A chandelier of mass 120.0kg is supported by two cords. The first makes an angle of 60° with the ceiling and the second supports it horizontally to the wall. Find the tension in the two cords (g=9.8ms²)
T2 = -T1*Cos60 = -0.5T1.
Eq1: T1 = -2T2.
T1*sin60 = 120.
T1 = 138.6 kg.
In Eq1, replace T1 with 138.6 and solve for T2.
let tl be tension in the tilted cord, th tension in the horizontal cord.
Horizontal:
Th=Tl*cos60
Vertical:
120g=Tl*sin60
solve for Tl in the vertical equation, then th
I don't understand the explanation on this question
To find the tension in the two cords, we need to analyze the forces acting on the chandelier and consider equilibrium.
Let's first draw a free-body diagram of the chandelier:
T₁ T₂
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| Chandelier |
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Weight (mg)
In the diagram, T₁ represents the tension in the cord making an angle of 60° with the ceiling, T₂ represents the tension in the cord supporting the chandelier horizontally, and mg represents the weight of the chandelier, where m = 120.0 kg and g = 9.8 m/s².
Now, let's break down the forces in the vertical (y) and horizontal (x) directions:
Vertical forces:
- T₁ * sin(60°): This component of tension is responsible for countering the downward force due to gravity. It is directed upward.
- mg: This is the weight of the chandelier, directed downward.
Horizontal forces:
- T₂: This tension is responsible for countering the horizontal component of the weight of the chandelier. It is directed towards the wall.
Since the chandelier is in equilibrium, the vertical forces must balance each other out, and the horizontal forces must balance each other out.
Equating the forces in the vertical direction:
T₁ * sin(60°) = mg
Solving for T₁:
T₁ = mg / sin(60°)
Substituting the values:
T₁ = (120.0 kg * 9.8 m/s²) / sin(60°)
T₁ ≈ 1371.3 N
Now, equating the forces in the horizontal direction:
T₂ = T₁ * cos(60°)
Substituting the values:
T₂ = 1371.3 N * cos(60°)
T₂ ≈ 685.65 N
Therefore, the tension in the cord making an angle of 60° with the ceiling (T₁) is approximately 1371.3 N, and the tension in the cord supporting the chandelier horizontally (T₂) is approximately 685.65 N.