Ch 17 · 1.8 Pressure · O Level Physics 5054

Topic 17 of 17 in Motion, Forces and Energy — O Level Physics 5054 — 58 lessons.

Introduction

Why do camels have wide feet and knives have sharp edges? Why are dams thicker at the bottom? Why do your ears hurt at the bottom of a swimming pool? All of these are about pressure: how a force is spread over an area, and how pressure builds up in liquids. (Syllabus section 1.8.)

Key ideas — Pressure

Pressure is the force per unit area:

🧑‍🏫 Teacher's explanation

Imagine you are standing on soft sand at the beach. If you stand on two feet, you sink a little bit. If you stand on one foot, you sink much deeper. Even though your weight (the force) hasn't changed, you are spreading that force over a much smaller area, which increases the pressure.

📖 Definitions

🔍 Worked example — Easy

A block exerts a force of 50 N on a table. The base of the block has an area of 0.2 m^2. Calculate the pressure exerted by the block.

🔍 Worked example — Standard

A diver is 5 m below the surface of the sea. Calculate the pressure exerted by the water at this depth. Assume the density of seawater is 1030 kg/m^3 and g = 10 m/s^2.

🔍 Worked example — Exam-style

A hydraulic piston has an area of 0.05 m^2. It supports a mass of 200 kg. Calculate the pressure exerted by the piston. Use g = 9.81 m/s^2.

⚠️ Common errors

🧠 Quick check 1

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🎯 Exam question

Key ideas — Force and area in everyday life

For the same force:

🧑‍🏫 Teacher's explanation

Imagine you are standing on a soft sponge. If you stand on your feet, you sink in a little bit. But if you stand on one thin stiletto heel, you sink in much deeper. Even though your weight (the force) hasn't changed, the way that weight is spread out has. Pressure is simply a measure of how 'concentrated' a force is over a surface.

📖 Definitions

🔍 Worked example — Easy

A wooden block exerts a force of 25 N on a table. The base of the block has an area of 0.05 m^2. Calculate the pressure exerted by the block on the table.

🔍 Worked example — Standard

A diver is swimming at a depth of 12 m below the surface of the sea. Calculate the pressure exerted by the water at this depth. (Assume the density of seawater is 1030 kg/m^3 and g = 10 m/s^2)

🔍 Worked example — Exam-style

A hydraulic jack is used to lift a car. The piston has an area of 0.02 m^2 and exerts a force of 400 N on the fluid. Calculate the pressure in the fluid.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Pressure acts at right angles to a surface

The pressure of a fluid on a surface produces a force perpendicular (at right angles) to that surface, whatever way the surface faces.

🧑‍🏫 Teacher's explanation

Imagine you are wearing high heels and walking on a soft sponge. Because your weight is concentrated on a tiny area, you sink deep into the sponge. Now imagine wearing flat sneakers; the same weight is spread over a much larger area, so you barely dent the sponge. This is the essence of pressure: it is how 'concentrated' a force is.

📖 Definitions

🔍 Worked example — Easy

A wooden block exerts a force of 25 N on a table. The contact area between the block and the table is 0.05 m^2. Calculate the pressure exerted by the block.

🔍 Worked example — Standard

A hydraulic piston has an area of 0.02 m^2. If the pressure applied to the piston is 4000 Pa, calculate the force exerted on the piston.

🔍 Worked example — Exam-style

A diver is 15 m below the surface of the sea. Calculate the increase in pressure due to the water. Assume the density of seawater is 1030 kg/m^3 and g = 9.81\ ext m/s^2.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — Pressure in a liquid

The pressure beneath the surface of a liquid:

🧑‍🏫 Teacher's explanation

Imagine you are at the bottom of a swimming pool. You feel a squeezing sensation on your ears. This is because the water above you is heavy, and its weight is pressing down on you. The deeper you go, the more water there is sitting on top of you, meaning the weight (and thus the pressure) increases.

📖 Definitions

🔍 Worked example — Easy

A rectangular block with a base area of 0.05 m^2 exerts a force of 20 N on a table. Calculate the pressure exerted by the block.

🔍 Worked example — Standard

A diver is swimming at a depth of 15 m in seawater. The density of seawater is 1030 kg/m^3. Calculate the pressure exerted by the seawater at this depth. (Use g = 10 m/s^2 for this calculation).

🔍 Worked example — Exam-style

An underwater sensor measures a pressure increase of 4.9 kPa when it descends 0.5 m in a liquid. Calculate the density of the liquid. (Use g = 9.8 N/kg)

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

Key ideas — The liquid barometer

A mercury barometer measures atmospheric pressure:

🧑‍🏫 Teacher's explanation

Imagine you are at the bottom of a swimming pool. You feel a 'squeeze' on your ears. This is because the weight of the water above you is pressing down on you. In a liquid, pressure isn't just about how much total weight there is, but how much weight is pushing on a specific area at a specific depth.

📖 Definitions

🔍 Worked example — Easy

A wooden block exerts a force of 25 N on a table. The area of the base of the block is 0.5 m^2. Calculate the pressure exerted by the block on the table.

🔍 Worked example — Standard

Calculate the pressure increase (Δ p) at a depth of 12 m below the surface of the ocean, given the density of seawater rho = 1025 kg/m^3 and g = 9.81 ms^-2.

⚠️ Common errors

🧠 Quick check 1

🧠 Quick check 2

🎯 Exam question

(a) State the name of the space above the mercury column in the tube. [1] (b) Calculate the atmospheric pressure in Pascals (Pa). Use rho = 13600 kg/m^3 and g = 9.81 m/s^2. [2] [3 marks]

Worked example

Example 1: pressure on the ground. A 60 kg student stands on both feet, total area 0.040\ m^2.

🔍 Worked example — Easy

A wooden block exerts a force of 25 N on a table. The base of the block has an area of 0.05 m^2. Calculate the pressure exerted by the block on the table.

🔍 Worked example — Standard

A diver is swimming in a lake with a density of 1000 kg/m^3. Calculate the increase in pressure when the diver descends from the surface to a depth of 12 m. (Use g = 9.8 m/s^2)

🔍 Worked example — Exam-style

An open container is filled with oil of density 850 kg/m^3 to a height of 0.50 m. Calculate the pressure exerted by the oil at the bottom of the container. (Assume atmospheric pressure is 1.0 × 10^5 Pa and g = 9.8 m/s^2)

⚠️ Common errors

Common mistakes

Practice

Answers: (1) 300 / 0.50 = 600\ Pa. (2) The sharp edge has a much smaller area, so the same force produces a much larger pressure. (3) 1000 × 9.8 × 3.0 = 29 400\ Pa ≈ 2.9 × 10^4\ Pa. (4) Atmospheric pressure on the mercury in the dish supports a column of mercury in the tube; the height of the column measures the pressure. If atmospheric pressure falls, the column becomes shorter. (5) Fill a bottle with small holes in different places with water; the water jets come out at right angles to the surface at each hole.

Ch 17 · 1.8 Pressure · O Level Physics 5054

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