A light pole is held in place by three tensioned cables forming angles of 60°, 75°, and 45° with each other at a common point. Assuming equilibrium, which theorem helps to determine the tensions in the cables?

Explanation:

Lami's theorem is used to determine the tensions in the cables when three forces are acting at a common point and are in equilibrium. The theorem states that if three forces are in equilibrium and act on a point, the magnitude of the forces is related to the sine of the angle between them.​

Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.

Then from Lami's theorem,

\(\frac{{{F_A}}}{{sin\alpha }} = \frac{{{F_B}}}{{sin\beta }} = \frac{{{F_C}}}{{sin\gamma }}\)

Additional Information

1. Varignon's theorem: Deals with the moment of forces about a point, not directly applicable here for calculating tensions in cables.

2. Parallel axis theorem: Used for calculating moments of inertia, not relevant to determining tensions in cables.

3. Newton's second law: While it governs the motion of objects, it isn't directly used in this scenario of static equilibrium where Lami's theorem is more applicable.