Not given in the exam, recall it.
What it is for
Pascal's principle is used in Pressure (SPM Physics Form 5). Keep the SI units in every line of working. Pressure
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| F₁ | force on small piston | N |
| A₁ | area of small piston | m² |
| F₂ | force on large piston | N |
| A₂ | area of large piston | m² |
Rearrangements
F₂ = F₁ × A₂ / A₁F₁ = F₂ × A₁ / A₂
Worked example
Common trap
Understanding Pascal's principle
In a hydraulic system, F₁ is the force on the small piston and A₁ its area; F₂ is the force on the large piston and A₂ its area. Forces are measured in newtons (N) and areas in square metres (m²).
Pascal's principle states that pressure applied to an enclosed liquid is transmitted equally in all directions, so the pressure on the small piston equals the pressure on the large piston: F₁ / A₁ = F₂ / A₂.
This lets a small input force lift a large load, a force multiplier. Rearrange to find the output force with F₂ = F₁ × A₂ / A₁, or the input force with F₁ = F₂ × A₁ / A₂.
Keep both areas in the same unit, because only their ratio matters.
A worked example, step by step
In a hydraulic brake the small piston has area A₁ = 2.0 cm² and the large piston A₂ = 10 cm². A driver applies F₁ = 40 N to the small piston.
Find the output force F₂.
- Only the ratio of areas matters, so the units can stay in cm².
- Write the formula: F₂ = F₁ × A₂ / A₁.
- Substitute with units: F₂ = 40 N × (10 cm² / 2.0 cm²) = 40 N × 5.0 = 200 N.
The answer is F₂ = 200 N, to two significant figures. The area ratio of 5 multiplies the force five times.
In return, the small piston must move five times as far as the large piston, so energy is conserved.
Common mistakes and how this is tested
A common error is inverting the area ratio, the larger area belongs to the larger force, so put A₂ on top when finding F₂. Another is mixing units, for example one area in cm² and the other in m²; keep them the same because only the ratio counts.
- Thinking the device gives free extra energy, the output force is larger, but the large piston moves a smaller distance, so work in equals work out.
- Forgetting the liquid must be incompressible to transmit the pressure fully.
Questions ask you to calculate the force a hydraulic jack produces, explain how a hydraulic system multiplies force, or state Pascal's principle. For the statement, say pressure applied to an enclosed liquid is transmitted equally throughout.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)