Pressure

Pressure tells us how concentrated a force is, it is defined as the force per unit area

$p = \frac{F}{A}$

Where:
- p = pressure in pascals (Pa)
  - 1 Pa = 1 N m^-2
- F = force in newtons (N)
- A = area in metres squared (m²)

Pressure, unlike force, is a scalar
Therefore pressure does not have a specific direction

If a force is spread over a large area it will result in a small pressure
If a force is spread over a small area it will result in a large pressure

Pressure of Different Styles of Shoes

Pressure on different areas, downloadable AS & A Level Physics revision notes

High-heedled shoes exert a greater pressure than flat shoes because the same force (weight) is spread over a smaller area

Worked example

A cylinder is placed on a horizontal surface as shown below.

The mass of the cylinder is 4.7 kg and the diameter is 8.4 cm.

Calculate the pressure produced by the cylinder on the horizontal surface.

Answer:

Step 1: List the known quantities and convert to SI units

Mass, m = 4.7 kg
Diameter of cylinder, d = 0.084 m

Step 2: State the pressure equation

$p = \frac{F}{A}$

Step 3: Calculate the force exerted by the cylinder

The force is the weight acting on the cylinder
Acceleration of free fall, g = 9.81 m s^-2

$F = W = m g$

$W = 4.7 \times 9.81$

$W = 46.1 N$

Step 4: Calculate the area

Only the base of the cylinder is in contact with the surface

$area of circle = π r^{2}$

$A = π {(\frac{d}{2})}^{2}$

$A = π {(\frac{0.084}{2})}^{2}$

$A = 5.5 \times 10^{- 3} m^{2}$

Step 5: Substitute the known values into the pressure equation to calculate

$p = \frac{46.1}{5.5 \times 10^{- 3}}$

$p = 8400 Pa (2 s . f .)$

Exam Tip

The area referred to is the ‘cross-sectional’ area of a 3D object. This is the area of the base that the force is applied on. For a cylinder, this will be a circle.

Pressure (CIE A Level Physics)

Revision Note

Pressure

Pressure of Different Styles of Shoes

Worked example

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Author: Leander