| English | Resolution of forces |
|---|---|
| Bahasa Melayu | Peleraian daya |
| 中文 | 力的分解 |
Definition
The process of splitting a single force into two components, usually perpendicular to each other.
What you need to know
Resolving a force means splitting one force into two components that act at right angles to each other, usually a horizontal component and a vertical component. This is useful because forces acting at an angle are harder to combine directly than forces acting along the same straight lines.
For a force F acting at angle θ to the horizontal, the horizontal component is Fₓ = F cos θ and the vertical component is F_y = F sin θ, with F, Fₓ and F_y all measured in newtons (N) and θ measured in degrees (°). These two formulas must be memorised, since the 4531 examination format does not provide a formula sheet.
Once a force is resolved into its horizontal and vertical components, each component can be combined separately with other horizontal or vertical forces acting on the same object. This is the basis for solving problems involving inclined forces, ramps, and objects pulled at an angle by a string or rope.
Worked example
A rope pulls a box across a floor with a force of F = 50 N, directed at θ = 30° above the horizontal. To resolve this force, calculate its horizontal and vertical components separately using the resolution formulas.
Horizontal component, Fₓ = F cos θ = 50 N × cos 30° = 50 N × 0.866 = 43.3 N.
Vertical component, F_y = F sin θ = 50 N × sin 30° = 50 N × 0.5 = 25 N.
The horizontal component of 43.3 N is responsible for moving the box forward along the floor, while the vertical component of 25 N acts upward and slightly reduces the normal force between the box and the floor. Both components are expressed in newtons (N), the same unit as the original force, and together they represent the same overall pulling effect as the single 50 N force acting at 30°.
How it is examined
In Paper 1, objective questions often ask candidates to calculate a horizontal or vertical component of a given force at a stated angle, or to identify the correct triangle diagram for resolving a force. In Paper 2, structured questions typically ask candidates to state the formulas Fₓ = F cos θ and F_y = F sin θ, sketch the component triangle, and calculate both components for a force described in a scenario such as a ladder or an inclined rope.
In Paper 3, practical tasks may involve using a force board or spring balances to verify that resolved components combine to reproduce the original force, requiring candidates to determine readings and compare them with calculated values.
A common mistake is confusing which trigonometric ratio applies to which component, or measuring the angle from the vertical instead of the horizontal without adjusting the formula accordingly. Candidates should always sketch the angle clearly on the diagram before substituting values, since a poorly labelled diagram often leads directly to an incorrectly resolved component even when the calculation method itself is sound.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)