Pressure depends on normal force and area
Definition
Pressure
The normal force acting per unit area of a surface.
- Pressure is calculated using P=FAP=\dfrac{F}{A}P=AF.
- Here, PPP is pressure in pascals, FFF is the force normal to the surface in newtons, and AAA is the contact area in square metres.
- One pascal is one newton per square metre: 1 Pa=1 N m−21\,\text{Pa}=1\,\text{N m}^{-2}1Pa=1N m−2.
Force and area have opposite effects
- At constant area, a larger normal force produces a larger pressure, so P∝FP\propto FP∝F.
- At constant force, a larger contact area spreads the force and produces a smaller pressure, so P∝1AP\propto\dfrac{1}{A}P∝A1.
- A sharp blade creates high pressure through a small area, while wide tyres reduce pressure on soft ground by increasing area.
Example
Calculating pressure
- A crate exerts a normal force of 720 N720\,\text{N}720N over an area of 0.24 m20.24\,\text{m}^20.24m2.
- P=FA=7200.24=3000 PaP=\dfrac{F}{A}=\dfrac{720}{0.24}=3000\,\text{Pa}P=AF=0.24720=3000Pa.
Rearrange and convert areas correctly
- Use F=PAF=PAF=PA to find force and A=FPA=\dfrac{F}{P}A=PF to find area.
- For areas, square the length conversion: 1 cm2=1×10−4 m21\,\text{cm}^2=1\times10^{-4}\,\text{m}^21cm2=1×10−4m2 and 1 mm2=1×10−6 m21\,\text{mm}^2=1\times10^{-6}\,\text{m}^21mm2=1×10−6m2.
Common Mistake
Do not divide by a length when the equation requires an area, and do not convert square units using the unsquared conversion factor.
Comparisons must control one variable
- When comparing designs, identify whether force or area is unchanged, then link the changed quantity to pressure.
- Show the equation, conversion, substitution and unit because a correct numerical value without Pa\text{Pa}Pa can lose a unit mark.
Self review
- What equation links pressure, force and area?
- What is one pascal?
- How does doubling area affect pressure at constant force?
- How is 1 cm21\,\text{cm}^21cm2 converted to square metres?
