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If three forces, acting at a point, be in equilibrium then each force is proportional to the sine of the angle between the other two. This theorem is called
- a)Law of triangle of forces
- b)Law of parallelogram of forces
- c)Lami's theorem
- d)Trigonometrical theorem
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If three forces, acting at a point, be in equilibrium then each force ...
The Concept of Lami's Theorem
Lami's Theorem is a fundamental principle in mechanics that applies to three forces acting at a single point. This theorem states that if three forces are in equilibrium, then each force is proportional to the sine of the angle between the other two forces.
Understanding the Theorem
- The theorem is mathematically represented as:
\[
\frac{F_1}{\sin A} = \frac{F_2}{\sin B} = \frac{F_3}{\sin C}
\]
where:
- \(F_1, F_2, F_3\) are the magnitudes of the three forces.
- \(A, B, C\) are the angles opposite to the respective forces.
Conditions for Equilibrium
- For Lami's Theorem to hold true:
- The forces must be concurrent, meaning they all act at the same point.
- The forces must be in equilibrium, which means the net force acting on the point is zero.
Applications of Lami's Theorem
- Lami's Theorem is widely used in mechanical engineering to analyze structures and systems where multiple forces act at a point.
- It simplifies the calculations required to determine unknown forces and their angles.
Conclusion
- Option 'C', Lami's Theorem, provides a practical method for solving problems involving three forces in equilibrium.
- This theorem is essential for engineers and physicists when dealing with statics and dynamics in mechanical systems.
Lami's Theorem is a fundamental principle in mechanics that applies to three forces acting at a single point. This theorem states that if three forces are in equilibrium, then each force is proportional to the sine of the angle between the other two forces.
Understanding the Theorem
- The theorem is mathematically represented as:
\[
\frac{F_1}{\sin A} = \frac{F_2}{\sin B} = \frac{F_3}{\sin C}
\]
where:
- \(F_1, F_2, F_3\) are the magnitudes of the three forces.
- \(A, B, C\) are the angles opposite to the respective forces.
Conditions for Equilibrium
- For Lami's Theorem to hold true:
- The forces must be concurrent, meaning they all act at the same point.
- The forces must be in equilibrium, which means the net force acting on the point is zero.
Applications of Lami's Theorem
- Lami's Theorem is widely used in mechanical engineering to analyze structures and systems where multiple forces act at a point.
- It simplifies the calculations required to determine unknown forces and their angles.
Conclusion
- Option 'C', Lami's Theorem, provides a practical method for solving problems involving three forces in equilibrium.
- This theorem is essential for engineers and physicists when dealing with statics and dynamics in mechanical systems.
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Community Answer
If three forces, acting at a point, be in equilibrium then each force ...
Lami's theorem:
It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.
Therefore,
Important Points
Triangle Law of Forces: It states that if two forces acting simultaneously on a particle, be represented in magnitude and direction by the two sides of a triangle, taken in order; their results may be represented in magnitude and direction by the third side of the triangle, taken in the opposite order.”
Law of the parallelogram of force:
It states that if two forces, acting at the point of a body, be represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram contained in between the two adjacent forces.
It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.
Therefore,
Important Points
Triangle Law of Forces: It states that if two forces acting simultaneously on a particle, be represented in magnitude and direction by the two sides of a triangle, taken in order; their results may be represented in magnitude and direction by the third side of the triangle, taken in the opposite order.”
Law of the parallelogram of force:
It states that if two forces, acting at the point of a body, be represented in magnitude and direction by the two adjacent sides of a parallelogram, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram contained in between the two adjacent forces.
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If three forces, acting at a point, be in equilibrium then each force is proportional to the sine of the angle between the other two. This theorem is calleda)Law of triangle of forcesb)Law of parallelogram of forcesc)Lamis theoremd)Trigonometrical theoremCorrect answer is option 'C'. Can you explain this answer?
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