Final answer:
The tensions T1 and T2 in two supporting wires are related to the angles at which the wires are positioned and the force exerted on them. Equal angles result in equal tensions while more horizontal wires bear greater tension. Equilibrium conditions can simplify the relationships into equations with fewer unknowns.
Step-by-step explanation:
The tensions T1 and T2 in two wires are related to the angles at which the wires are positioned and the force that is applied. In scenarios where a force, such as the weight of a tightrope walker, is distributed between two cables at different angles, the equilibrium conditions of the system can be used to find a relationship between the two tensions. If the angles on either side are the same, then the tensions will also be equal. However, if one wire is shorter, and therefore more horizontal than the other, its tension will be greater. This is due to the fact that a more horizontal wire has a greater component of tension counteracting the vertical force exerted by the weight. As a result, in a non-symmetrical setup, the tension in the shorter (or more horizontal) wire will be higher than in the longer (or less horizontal) wire.
An example is provided where the equilibrium equation informs us that the tension T1 in a 5.0 cm string is twice the tension T2 in a 10.0 cm string. This implies that the shorter string has more tension and is more likely to snap. When we substitute the expression for T2 in terms of T1, we can simplify the system to one equation with one unknown, allowing us to solve for the tension in the shorter string or the mass suspended by the system.