Not given in the exam, recall it.
What it is for
Horizontal component of a force is used in Force and Motion II (SPM Physics Form 5). Keep the SI units in every line of working. Force and Motion II
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| Fₓ | horizontal component of force | N |
| F | force | N |
| θ | angle to the horizontal | ° |
Rearrangements
F = Fₓ / cos θcos θ = Fₓ / F
Worked example
Common trap
Understanding the horizontal component of a force
The formula Fₓ = F cos θ resolves a force into its horizontal part. Fₓ is the horizontal component, measured in newtons (N). F is the full force, also in newtons. θ is the angle the force makes with the horizontal, in degrees (°).
Cosine appears because the horizontal side is adjacent to the angle. As θ grows, cos θ shrinks, so less of the force acts horizontally, a force pointing almost straight up has a tiny horizontal component.
Rearrange when needed: F = Fₓ / cos θ recovers the full force from its horizontal part, and cos θ = Fₓ / F gives the angle. Make sure the calculator is in degree mode and that θ is measured from the horizontal, not the vertical.
A worked example, step by step
A rope pulls a crate with a force F = 120 N at θ = 40° above the horizontal ground. Find the horizontal component that drags the crate forward.
Apply the formula with units:
- Fₓ = F cos θ = 120 N × cos 40°
- Fₓ = 120 N × 0.766 = 91.9 N
So the horizontal pull is Fₓ = 91.9 N (3 significant figures). Only this part moves the crate along the ground; the rest of the 120 N lifts it slightly.
As a sanity check, Fₓ (91.9 N) is smaller than F (120 N), as it must be, a component can never exceed the whole force.
Common mistakes and how this is tested
The main trap: use cos for the component adjacent to the angle (usually horizontal), and measure θ from the horizontal.
Other common errors:
- Swapping cos and sin, which gives the vertical component instead.
- Leaving the calculator in radian mode, so cos 40° comes out wrong.
- Measuring the angle from the vertical without adjusting the formula.
Questions ask you to calculate the horizontal component of a pull or push, to define resolution of forces, or to explain why only the horizontal part does the work of moving an object across level ground.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)