DSE Physics — Pressure and Buoyancy Lesson-Prep Guide (for tutors) — p = rho g h, floating conditions and hydraulic presses

2026-11-03

Tutor lesson-prep guides · Secondary Physics

Students can recite p = F/A and p = rho g h, but freeze when asked what fraction of a wooden block floats below the surface. This lesson separates “pressure depends on depth” from “buoyancy depends on displaced liquid”.

Objectives — Students can: (1) use p = F/A for solids and p = rho g h for liquids and say when the two cannot be swapped; (2) find buoyancy from F = rho g V and use the floating condition to describe the state of an object; (3) use equal pressure to show that a hydraulic press multiplies force by the area ratio.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Density	Mass 200 g, volume 50 cm3, density?	4 g/cm3, that is 4000 kg/m3
Weight	Weight of 1.2 kg with g = 10	12 N
Area units	1 cm2 in m2	1e-4 m2

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-8 min	Definition	Same force, different areas	Answer three oral questions
8-20 min	Liquid pressure	Compare 3 m and 20 m depth	Get 30 000 Pa and 200 000 Pa
20-32 min	Buoyancy	Displacement and spring-balance readings	Fully submerged force is 20 N
32-44 min	Floating	Wood of density 600 kg/m3	Immersion 0.6, buoyancy 12 N
44-54 min	Hydraulic press	Same pressure, different areas	200 N becomes 10 000 N
54-60 min	Exit check	Three questions collected and marked	Independent

03 Teaching script (read it out)

Scene 1: Pressure: the same force, but the area decides

Pressure p = F/A in pascals. A force of 300 N on a 0.02 m2 plate gives 15 000 Pa.
The same force on a needle tip of 1e-6 m2 gives 3e8 Pa, two hundred thousand times larger, which is why a needle enters skin and a palm does not.
Students must state both proportionalities: pressure rises with force and falls with area.

Ask the student to repeat: same force, smaller area, larger pressure.

Scene 2: Liquid pressure depends only on depth and density

For p = rho g h, h is measured vertically from the free surface, not from the bottom of the container.
At 3 m: 1000 x 10 x 3 = 30 000 Pa without the atmosphere, and about 130 000 Pa with it. At 20 m the value is 200 000 Pa, roughly two atmospheres.
A window of 0.5 m2 at 3 m feels 15 000 N, which is why dam walls thicken with depth.

Ask the student to repeat: liquid pressure follows depth, not the shape of the vessel, and it acts equally in all directions.

Scene 3: Archimedes: buoyancy equals the weight of displaced liquid

A block of volume 0.002 m3 and density 600 kg/m3 has mass 1.2 kg and weight 12 N.
Fully submerged, buoyancy is 1000 x 10 x 0.002 = 20 N, larger than the weight, so the block rises.
At equilibrium buoyancy equals 12 N, so only 0.6 of the volume is submerged and 40 percent floats above the surface. Ice at 920 kg/m3 floats with about 92 percent below water.

Ask the student to repeat: buoyancy looks at displaced liquid, not at the weight of the object.

04 Question types and worked steps

Type	Example	Steps	Answer
Calculate	Pressure and force at depth	p = rho g h then F = pA	3 m gives 30 000 Pa and 15 000 N
Calculate	Buoyancy and submerged volume	F = rho g V, then F = W for a floater	0.0012 m3 and 12 N
Judge	Floating or sinking	Compare densities, or weight with maximum buoyancy	600 below 1000 so it floats
Calculate	Hydraulic press	Equal pressure gives F2 = F1 A2 / A1	200 N becomes 10 000 N

Sanity check (teach this): A floating body always has buoyancy equal to its weight and a submerged volume smaller than its total volume; a larger answer means the density comparison is wrong. Liquid pressure always rises with depth, so a 3 m answer above a 20 m answer is a substitution error. A press that multiplies force by 50 divides displacement by 50, so force and displacement never both increase.

05 Independent practice (3 questions)

Question	Answer	What to watch
Pressure at 20 m depth, ignoring the atmosphere	200 000 Pa or 200 kPa	Was g included?
Submerged volume of a 600 kg/m3 block of 0.002 m3	0.0012 m3	Using the density ratio rather than halving
Force on a 0.05 m2 piston when 200 N acts on 0.001 m2	10 000 N	Is the area ratio the right way up?

06 Common mistakes and what to say

Mistake	Student writes	Say this
Omitting g	Gets 3000 Pa	“The formula has three symbols: rho, g and h. Never drop g.”
Using the weight of the object	Calls 12 N the buoyancy	“Buoyancy is the liquid pushing up, so use liquid density and displaced volume.”
Multiplying by the immersed fraction when fully submerged	Uses 0.6 for a fully submerged block	“Fully submerged means displaced volume equals total volume, so no extra fraction.”
Inverting the area ratio in a press	Gets 4 N	“Force follows area: 50 times the area gives 50 times the force.”

07 Homework (paper, section and question numbers)

DSE Physics practice paper (Section A and Section B) — Section B structured questions on pressure, buoyancy and moments
Secondary physics chapter index — All chapters

08 Exit check (last 5 minutes)

Question	Answer	Decision
Pressure at 3 m depth, ignoring the atmosphere	30 000 Pa	Three correct means move on to heat
Fraction of the wooden block below the surface	0.6, that is 60 percent	One wrong means reteach floating
What sets the force multiplication of a press	The ratio of piston areas	Two wrong means restart act one

09 Tutor FAQ

Why are dam walls thicker at the bottom?

Pressure grows linearly with depth, so at 20 m it is about 6.7 times the value at 3 m.

Does buoyancy change with the weight of the object?

No. Buoyancy depends only on liquid density and displaced volume; weight decides whether the object floats.

How does a submarine dive?

It takes water into ballast tanks so its weight exceeds maximum buoyancy, and blows the tanks to rise.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.

Practice papers: Paper 1 (S4 Physics)