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Solved Problems on Lami’s Theorem for IIT JEE

Limitation of Lami’s Theorem

Practice Problems on Lami’s Theorem

Problem 1. Consider a cable-stayed bridge where three cables converge at a single point, forming angles α=60°, β=90°, and γ=30° with the horizontal. If the tension in one cable is 800 N, use Lami’s Theorem to find the tensions in the other two cables.

Solution:

Applying Lami’s Theorem:

Solving for T2 and T3, we get

T2 = 800N × ((√3)⁄2) ≈ 692.82N

T3 = 800N × (1 ⁄2) ≈ 400N

Problem 2: In a mechanical linkage system, three forces F1 =200N, F2 = 300N and F3 = 400N act concurrently at a joint. If the angles between these forces are α=45°, β=60°, and γ=75°, use Lami’s Theorem to find the resultant force at the joint.

Solution:

Applying Lami’s Theorem:

Solving for the resultant force:

Resultant force ≈ 141.42+259.81+400 ≈ 801.23N

Problem 3: A sailing yacht experiences three wind forces F1 = 500N, F2 = 600N and F3 = 800N act concurrently at angles α=30°, β=45°, and γ=60°, with the sail. Determine the total force and its direction, considering Lami’s Theorem.

Solution:

Applying Lami’s Theorem:

Total force= 500 × 2 + 600 × (√2)⁄2 + 800 × (√3)⁄2 ≈ 2298.45N

To find the direction, calculate the angle θ opposite to the resultant force

⇒ θ ≈ 52.6°

Hence, the total force acting is approximately 52.6° with the horizontal.

Lami’s Theorem

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.

Table of Content

  • What is Lami’s Theorem?
  • Assumption in Lami’s Theorem
  • Application of Lami’s Theorem
  • Limitation of Lami’s Theorem

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What is Lami’s Theorem?

Lami’s Theorem, named after the 18th-century Armenian-French mathematician Gabriel Lami; is a principle in static and structural engineering. Lami’s Theorem verifies the equilibrium of the system under concurrent forces....

Assumption in Lami’s Theorem

Certain assumptions need to be followed when using Lami’s Theorem and the assumptions are:...

Application of Lami’s Theorem

Lami’s Theorem can analyze concurrent forces in equilibrium, and its practical applications involve structural engineering and physics. Here are some practical applications:...

Limitation of Lami’s Theorem

There are some limitation of Lami’s Theorem, these are listed as follows:...

Solved Problems on Lami’s Theorem for IIT JEE

Problem 1. Consider a cable-stayed bridge where three cables converge at a single point, forming angles α=60°, β=90°, and γ=30° with the horizontal. If the tension in one cable is 800 N, use Lami’s Theorem to find the tensions in the other two cables....

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....

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Limitation of Lami’s Theorem

Practice Problems on Lami’s Theorem