IGCSE Physics 0625: Comprehensive Notes on Pressure in Solids, Liquids, Atmosphere, and Hydraulic Systems

Definition: Pressure is defined as the force acting per unit area.
Mathematical Formula: $P = \frac{F}{A}$
- $P$ represents Pressure, measured in pascals ( $Pa$ ).
- $F$ represents Force, measured in newtons ( $N$ ).
- $A$ represents Area, measured in square meters ( $m^2$ ).
Units of Measurement:
- The standard SI unit for pressure is the Pascal ( $Pa$ ).
- Definition of 1 Pascal: $1\,Pa = 1\,N/m^2$ . This specifically denotes a force of $1\,N$ acting on an area of $1\,m^2$ .

Increasing Pressure: Pressure increases when the force applied increases or when the area over which the force is applied decreases.
Decreasing Pressure: Pressure decreases when the force applied decreases or when the area over which the force is applied increases.
Practical Examples and Situations:
- Sharp Knife: Possesses a small surface area, which results in high pressure at the edge, allowing for easier cutting.
- Snowshoes: Provide a large surface area to reduce the pressure exerted on the snow, preventing the wearer from sinking.
- High Heels: The small area of the heel exerts very high pressure on the ground.
- Tractor Tyres: Have a large surface area to ensure low pressure on the soil, preventing the heavy vehicle from sinking into soft ground.

Worked Example 1:
- Input: A force of $200\,N$ acts on an area of $0.5\,m^2$ .
- Calculation: $P = \frac{F}{A} = \frac{200}{0.5}$ .
- Result: $400\,Pa$ .
Worked Example 2:
- Input: A woman wearing high heels exerts $500\,N$ on an area of $0.002\,m^2$ .
- Calculation: $P = \frac{500}{0.002}$ .
- Result: $250,000\,Pa$ .

Key Concepts:
- Liquid pressure increases as depth increases.
- Liquid pressure acts in all directions within the fluid.
Why Pressure Increases with Depth: At greater depths, there is a larger volume of liquid above the point of measurement. This leads to a greater weight pressing downward, which in turn increases the pressure.
Mathematical Formula for Liquids: $p = \rho g h$
- $p$ represents Pressure ( $Pa$ ).
- $\rho$ (rho) represents the density of the liquid ( $kg/m^3$ ).
- $g$ represents gravitational field strength (typically $10\,N/kg$ or $9.8\,N/kg$ depending on the context).
- $h$ represents depth (vertical distance from the surface) measured in meters ( $m$ ).
Critical Relationships:
- Pressure is directly proportional to depth ( $h$ ).
- Pressure is directly proportional to the density ( $\rho$ ) of the liquid.

Characteristics and Behavior:
- Pressure acts equally in all directions.
- Pressure increases linearly with depth.
- At the same depth within the same liquid, the pressure is identical.
- Pressure is completely independent of the container's shape.
Worked Example 3:
- Task: Calculate pressure at a depth of $4\,m$ in water.
- Given: $\rho = 1000\,kg/m^3$ , $g = 9.8\,N/kg$ , $h = 4\,m$ .
- Calculation: $p = 1000 \times 9.8 \times 4$ .
- Result: $39,200\,Pa$ .
Real-World Manifestations:
- Dam Walls: Constructed to be significantly thicker at the bottom than at the top to withstand the higher pressure found at greater depths.
- Water Sprays: Water will spray further from holes located lower in a container because the pressure is higher there.
- Submarines: Must be built with strong hulls to withstand the immense pressures encountered deep underwater.

Definition: Atmospheric pressure is the pressure exerted by the air surrounding the Earth.
Cause of Atmospheric Pressure: Air possesses both mass and weight. Gravity pulls the air downward toward the Earth's surface, creating pressure.
Practical Effects and Examples:
- Drinking through a straw (creating a pressure difference).
- The operation of suction cups.
- The function of syringes.
- Measuring pressure with barometers.
Changes in Atmospheric Pressure:
- Sea Level: Pressure is at its highest.
- High Mountains: Pressure is lower because there is less air above.

The Hydraulic Principle: Pressure applied to an enclosed liquid is transmitted equally in all directions throughout the liquid.
Mathematical Equation: $\frac{F_1}{A_1} = \frac{F_2}{A_2}$
- $F_1$ : Input force.
- $A_1$ : Input area of the smaller piston.
- $F_2$ : Output force.
- $A_2$ : Output area of the larger piston.
Mechanism of Action:
- A small force applied to a small piston creates a specific pressure in the liquid.
- This same pressure is transmitted to a larger piston.
- Because the area is larger ( $F = P \times A$ ), a much larger output force is produced.
Applications of Hydraulics:
- Car braking systems.
- Hydraulic lifts.
- Barber chairs.
- Excavators.
- Car jacks.
Worked Example 4:
- Small piston: $A_1 = 0.01\,m^2$ , $F_1 = 50\,N$ .
- Large piston: $A_2 = 0.5\,m^2$ .
- Calculation: $\frac{50}{0.01} = \frac{F_2}{0.5}$ .
- $\frac{50}{0.01} = 5000$ .
- $F_2 = 5000 \times 0.5 = 2500\,N$ .
Key Advantages:
- Force multiplication (lifting heavy loads with minimal effort).
- Smoothness of operation.

Unit Conversion: Forgetting to convert area units to square meters ( $m^2$ ). Always use $m^2$ .
Concept Confusion: Confusing pressure with force. Remember that pressure is force per unit area.
Inaccurate Depth Measurement: Using the wrong depth for liquid calculations. Depth must always be measured vertically downward from the surface.
Container Shape Fallacy: Assuming that the shape of a container affects the pressure level. Only the vertical depth matters.
Unit Omission: Forgetting to include units in the final answer. Always specify $Pa$ or $N/m^2$ .

Question 1: A force of $300\,N$ acts on an area of $0.6\,m^2$ . Find the pressure.
Question 2: Calculate the water pressure at a depth of $6\,m$ . Use $\rho = 1000\,kg/m^3$ and $g = 9.8\,N/kg$ .
Question 3: A hydraulic lift has an input force of $40\,N$ , a small piston area of $0.02\,m^2$ , and a large piston area of $0.4\,m^2$ . Find the output force.

Always state the formula before performing calculations.
Ensure all measurements are in SI units before beginning.
Pay close attention to area conversions, especially when converting $cm^2$ to $m^2$ .
Keep in mind that pressure in liquids is strictly dependent on depth, not shape.
Recognize that hydraulic systems are used primarily to multiply force.
Explicitly include units such as $Pa$ or $N/m^2$ with every answer.
Show all steps of your working clearly to maximize marks.