Pressure Revision Notes

Pressure is the amount of force exerted on a surface divided by the area over which the force is distributed.

It is a scalar quantity, meaning it has magnitude but no direction.

Pressure is important in understanding how forces affect materials and fluids.

• Pressure (p) = Force (F) ÷ Area (A)
• Units: Pressure in pascals (Pa), Force in newtons (N), Area in square metres (m²)

The formula for pressure is: p = F/A, where: p is pressure in pascals (Pa), F is the force applied perpendicular to the surface in newtons (N), and A is the area of the surface in square metres (m²).

1 pascal (Pa) is defined as 1 newton per square metre (1 Pa = 1 N/m²).

• p = F/A (pressure equals force divided by area)
• 1 Pa = 1 N/m²

Example: A force of 50 N is applied uniformly over an area of 0.25 m². Calculate the pressure exerted.

Step 1: Write down the formula: p = F/A. Step 2: Substitute values: p = 50 N / 0.25 m². Step 3: Calculate: p = 200 Pa.

Answer: The pressure exerted is 200 pascals (Pa). This means each square metre of the surface experiences 200 newtons of force.

• Formula: p = F/A
• Substitution: p = 50 N / 0.25 m²
• Calculation: p = 200 Pa
• Answer: 200 pascals

Pressure increases if the force applied increases while the area remains constant.

Pressure decreases if the area over which the force is applied increases while the force remains constant.

This explains why sharp objects (small area) exert higher pressure and can penetrate surfaces more easily than blunt objects (large area).

• Increasing force → increases pressure (if area constant)
• Increasing area → decreases pressure (if force constant)

To draw a diagram illustrating pressure: 1. Draw a horizontal surface and label its area A (in m²). 2. Draw a downward arrow perpendicular to the surface representing the force F (in N). 3. Label the force arrow with its magnitude and direction.

This diagram helps visualise how force acts over an area to produce pressure.

• Surface labelled with area A
• Force arrow perpendicular to surface labelled F
• Indicate units (N for force, m² for area)

Pressure is defined as the force applied perpendicular to a surface divided by the area over which the force is distributed.

Mathematically, pressure (p) is given by the formula:

\[ p = \frac{F}{A} \] where: p is pressure in pascals (Pa), F is force in newtons (N), and A is area in square metres (m²).

• Pressure is a scalar quantity with units of pascals (Pa).
• 1 pascal equals 1 newton per square metre (1 Pa = 1 N/m²).
• Force must be perpendicular to the surface for this formula to apply.

If the area remains constant, increasing the force increases the pressure proportionally.

For example, pushing harder on a surface increases the pressure exerted on that surface.

This is because pressure is directly proportional to force when area is fixed.

• Doubling the force doubles the pressure if area is unchanged.
• Halving the force halves the pressure if area is unchanged.

If the force remains constant, increasing the area decreases the pressure.

This is because the same force is spread over a larger area, reducing the pressure at any point.

Conversely, decreasing the area increases the pressure because the force is concentrated on a smaller surface.

• Pressure is inversely proportional to area when force is constant.
• A smaller contact area results in higher pressure.

A sharp knife cuts better than a blunt knife because the sharp knife has a smaller contact area, resulting in higher pressure for the same applied force.

Snowshoes help prevent sinking into snow by increasing the area over which a person's weight acts, thus reducing pressure on the snow.

High-heeled shoes exert more pressure on the ground than flat shoes because the area of contact is smaller, which can damage soft floors or cause discomfort.

• Sharp knife: small area, high pressure, easier cutting.
• Snowshoes: large area, low pressure, prevents sinking.
• High heels: small area, high pressure, can damage surfaces.

Calculate the pressure exerted by a person weighing 600 N standing on one foot with a sole area of 0.02 m².

Using the formula: \[ p = \frac{F}{A} = \frac{600\ \text{N}}{0.02\ \text{m}^2} = 30000\ \text{Pa} \]

If the person stands on both feet, doubling the area to 0.04 m², the pressure becomes: \[ p = \frac{600\ \text{N}}{0.04\ \text{m}^2} = 15000\ \text{Pa} \] which is half the pressure when standing on one foot.

• Show substitution of values with correct units.
• Demonstrate how doubling area halves pressure.
• Highlight importance of units in calculations.

Pressure is defined as the force exerted per unit area on a surface. In liquids, pressure acts equally in all directions at a given depth.

The unit of pressure is the pascal (Pa), where 1 Pa = 1 newton per square metre (N/m²).

In liquids, pressure arises from the weight of the liquid above the point considered.

• Pressure = Force ÷ Area
• Unit of pressure: pascal (Pa) = N/m²
• Pressure in liquids acts in all directions

As you go deeper into a liquid, the amount of liquid above increases. This means the weight of the liquid pressing down increases.

