Answer :

Final answer:

The question explores the safety and physics of rock climbers using multiple anchors connected by a carabiner. The angle between the anchors should be kept less than 90 degrees to minimize stress and prevent anchor failure. As the angle approaches 180 degrees, the stresses increase, making two anchors less safe than one.

Explanation:

The question deals with the concept of rock-climbing anchors and the physics involved in the distribution of forces when using multiple anchors. In rock climbing or mountaineering, it is common practice to use a climbing harness and tie in to multiple anchors to distribute load and ensure redundancy.

Anchors such as pitons or snow anchors are placed and a carabiner is used to connect the climber's rope to these anchors. A climber hanging from two anchors will form a symmetrical "Y" at an angle ϴ, with the advice being to keep ϴ less than 90° to minimize stress on the anchors.

When ϴ is increased, the stress on each anchor can become much greater than the actual load (L), making two anchors potentially less safe than one. For instance, if ϴ approaches 180°, essentially forming a straight line, immense forces are placed on the anchors, increasing the likelihood of anchor failure.

The safest setup is to ensure that ϴ is kept as small as possible, which also keeps the force on each anchor (S) closer to the actual load on the system. If S exceeds L, there is an increased chance of anchor failure compared to using a single anchor. Therefore, it is crucial to understand the angle and forces involved for the safety of the climbers.

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