Equilibrium of Coplanar Forces
Translational equilibrium (ΣF = 0), Triangle of Forces, Polygon of Forces, Lami’s Theorem, and verification using Gravesande’s force board.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Apply equilibrium conditions (ΣF_x = 0, ΣF_y = 0) and Lami’s Theorem to systems of concurrent coplanar forces.
- Understand the experimental protocol and parallax elimination techniques on Gravesande’s force board.
Core Theory & Concepts
A particle is in static equilibrium when the resultant vector sum of all external forces acting upon it is zero. For three concurrent forces, the vector sum closes into a planar triangle, leading directly to the Triangle Law and Lami’s Theorem.
Lami’s Theorem
If three coplanar concurrent forces act on a body in equilibrium, each force magnitude is proportional to the sine of the angle between the other two forces: P / sin α = Q / sin β = R / sin γ.
Gravesande’s Force Board Verification
Forces P and Q suspended over frictionless pulleys balance counterweight R at knot O: resultant F_diag = √(P² + Q² + 2PQ cos θ) ≈ R.
Common Misconceptions
Assuming three forces of magnitudes 10 N, 20 N, and 35 N can maintain static equilibrium.
Syllabus Topic Outline
- 1Condition of translational equilibrium ΣF = 0
- 2Triangle of Forces: closure of tip-to-tail vector polygon
- 3Lami’s Theorem for three coplanar concurrent forces
- 4Gravesande’s force board experimental procedure and error sources