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Answer :
Final Answer:
The force acting in cable ab for equilibrium is 147 N, which corresponds to option a).
Explanation:
To determine the force acting in cable ab, let's first analyze the forces acting on the pot. The weight of the pot, denoted as W, is equal to the mass of the pot multiplied by the acceleration due to gravity. Given that the pot weighs 45 kg, we have [tex]\( W = 45 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 441 \, \text{N} \)[/tex].
Next, we'll consider the equilibrium of forces in the horizontal direction. The horizontal component of tension in cable ab, denoted as [tex]\( T_{\text{ab}} \cos\theta \)[/tex], must balance the horizontal component of the weight of the pot. Here, [tex]\( \theta \)[/tex] represents the angle between cable ab and the horizontal direction. Since the pot is directly below cable ab, [tex]\( \theta \)[/tex] is 90 degrees, and thus [tex]\( \cos\theta = 0 \)[/tex]. Therefore, the horizontal component of tension in cable ab is 0, indicating that cable ab does not contribute to the horizontal equilibrium.
Now, let's focus on the vertical equilibrium. The vertical component of tension in cable ab, denoted as [tex]\( T_{\text{ab}} \sin\theta \),[/tex] along with the vertical components of tensions in the other two cables, must balance the weight of the pot. Given that the pot is supported symmetrically by three cables, each cable carries one-third of the weight of the pot. Therefore, the vertical component of tension in cable ab is [tex]\( \frac{1}{3} \times W = \frac{1}{3} \times 441 \, \text{N} = 147 \, \text{N} \)[/tex].
Hence, the force acting in cable ab for equilibrium is 147 N. Therefore, option a) 147 N is the correct choice.
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Final answer:
In this case, the force acting in cable [tex]\( \text{ab} \)[/tex] for equilibrium is approximately 147 N
The answer is option~A
Explanation:
To determine the force acting in cable [tex]\( \text{ab} \)[/tex] for equilibrium, we can follow these steps:
1. Draw a free-body diagram of the pot:
- The weight of the pot acts downward (vertically) with a force of [tex]\( \text{Weight} = 45 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 442.95 \, \text{N} \)[/tex]
2. Analyze the forces acting on the pot:
- The tension in cable ab will support part of the weight vertically.
- The horizontal component of the tension in cable ab will counterbalance the horizontal forces.
- The vertical components of the tensions in cables ac and ad will also contribute to supporting the weight of the pot.
3. Calculate the force acting in cable [tex]\( \text{ab} \)[/tex] for equilibrium:
- Considering the equilibrium of forces in the vertical direction:
[tex]\[ T_{ab} = \frac{442.95 \, \text{N}}{3} = 147 \, \text{N} \][/tex]
Therefore, the force acting in cable [tex]\( \text{ab} \)[/tex] for equilibrium is approximately 147 N
The answer is option~A
