Final answer:
To determine the tensions in cables AB, AC, and AD, we can use Newton's second law of motion and analyze the forces acting on the object. The tension in cable AB is equal to the weight of the object. The tensions in cables AC and AD can be determined using trigonometry.
Step-by-step explanation:
Determine the tensions in cables AB, AC, and AD.
In order to determine the tensions in the cables, we first need to analyze the forces acting on the object. We can use Newton's second law of motion, which states that the sum of all forces acting on an object is equal to the mass of the object multiplied by its acceleration. Since the object is not accelerating, the sum of the forces must be zero.
For cable AB, the tension is equal to the vertical component of the weight of the object. Since the object is in equilibrium, the tension in cable AB must be equal to the weight of the object.
For cable AC, we can break down the tension into its horizontal and vertical components. The vertical component is equal to the weight of the object, just like in cable AB. The horizontal component can be determined using trigonometry, as it is equal to the horizontal force required to keep the object in equilibrium.
For cable AD, we can again break down the tension into its horizontal and vertical components. The vertical component is equal to the weight of the object. The horizontal component can be determined using trigonometry, similar to cable AC.
Overall, the tensions in cables AB, AC, and AD are equal to the weight of the object in the vertical direction, and can be determined using trigonometry in the horizontal direction.