Pressure: the same force over a different area
You will be able to: Calculate pressure from perpendicular force and area and distinguish pressure from force.
Why does a wider contact spread a push?
Push down with 20 N over 0.01 m² and the average pressure is 2000 Pa. Spread the same force across twice the area and the pressure halves. Pressure describes how concentrated the normal push is.
A useful starting point: Measure density with volume changes and graphs →
Words and symbols before equations
- Pressure P
- Perpendicular force per area, in pascals (Pa).
- Normal force component F_perp
- The part of a force perpendicular to a surface.
- Area A
- Surface area in m²; 1 cm²=10⁻⁴ m².
- Scalar
- A quantity without a direction; pressure is scalar, while its force on a surface is directional.
What this picture assumes
Uniform normal force over a surface. 1 cm²=0.0001 m². The graph varies area while holding the selected force fixed; the teal dot marks the selected area.
Connect the picture to the physics
For uniform pressure, P=F_perp/A and F_perp=PA. If pressure varies over a large surface, a single value times area is not generally the total force; this lesson uses uniform pressure or an average pressure.
Pressure acts through normal forces on boundaries. In a fluid at rest, pressure at a point is the same for different surface orientations, but the force on each small surface points perpendicular to that surface. Equal pressure on opposite equal-area faces gives equal opposite forces.
If both sides of a piston are exposed to pressures P_1 and P_2, the net pressure force is (P_1−P_2)A. Do not use one side’s pressure alone while ignoring the force from the other side. When using cm², convert the area itself, not just one length.
A worked example, step by step
A 60 N perpendicular force is spread uniformly over 0.03 m². Find pressure, then the force the same pressure exerts on 0.05 m².
- P=F/A=60/0.03=2000 Pa.
- 2000 Pa means 2000 N per m².
- At the same P, F=PA=2000(0.05)=100 N.
- Larger area gives greater force at fixed pressure; larger area gives smaller pressure at fixed force. State which quantity stays fixed.
Pressure and force are not interchangeable. Equal pressures need not give equal forces if areas differ.
A force lies entirely parallel to a surface. Does that component contribute to P=F_perp/A?
Compare with an explanation
No. This pressure definition uses the perpendicular component.
Predict. Change one thing. Explain.
Hold force fixed and change area, then hold area fixed and change force. Explain why doubling both leaves the pressure unchanged.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
F_perp=20 N; A=100 cm²=0.01 m². P=2000 Pa=2 kPa. The curve holds force fixed while varying area.
Uniform normal force over a surface. 1 cm²=0.0001 m². The graph varies area while holding the selected force fixed; the teal dot marks the selected area.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant force, motion or energy relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA piston of area 0.01 m² has 120 kPa on one side and 100 kPa on the other. (a) Convert the pressure difference to Pa. (b) Find net pressure force. (c) State its direction. (d) Explain why 120 kPa times area alone is not the net force.
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Compare with the answer and four-point rubric
- 1 point: ΔP=20,000 Pa.
- 1 point: F_net=20,000(0.01)=200 N.
- 1 point: From the higher-pressure side toward the lower-pressure side.
- 1 point: The 100 kPa side also exerts an opposing force and must be included.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Pressure units?
Pa=N/m².
RECALL 2Does pressure itself have a direction?
No. The associated force is normal to the surface.
RECALL 3Which force matters when both sides have pressure?
The difference of the opposing pressure forces.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Pressure: the same force over a different area
- P=F_perp/A; 1 Pa=1 N/m².
- For two uniform opposing pressures: F_net=(P_1−P_2)A.
Remember: Pressure and force are not interchangeable. Equal pressures need not give equal forces if areas differ.
Conditions: Uniform normal force over a surface. 1 cm²=0.0001 m². The graph varies area while holding the selected force fixed; the teal dot marks the selected area.
Refresh Kid · Unit 8 · Objectives 8.2.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 8.2, objectives 8.2.A. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026. Fall-2026 corrections also checked. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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