Pressure | CAIE 9702 Paper 1 Notes · Conquer Your A Levels

Chapters

Paper 1

Physics9702

Pressure

The same force can be gentle or sharp. Spread over a palm it presses lightly; behind a pin it goes through wood.

Pressure measures how concentrated a force is on an area.

The definition

Definition

1 mark

What is meant by pressure?

Model answer: The normal force per unit cross-sectional area.

p = \dfrac{F}{A}

Symbols

$p$ = pressure (Pa)
$F$ = force at right angles (normal) to the surface (N)
$A$ = cross-sectional area (m²)

Normal force means the component of force at right angles to the surface. This direction is part of the definition (9702/21/O/N/25 Q2(a)(i)).
The unit is the pascal: $1 \text{ Pa} = 1 \text{ N m}^{-2}$ . In base units that is kg m⁻¹ s⁻².
Pressure is a scalar. It has no direction of its own. At a point in a fluid, pressure has the same value in every direction; the force that pressure produces on a surface acts normal to that surface (9702/22/O/N/25 Q1(a)).

Worked example

Smallest case: a box on the floor

A box pushes down with 20 N on an area of 0.50 m². Find the pressure on the floor.

$p = \dfrac{F}{A} = \dfrac{20}{0.50} = 40 \text{ Pa}$ .

Answer

p = 40 \text{ Pa}

Your turnExam-style

A person of weight 600 N stands with both feet flat on the floor. Estimate the pressure exerted on the floor.

Show worked answer

Two feet cover roughly $0.06 \text{ m}^2$ (each about 30 cm × 10 cm).
$p = \dfrac{600}{0.06} = 1 \times 10^{4} \text{ Pa}$ .

Answer: about 1 × 10⁴ Pa. A reasonable contact area gives an answer of this order of magnitude.

Same block, different faces

The same rectangular block lies on its broad face on the left and stands on its narrow face on the right. — Only the contact area changes. The block's weight is unchanged, so the narrow face produces the greater pressure.

A block resting on its smallest face puts the largest pressure on the ground: same weight, smallest area.
Seen from the fluid side, that is also the block standing as a tallest column: pressure from a column of material is $\rho g h$ (next lesson), and the smallest face goes with the biggest height.

Worked example

Largest pressure of a lead block

A lead block (density 1.13 × 10⁴ kg m⁻³) has sides 12 cm, 15 cm and 10 cm. Find the largest pressure it can put on the ground.

Weight: $W = \rho V g = 1.13 \times 10^{4} \times (0.12)(0.15)(0.10) \times 9.81 = 200 \text{ N}$ .
Smallest face: 12 cm × 10 cm = $0.012 \text{ m}^2$ .
$p = \dfrac{200}{0.012} = 1.7 \times 10^{4} \text{ Pa}$ .

Answer

p \approx 1.7 \times 10^{4} \text{ Pa}

Pressure

The same force can be gentle or sharp. Spread over a palm it presses lightly; behind a pin it goes through wood.

Pressure measures how concentrated a force is on an area.

The definition

Definition

1 mark

What is meant by pressure?

Model answer: The normal force per unit cross-sectional area.

p = \dfrac{F}{A}

Symbols

$p$ = pressure (Pa)
$F$ = force at right angles (normal) to the surface (N)
$A$ = cross-sectional area (m²)

Normal force means the component of force at right angles to the surface. This direction is part of the definition (9702/21/O/N/25 Q2(a)(i)).
The unit is the pascal: $1 \text{ Pa} = 1 \text{ N m}^{-2}$ . In base units that is kg m⁻¹ s⁻².
Pressure is a scalar. It has no direction of its own. At a point in a fluid, pressure has the same value in every direction; the force that pressure produces on a surface acts normal to that surface (9702/22/O/N/25 Q1(a)).

Worked example

Smallest case: a box on the floor

A box pushes down with 20 N on an area of 0.50 m². Find the pressure on the floor.

$p = \dfrac{F}{A} = \dfrac{20}{0.50} = 40 \text{ Pa}$ .

Answer

p = 40 \text{ Pa}

Your turnExam-style

A person of weight 600 N stands with both feet flat on the floor. Estimate the pressure exerted on the floor.

Show worked answer

Two feet cover roughly $0.06 \text{ m}^2$ (each about 30 cm × 10 cm).
$p = \dfrac{600}{0.06} = 1 \times 10^{4} \text{ Pa}$ .

Answer: about 1 × 10⁴ Pa. A reasonable contact area gives an answer of this order of magnitude.

Same block, different faces

A block resting on its smallest face puts the largest pressure on the ground: same weight, smallest area.
Seen from the fluid side, that is also the block standing as a tallest column: pressure from a column of material is $\rho g h$ (next lesson), and the smallest face goes with the biggest height.

Worked example

Largest pressure of a lead block

A lead block (density 1.13 × 10⁴ kg m⁻³) has sides 12 cm, 15 cm and 10 cm. Find the largest pressure it can put on the ground.

Weight: $W = \rho V g = 1.13 \times 10^{4} \times (0.12)(0.15)(0.10) \times 9.81 = 200 \text{ N}$ .
Smallest face: 12 cm × 10 cm = $0.012 \text{ m}^2$ .
$p = \dfrac{200}{0.012} = 1.7 \times 10^{4} \text{ Pa}$ .

Answer

p \approx 1.7 \times 10^{4} \text{ Pa}