Section 6.2: Pressure
Pressure is defined as the force applied per unit area. It is a fundamental concept in fluid mechanics and engineering:
Definition and Formula
\[
P = \frac{F}{A}
\]
where:
\( P \) = pressure (Pa = N/m²)
\( F \) = force applied (N)
\( A \) = area over which the force acts (m²)
Higher pressure can be achieved either by increasing the force or by decreasing the area over which the force is applied.
Example 1
A 200 N force is applied on a 0.02 m² surface. Calculate the pressure.
\(\displaystyle P = \frac{F}{A} = \frac{200}{0.02} = 10{,}000 \, \text{Pa}\)
The pressure on the surface is 10,000 Pa.
Example 2
A person weighing 700 N stands on one foot with an area of 0.03 m². Find the pressure exerted on the ground.
\(\displaystyle P = \frac{700}{0.03} \approx 23{,}333 \, \text{Pa}\)
The pressure exerted on the ground is approximately 23,333 Pa.
Practice Problems
- A block of mass 50 kg exerts a force due to gravity on a table. If the area of contact is 0.25 m², calculate the pressure.
- A hydraulic press applies a force of 5000 N over an area of 0.05 m². Find the pressure.
- A nail with a tip area of 0.0001 m² experiences a force of 200 N. Determine the pressure at the tip.
- A diver exerts a force of 800 N over a surface area of 0.04 m². Calculate the pressure underwater.
- A cube of metal has a face area of 0.1 m². If a force of 1000 N acts on it, what is the resulting pressure?