Final answer:
The question involves calculating the tension in cables under different forces, which is a physics problem generally solved by using Newton's laws of motion and equilibrium. It requires understanding the mass of the system, the acceleration due to gravity, and any other acceleration impacting the system.
Step-by-step explanation:
The question asks about the tension in cables when subjected to different forces and conditions. For instance, calculating the tension in an elevator cable as it starts from rest and accelerates its load, or determining the tension in a crane's cable when lifting a heavy load. To answer these types of questions, one would typically use principles of classical mechanics, specifically those found in Newton's laws of motion and equilibrium conditions.
In the case of the elevator, the tension in the elevator cable is found by considering the mass of the elevator and the load, the acceleration due to gravity, and any additional acceleration the elevator experiences as it moves upward. When calculating tension during acceleration, Newton's second law F = ma is applied, where 'm' is the mass of the system and 'a' is the total acceleration. The tension is the sum of the force needed to overcome gravity (mg) and the force needed to accelerate the mass (ma).
Similarly, for the cranes' cable and the gymnast climbing the rope, you need to consider the mass of the objects being lifted and the gravitational force, along with the additional forces acting upon the system. In each scenario, the aim is to find the total force exerted by the cable which is equal to the tension.