Because pressure is caused by the weight of the liquid above, pressure increases with depth.

This increase is linear: doubling the depth roughly doubles the pressure, assuming constant density and gravitational field strength.

• Pressure increases with depth due to increasing weight of liquid above
• Pressure acts equally in all directions at a given depth
• Pressure-depth relationship is linear

Density (ρ) is the mass per unit volume of a substance, measured in kilograms per cubic metre (kg/m³).

Denser liquids have more mass in the same volume, so their weight per unit volume is greater.

Therefore, at the same depth, a denser liquid exerts a higher pressure than a less dense liquid.

• Density (ρ) = mass ÷ volume, units: kg/m³
• Higher density means greater weight of liquid above per unit volume
• Pressure at a depth is greater in denser liquids

The pressure at a depth h in a liquid of density ρ under gravitational field strength g is given by:

P = h × ρ × g, where: P is pressure in pascals (Pa), h is depth in metres (m), ρ is density in kilograms per cubic metre (kg/m³), and g is gravitational field strength in newtons per kilogram (N/kg) or metres per second squared (m/s²).

This formula shows pressure increases proportionally with depth, density and gravitational field strength.

• P = h × ρ × g
• P in pascals (Pa), h in metres (m), ρ in kg/m³, g ≈ 9.8 m/s²
• Pressure increases linearly with depth and density

The pressure at a point in a liquid is caused by the weight of the liquid column above that point.

Because weight is mass times gravitational field strength, and mass depends on density and volume, pressure depends on depth and density.

This explains why submarines and deep-sea divers experience higher pressure at greater depths, and why mercury (a dense liquid) exerts more pressure than water at the same depth.

• Pressure caused by weight of liquid column above point
• Weight depends on mass (density × volume) and gravity
• Higher density liquids exert more pressure at same depth

Pressure is defined as the force exerted per unit area on a surface. In liquids, pressure arises from the weight of the liquid above the point considered. Because liquids are nearly incompressible, pressure increases with depth due to the increasing weight of the liquid column above.

Mathematically, pressure (p) is measured in pascals (Pa), where 1 Pa = 1 N/m².

• Pressure (p) = Force (F) / Area (A)
• Unit of pressure: pascal (Pa) = newton per square metre (N/m²)

When moving downwards in a liquid by a vertical distance Δh, the pressure increases because of the weight of the additional liquid above. The change in pressure, Δp, depends on the density of the liquid (ρ), gravitational field strength (g), and the change in depth (Δh).

The relationship is given by the formula: Δp = ρgΔh, where:

Δp is the increase in pressure (Pa) between two depths,

• ρ (rho) is the density of the liquid in kilograms per cubic metre (kg/m³)
• g is the gravitational field strength in newtons per kilogram (N/kg), approximately 9.8 N/kg near Earth's surface
• Δh is the vertical change in depth in metres (m)

The pressure at a certain depth in a liquid is caused by the weight of the liquid column above that point. The weight (W) of this column is the mass (m) times gravitational field strength (g). The mass is the density (ρ) times the volume (V) of the liquid column.

For a column of cross-sectional area A and height Δh, volume V = A × Δh, so:

Mass m = ρ × A × Δh, and weight W = m × g = ρ × A × Δh × g.

• Pressure change Δp = Force / Area = W / A = (ρ × A × Δh × g) / A = ρgΔh

Calculate the increase in pressure when descending 5.0 m below the surface of freshwater (density 1000 kg/m³). Use g = 9.8 N/kg.

Given: ρ = 1000 kg/m³, g = 9.8 N/kg, Δh = 5.0 m. Using Δp = ρgΔh:

Δp = 1000 × 9.8 × 5.0 = 49,000 Pa or 4.9 × 10⁴ Pa.

• Step 1: Write down the formula: Δp = ρgΔh
• Step 2: Substitute values: Δp = 1000 × 9.8 × 5.0
• Step 3: Calculate: Δp = 49,000 Pa
• Step 4: State answer with units: 49,000 pascals (Pa)

To measure pressure change with depth, a pressure sensor or manometer can be used at different depths in a liquid column. The apparatus includes a transparent container filled with liquid, a ruler or scale to measure depth, and a pressure sensor connected to a data logger.

Variables: Depth (independent variable), Pressure (dependent variable).

Procedure: Record pressure readings at various depths, ensuring the sensor is vertical and stable. Repeat measurements to improve accuracy. Plot pressure against depth to verify the linear relationship predicted by Δp = ρgΔh.

• Use a pressure sensor calibrated in pascals
• Measure depth accurately with a ruler or depth gauge
• Repeat readings to reduce random errors
• Ensure liquid is at rest to avoid dynamic pressure effects
• Safety: Handle glassware carefully and avoid spills