Determine the tension in the cable and the horizontal and vertical components of the reaction at pin A. The pulley at D is frictionless and the cylinder weighs 84 lb. (Figure 1)

A. Determine the tension in the cable.

B. Determine the horizontal and vertical components of the reaction at pin A. Assume that the positive x and y axes are directed to the right and upward, respectively.

In order to determine the tension in the cable, we need to consider the equilibrium of forces acting on the cylinder. Since the pulley at point D is frictionless, we can assume that there is no horizontal force acting on the cylinder. Therefore, the tension in the cable is equal to the weight of the cylinder, which is given as 84 lb.

Now, let's analyze the components of reaction at pin A. Since the cylinder is in equilibrium, the vertical components of the forces acting on it must cancel out. Thus, the vertical component of reaction at pin A is equal to the weight of the cylinder, which is 84 lb.

However, since there are no horizontal forces acting on the cylinder, the horizontal component of reaction at pin A is zero. This means that there is no horizontal force exerted by the cylinder on pin A.

To summarize, the tension in the cable is 84 lb, while the horizontal component of reaction at pin A is 0 lb, and the vertical component of reaction at pin A is 84 lb.

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