Practice Problems on Lami’s Theorem

Problem 1: Consider a truss where three forces F₁, F₂, F₃ are applied concurrently at a joint, forming angles α=30°, β=60°, and γ=90° with the horizontal, respectively. The magnitudes of forces are given as follows: F₁ = 500N, F₂ = 600N, F₃ = 800N . Use Lami’s Theorem to find the magnitudes of these forces.

Problem 2: Imagine a bracket subjected to three forces F₁ = 100N, F₂ = 150N and F₃ = 200N, with α=45°, β=45°, and γ=90°. Use Lami’s Theorem to find the tension in each force.

Problem 3: A uniform beam is supported by two cables attached to its ends. If the angles between the cables and the beam are known, determine the tensions in the cables to keep the beam in equilibrium.

Problem 4: A triangular plate is subjected to three forces at its vertices. If the forces are concurrent and in equilibrium, find the magnitude and direction of each force.

Problem 5: Three forces of magnitudes 10 N, 15 N, and 20 N are applied to a point. If the angles between the forces are 30 degrees and 150 degrees, find the resultant force.

Lami’s Theorem, also known as Lami’s Law, is a principle in statics and mechanics of materials that relates the forces acting on a body in static equilibrium. It is named after the Italian mathematician and physicist Bernard Lami. Lami’s Theorem is typically applied to a body or structure subjected to concurrent forces. Imagine three friends pulling a string simultaneously from different directions, considering the plane is coplanar. Through the help of Lami’s theorem, one can easily find the forces each friend is exerting.

Further in this article, we will learn about the statement, formula, step-by-step proof, essential assumptions, and practical applications of Lami’s Theorem. Additionally, there will be a few practice problems for better understanding and clarification.