| English | Forces in equilibrium |
|---|---|
| Bahasa Melayu | Daya dalam keseimbangan |
| 中文 | 力的平衡 |
Definition
The condition in which the resultant of all forces acting on an object is zero, so it stays at rest or moves with constant velocity.
What you need to know
An object is in equilibrium when the resultant force acting on it is zero, so it remains at rest or continues moving at constant velocity. A common situation in the 4531 syllabus involves three forces keeping an object in equilibrium, such as a lamp hung from the ceiling by two strings at different angles.
Two main methods solve equilibrium problems with three forces. The first is resolving forces into horizontal and vertical components and applying the conditions ΣFₓ = 0 N and ΣF_y = 0 N, meaning the sum of horizontal components equals zero and the sum of vertical components equals zero.
The second is drawing a closed triangle of forces, where the three forces are drawn head to tail as vectors; if the object is in equilibrium, the triangle closes completely with no gap.
Both methods rely on accurate diagrams showing the direction and estimated size of each force, since an incorrect diagram usually leads to an incorrect equation and a wrong final answer, even if the arithmetic itself is correct.
Worked example
A lamp of weight 20 N hangs in equilibrium from a horizontal ceiling by two strings. String A makes an angle of 60° with the ceiling and string B makes an angle of 30° with the ceiling, on opposite sides of the lamp.
Resolving vertically, the sum of the vertical components of the tensions in the two strings must support the full weight: T_A sin 60° + T_B sin 30° = 20 N.
Resolving horizontally, the horizontal components of the two tensions must cancel each other: T_A cos 60° = T_B cos 30°.
Solving these two simultaneous equations together gives the tension in each string, for example T_A ≈ 17.3 N and T_B ≈ 10 N, both expressed correctly in newtons (N). Checking the answer by substituting both values back into the original vertical and horizontal equations confirms that the resultant force on the lamp is indeed 0 N. This checking step is good practice for any three-force equilibrium problem, since it quickly reveals an arithmetic slip or an incorrectly assigned angle before the final answer is written down.
How it is examined
In Paper 1, objective questions often ask candidates to determine which combination of three forces produces equilibrium, or to identify a correctly closed triangle of forces from a diagram. In Paper 2, structured questions typically ask candidates to state the condition for equilibrium, sketch a triangle of forces for a described system, and calculate an unknown force or tension using resolution of forces.
In Paper 3, practical tasks may involve suspending a weight with strings over pulleys at measured angles, then asking candidates to determine tensions experimentally and compare them with calculated values.
A common mistake is applying ΣFₓ = 0 N and ΣF_y = 0 N inconsistently, mixing up which angle belongs to which string, or drawing a triangle of forces with arrows that do not follow head-to-tail order, which produces an open triangle even for a genuinely balanced system. Candidates are advised to label each force clearly with its magnitude and direction before attempting either method, since an unclear diagram is one of the most common reasons for losing method marks in this topic.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)