Final answer:
The rope intended to prevent a worker from falling is known as a lifeline. By applying conservation of energy and knowing specific properties of the rope, we can determine how much the rope would stretch during a climber's fall of 2.00 meters before it runs out of slack.
Step-by-step explanation:
The rope intended to prevent a worker from falling is commonly referred to as a lifeline. When considering the scenario where a climber experiences a free-fall of 2.00 meters before the lifeline runs out of slack, we can use the principle of conservation of energy to determine how much the rope would stretch to break the climber's fall.
According to conservation of energy, the total mechanical energy of the climber is conserved if we neglect air resistance and assume the rope doesn't absorb any energy through internal friction. This means that the potential energy (mgh) at the beginning of the fall will be equal to the kinetic energy (0.5mv^2) just before the rope starts to stretch, plus the energy stored in the stretched rope, which is potential energy again once the climber is momentarily at rest at the lowest point of the swing.
To calculate the amount of stretch in the rope, one would need the specifics of the rope's material properties, such as its spring constant (k). However, the conservation of energy can be expressed as mgh = 0.5mv^2 + 0.5kx^2, where x is the stretch. By knowing the mass of the climber (m), the height of the fall (h), and the spring constant (k), we can solve for x to find the stretch.