Pressure

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Notes

Definition and Formula

**Pressure** is defined as the **force per unit area**.
Measured in **pascals (Pa)**, where 1 $Pa = 1 \frac{N}{m}^{2}$ .
Formula: $p = \frac{F}{A}$ , with $p$ = pressure (Pa), $F$ = force (N), $A$ = area $(m^{2})$ .
A formula triangle can be used to rearrange the equation: cover the quantity you want to find.

Effect of Area on Pressure

For a given force, **increasing area decreases pressure**; **decreasing area increases pressure**.
Large area → small pressure (e.g., tractor tyres).
Small area → large pressure (e.g., drawing pin tip, high heels).

Examples of Pressure in Action

**Tractors** have wide tyres to spread weight over a large area, reducing pressure and preventing sinking into mud.
**Drawing pins** have a sharp point with very small area, concentrating force to produce large pressure so it can be pushed into a wall.
**High heels** have a small contact area, producing high pressure that causes them to sink into soft surfaces; flat shoes spread weight over a larger area, reducing pressure.

Calculating Pressure, Force, or Area

Use $p = \frac{F}{A}$ to find pressure when force and area are known.
Rearrange to $F = p \times A$ to find force, or $A = \frac{F}{p}$ to find area.
Always use SI units: force in N, area in $m^{2}$ , pressure in Pa.
Worked example: A pump creates pressure of $5.28 \times 10^5 \, \text{Pa}$ on a piston of area $2.73 \times 10^{-2} \, \text{m}^2$ . Force = $p \times A = 14\,400 \, \text{N}$ (14.4 kN).

Key Points from Past Papers

Pressure depends on both force and area; changing the area while keeping force constant alters pressure.
To reduce sinking in snow, increase the area of contact (e.g., wear larger shoes).
When calculating pressure exerted by an object on a surface, use the area of contact between the object and the surface.
Smallest pressure for a given force comes from the largest area (e.g., 40 N over $2.0 m^{2}$ gives 20 Pa).

Formula triangle for pressure: p = F/A, F = p × A, A = F/p.

Practice questions

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1.A woman is in contact with the floor. In which of these poses does she produce the most pressure on the floor? Assume she is wearing flat shoes in each pose.
Easy
- AStanding on one foot
- BStanding on two feet
- CLying down
- DSitting on a chair
2.Which is an example of a force acting over a small area to produce a large pressure?
Easy
- AA skier wearing large skis on snow
- BA hammer being used to push a nail into a piece of wood
- CA tractor having very wide tyres
- DA person lying down, rather than walking upright on a roof
3.A water-filled tank is resting on a table. The tank has a rectangular base of length 0.5 m and width 0.5 m. Using the measurements, determine the area which should be used to calculate the pressure the tank exerts on the table.
Easy
- A $0.25 m^{2}$
- B $0.5 m^{2}$
- C $0.75 m^{2}$
- D $1.0 m^{2}$
4.A briefcase, with flat, rectangular sides rests on the floor. The briefcase is now turned so that it rests with its large, flat side on the floor. How has the change affected the force on the floor, and the pressure exerted by the briefcase on the floor?
Medium
- AForce unchanged, pressure decreased
- BForce unchanged, pressure unchanged
- CForce decreased, pressure decreased
- DForce decreased, pressure unchanged
5.A wooden block rests on a table. The block has dimensions: side A (1 cm x 2 cm), side B (2 cm x 3 cm), side C (1 cm x 3 cm). On which surface should the block be laid to produce the largest pressure on the table?
Medium
- ASide A
- BSide B
- CSide C
- DAny side, they will all produce the same pressure
6.An object has a weight of 12 N and a contact area of $2.0 m^{2}$ . What pressure does it exert on the ground?
Medium
- A4.0 Pa
- B6.0 Pa
- C12 Pa
- D24 Pa
7.The table gives four combinations of the force applied to a surface and the area over which it acts. Which row gives the smallest pressure exerted on the surface?
Hard
- AForce 40 N, Area $0.5 m^{2}$
- BForce 40 N, Area $2.0 m^{2}$
- CForce 80 N, Area $0.5 m^{2}$
- DForce 80 N, Area $2.0 m^{2}$
8.A person walking through snow sinks into it. The person makes a change so that they do not sink as far next time they go out. What do they do?
Hard
- ACrouch as they walk to lower their centre of mass
- BRun as fast as they can to increase the power they dissipate
- CWear shoes with a much larger area on the bottom to increase the area of their feet in contact with the snow
- DWear a heavy backpack to increase their weight and so make them more stable

Slides

What is Pressure?

Pressure is defined as the force per unit area.
It is measured in pascals (Pa), where 1 $Pa = 1 \frac{N}{m}^{2}$ .
The equation is: pressure = force / area, or $p = F / A$ .

Which of the following is the correct unit for pressure?

Pressure and Area

If a force is spread over a large area, it results in a small pressure.
If a force is concentrated over a small area, it results in a large pressure.
Example: A tractor has wide tyres to spread its weight and reduce pressure, preventing it from sinking into mud.

A drawing pin has a sharp point with a very small area. Why does this allow it to be pushed into a wall easily?

It increases the force applied.
It decreases the pressure on the wall.
It increases the pressure on the wall.
It decreases the area of the pin head.

Examples of Pressure in Everyday Life

High heels: small area → high pressure → sink into soft surfaces.
Flat shoes: larger area → lower pressure → less sinking.
Tractors: wide tyres spread weight → low pressure → stay on top of mud.

Which of these are true about pressure?

A sharp knife cuts better because it has a small area, creating high pressure.
A person lying down on snow exerts more pressure than when standing.
Pressure is calculated by multiplying force and area.
A tractor with wide tyres reduces pressure on the ground.

Calculating Pressure

Use the formula: $p = F / A$ .
Rearrange using the formula triangle: $F = p \times A, A = F / p$ .
Always use SI units: force in N, area in $m^{2}$ , pressure in Pa.

A force of 100 N is applied over an area of $2 m^{2}$ . The pressure $is ____ Pa$ .

Worked Example: Force from Pressure

A pump creates a pressure of $5.28 \times$ 10⁵ Pa on a piston of area $2.73 \times$ 10⁻² $m^{2}$ .
Calculate the force: $F = p \times A = (5.28 \times$ 10⁵) $\times (2.73 \times$ 10⁻²) $= 14 414.4 N$ ≈ 14.4 kN.

A pressure of 200 Pa acts on an area of $0.5 m^{2}$ . What is the force?

100 N
400 N
40 N
200 N

Pressure in Liquids and Gases

Pressure in a liquid increases with depth.
Pressure in a gas is caused by particles colliding with surfaces.
The same pressure equation applies, but the force is often the weight of the fluid above.

A water tank exerts a pressure on the table. Which area should be used to calculate the pressure?

The area of the tank's base
The area of the tank's side
The area of the table
The volume of the tank

Summary

Pressure = force / area.
Small area → large pressure; large area → small pressure.
Examples: drawing pins (high pressure), tractor tyres (low pressure).

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