Why Does The Same Force Sometimes Cause Very Different Effects?
Definition
Pressure
Pressure is force exerted per unit area on a surface.
- Pressure describes how concentrated a force is when it acts on a surface.
- The effect of a force depends not only on how large the force is, but also on the size of the area over which it is applied.
- A force acting on a small area produces a larger effect than the same force acting on a larger area.
- Pressure helps explain everyday experiences such as cutting, piercing, and sinking.
Example
- Walking barefoot on sand feels easier than walking on sharp shingle.
- Your weight (force) is similar in both situations, but the contact area is much smaller on the sharp stones, so the pressure on your skin is larger.
Calculating Pressure
In the simplest situations, pressure is calculated using
$$P=\frac{F}{A}$$
where $P$ is pressure, $F$ is the force acting perpendicular (normal) to the surface, and $A$ is the contact area.
Relationship Between Pressure, Force, and Area
- Pressure increases when a force is applied over a smaller contact area.
- Pressure decreases when the same force is spread over a larger contact area.
- Both force and area must be considered together to understand pressure.
Note
Changing the contact area changes the pressure even if the force remains constant.
Units And Conversions Matter
- The SI unit of pressure is the pascal (Pa): $$1\ \mathrm{Pa}=1\ \mathrm{N\ m^{-2}}$$
- In everyday contexts, you often see:
- kPa: $1\ \mathrm{kPa}=10^3\ \mathrm{Pa}$
- MPa: $1\ \mathrm{MPa}=10^6\ \mathrm{Pa}$
- hPa (hectopascal): $1\ \mathrm{hPa}=100\ \mathrm{Pa}$ (common in weather maps)
- bar: $1\ \mathrm{bar}=10^5\ \mathrm{Pa}$ (so $1\ \mathrm{mbar}=1\ \mathrm{hPa}$)
Common Mistake
Forgetting to convert areas into $\mathrm{m^2}$ because area depends on length squared, converting cm to m changes the numerical value a lot.
A Small Area Creates A Huge Pressure
- When a force is concentrated onto a tiny area, the pressure can become enormous.
- This is why sharp tools work as they create high pressure at the cutting edge.
Exam technique
- Whenever you see pressure questions, write the units beside each value before substituting.
- If your final unit is not $\mathrm{Pa}$ (or an equivalent like $\mathrm{N\ m^{-2}}$), you have probably used the wrong area unit.
What Is Atmospheric Pressure?
Definition
Atmospheric pressure
Atmospheric pressure is the pressure exerted by the weight of the air above a surface.
- Atmospheric pressure is caused by the weight of the air above a surface.
- Air pressure acts in all directions, not just downward.
- We do not normally feel atmospheric pressure because it acts equally on our bodies.
- At sea level, atmospheric pressure is approximately 101 kPa.
- Air pressure acts on objects from all sides.
- Changes in air pressure can be felt in the ears during altitude changes.
Why Your Ears Pop On A Mountain Or In An Airplane
- At a higher altitude, there is less air above you, so atmospheric pressure is lower.
- Your ears pop as the pressure on either side of the eardrum equalizes.
Pressure Changes with Height
- Atmospheric pressure decreases with increasing altitude.
- There is less air above you at higher altitudes, so the weight of air is lower.
- This causes pressure to drop as height increases.
Tip
Always explain lower pressure at high altitude using the idea of less air above.
How can atmospheric pressure be measured?
- Atmospheric pressure is measured using a barometer.
- A traditional mercury barometer uses a column of mercury in a tube with a vacuum at the top.
- Atmospheric pressure pushes mercury up until the pressure from the mercury column matches the air pressure.
- Using $P=h\rho g$, a height of about $760\ \mathrm{mm}$ corresponds to approximately 1 atmosphere.
Tip
- Older units like mmHg are based on the barometer idea.
- They are less common today because SI units (Pa, kPa) make calculations and communication more consistent across science and engineering.
Pressure In Fluids Comes From The Weight Of The Fluid Above
- In a fluid (liquid or gas), pressure at a point increases with the height (or depth) of fluid above it because the fluid has weight. $$P=h\rho g$$
- where $h$ is the height of fluid above the point (or depth below the surface), $\rho$ is the density of the fluid, and $g$ is the gravitational field strength.
Note
- This equation gives the pressure due to a column of fluid.
- In water problems at depth, you often calculate the additional pressure $\Delta P=\rho g h$ and then add atmospheric pressure if asked for the total pressure.
Pressure in Liquids
- Pressure in a liquid increases with depth.
- Pressure depends on the density of the liquid and the depth below the surface.
- Pressure is the same at the same depth, regardless of container shape.
Underwater Pressure
- Water pressure increases rapidly with depth.
- For every 10 m increase in depth, pressure increases by about one atmosphere.
Example
- Divers experience much higher pressures underwater than at the surface.
- Divers must ascend slowly to avoid injury caused by rapid pressure changes.
Example
A free diver reaches $160\ \mathrm{m}$ depth in seawater of density $1025\ \mathrm{kg\ m^{-3}}$. The additional pressure is
$$\Delta P=\rho g h=1025\times 9.8\times 160\approx 1.61\times 10^6\ \mathrm{Pa}=1607\ \mathrm{kPa}.$$
In atmospheres ($1\ \mathrm{atm}=101.325\ \mathrm{kPa}$):
$$\frac{1607}{101.325}\approx 15.9\ \mathrm{atm}.$$
Common Mistake
- Do not confuse pressure with force.
- At depth you may calculate a huge pressure, but the force on an object still depends on the area: $F=PA$.
Pressure in Gases
- Gas pressure is caused by particles colliding with the walls of a container.
- Faster-moving particles cause more frequent and harder collisions.
- Gas pressure increases when particles are compressed into a smaller volume.
Gas Pressure Changes When Volume Changes (Boyle's Law)
Definition
Boyle’s law
Boyle’s law states that pressure is inversely proportional to volume at constant temperature.
- When gas volume decreases, particles collide more frequently with container walls.
- This increases gas pressure.
- When gas volume increases, collisions occur less often, reducing pressure.
Analogy
People bump into walls more often in a crowded room than in a large hall.
Pressure-Volume Graphs
- Pressure–volume graphs show a curved line.
- As volume increases, pressure decreases.
- These graphs demonstrate inverse proportionality.
Temperature Effect on Gas Pressure
- Heating a gas increases particle kinetic energy.
- Particles move faster and collide more often with container walls.
- This increases pressure if the volume remains constant.
Using A Smartphone Barometer To Estimate Air Density
- If your phone has a pressure sensor, you can measure pressure at different heights in a stairwell.
- Plot pressure (Pa) against height (m).
- The gradient is $$\text{gradient}=\frac{\Delta P}{\Delta h}.$$
- From $P=h\rho g$, changes obey
$$\frac{\Delta P}{\Delta h}=\rho g\quad\Rightarrow\quad \rho=\frac{\text{gradient}}{g}.$$
Exam technique
On a graph of pressure near $100{,}000\ \mathrm{Pa}$, do not start the $y$-axis at zero, or the line will look almost flat and the gradient will be hard to measure accurately.
Self review
- Define pressure and state its equation with units.
- Explain how changing area affects pressure for the same force.
- Explain why large buildings need wide foundations.
- Describe why atmospheric pressure decreases with altitude.
- Explain why liquid pressure increases with depth.
- Explain gas pressure using particle motion.
- Describe Boyle’s law.
- Explain how temperature affects gas pressure.
