Question

Q2) Show that the forces in cable AB and BC are given by: f(c) = w * cos(θ(a)) / sin(θ(a) +θ(c)) and f(a) = w * cos(θ(c)) / sin(θ(a) +θ(c)).

Answer 1

Forces in cables AB and BC in static equilibrium can be calculated using trigonometry, where the tension in each cable is given by specific formulas involving the weight and the angles of the cables with respect to the vertical.

Step-by-step explanation:

The question requires an application of physics concepts to determine the forces in cables AB and BC, denoted as f(c) and f(a) respectively. The expressions provided suggest a problem involving static equilibrium, where the weight w is being supported by two cables at different angles θ(a) and θ(c). Using trigonometry and the principles of equilibrium, it can be shown that the tensions in the cables are given by the formulas:

f(c) = w * cos(θ(a)) / sin(θ(a) +θ(c))
and
f(a) = w * cos(θ(c)) / sin(θ(a) +θ(c))

To derive these expressions, one must apply the components of the forces along the direction of the cables and set them against the weight, thereby ensuring that the sum of all forces in any direction equals zero, which is a condition for static equilibrium. The usage of sine and cosine in these formulas accounts for the directional components of the forces contributed by each cable.