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The stiff-leg derrick used on ships is supported by a ball-and-socket joint at D and two cables BA and BC. The cables are attached to a smooth collar ring at B, which allows rotation of the derrick about the Z axis. The derrick supports a crate having a mass of 140 kg.

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Final answer:

The question involves applying principles of static equilibrium and mechanics, specifically concerning forces and tensions in structures such as cranes, bridges, and drilling equipment in physics.

Step-by-step explanation:

The student's question pertains to the analysis of forces and tensions in various static structures and systems, such as cranes, bridges, ships, and drilling equipment. These scenarios involve applying principles of static equilibrium, where the sum of forces and torques acting on a body are zero. To solve these problems, one needs to understand and apply concepts such as tension, torque, center of mass, moments, and forces. These are covered in physics, specifically in the subfield of mechanics, which deals with the motion of bodies under the action of forces. For example, to calculate the tension in the cable and the force at the axle for a crane boom, or to determine the stretch of a drill pipe, one uses Newton's laws of motion and the relations for elasticity.

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