin40° - 29.4 = 0
1.88*T₂ = 29.4
T₂ = 29.4/1.88
T₂ = 15.64N
We replace T₂ = 15.64N in the Equation (1) to calculate T₁:
T₁ = 1.24×15.64N
T₁ = 19.39N