When you see a picture hanging on a wall or a bridge standing firm, you are looking at objects in equilibrium. This lesson explains the conditions that must be met for an object to be balanced and stable.

1. Short Notes: Core Concepts

A. What is Equilibrium?

• Definition: An object is in equilibrium when the forces acting on it are perfectly balanced. This means:

  1. The resultant force is zero.

  2. The resultant moment is zero.

• Effect: The object will not accelerate. It will either remain stationary (at rest) or move at a constant velocity. For O/L, we usually focus on stationary objects.

B. Equilibrium under TWO Forces

• This is the simplest case. For an object to be in equilibrium under two forces, the forces must be:

  1. Equal in magnitude.

  2. Opposite in direction.

  3. Collinear (acting along the same straight line).

• Example: A book (weight = 5 N) resting on a table. The downward force of its weight (5 N) is perfectly balanced by the upward reaction force from the table (5 N).

C. Equilibrium under THREE Coplanar Parallel Forces

• "Coplanar" means the forces are all in the same flat plane. "Parallel" means their lines of action never cross.

• Conditions:

  • One force must act in the opposite direction to the other two.

  • The magnitude of the single force must equal the sum of the magnitudes of the other two forces.

• Example: A child (weight = 300 N) sitting on a swing. The downward force (weight) is balanced by the two upward forces (tensions) in the ropes.

  • Downward Force = Sum of Upward Forces

  • 300 N = Tension 1 + Tension 2

D. Equilibrium under THREE Non-Parallel Forces

• This applies to situations like a picture frame hanging by two strings.

• Conditions:

  1. The three forces must be coplanar (in the same plane).

  2. The lines of action of the three forces must meet at a single point (they must be "concurrent").

  3. The resultant of any two of the forces must be equal in magnitude and opposite in direction to the third force. (This is often visualized with a "triangle of forces," but you just need to know the principle).

2. Tips & Tricks for the Exam

• "Equilibrium" = "Balanced": Whenever you see the word equilibrium, immediately think "all forces cancel out."

• Think Up vs. Down, Left vs. Right: For parallel forces, the rule is simple: Total Upward Forces = Total Downward Forces.

• Draw the Forces: Always sketch the object and draw arrows for all the forces acting on it (weight, tension, reaction forces). This helps you identify which forces are balancing each other.

3. Important Points & Common Exam Questions

• Identify the Equilibrium Type: You might be shown a picture (e.g., a person on a ladder against a wall, a hanging sign) and asked to identify the forces keeping it in equilibrium.

• Simple Calculations with Parallel Forces:

  • "A light rod is supported by two strings. A weight of 50 N hangs from the rod. What is the total upward tension in the two strings if the rod is in equilibrium?"

  • Answer: For equilibrium, Total Upward Force = Total Downward Force. Therefore, the total tension is 50 N.

• Conceptual Questions:

  • "Why does a book on a table not fall down, even though gravity is pulling it?"

  • Answer: The book is in equilibrium. The downward force of its weight is balanced by an equal and opposite upward reaction force from the table.