To solve this problem, we need to analyze the forces acting on each block and set up equilibrium equations.
First, let's consider Block A. The weight of Block A is W, which acts vertically downward. The tension in the cord T1 acts horizontally to the right and is responsible for preventing Block A from accelerating horizontally. There is no horizontal force acting on Block A since it is in equilibrium. The vertical forces acting on Block A are the tension in the cord T2 and the normal force N from the table. Since Block A is not accelerating vertically, the vertical forces are balanced, so we have the following equation:
T2 + N = W ...(1)
Now let's consider Block B. The weight of Block B is 0.25W, which acts vertically downward. The tension in the cord T1 acts horizontally to the right and is responsible for preventing Block B from accelerating horizontally. The vertical forces acting on Block B are the tension in the cord connecting it to Block A (which is T2) and the normal force N from the table. Since Block B is not accelerating vertically, the vertical forces are balanced, so we have the following equation:
T2 + N = 0.25W ...(2)
Finally, let's consider Block C. The weight of Block C is W, which acts vertically downward. The tension in the cord T1 acts horizontally to the right and is responsible for preventing Block C from accelerating horizontally. The vertical forces acting on Block C are the tension in the cord connecting it to Block B (which is T2) and the normal force N from the table. Since Block C is not accelerating vertically, the vertical forces are balanced, so we have the following equation:
T2 + N = W ...(3)
From equations (1) and (3), we can see that N = 0.
Substituting N = 0 into equations (1), (2), and (3), we have:
T2 = W ...(4)
T2 = 0.25W ...(5)
T2 = W ...(6)
From equations (4), (5), and (6), we can conclude that T2 = W = 0.25W. Therefore, W = 0.25W.
Since W is the weight of Block A and C, and C is W, we have:
W = 0.25W + W = 1.25W
Therefore, W = 0.
This means that the weights of the blocks A and C are zero, which implies that the blocks A and C are not in equilibrium. Therefore, it is not possible to determine the angle 0 for equilibrium with the given information.
Three blocks are supported using the cords and two pulleys as in Fig. 1. Given that weights of A, B and C are W, 0.25W and W, respectively, determine the angle 0 for equilibrium.
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