Pressure: Question 2

Worked solution

Part (a): The pressure equation

Pressure is defined as force per unit area, acting at right angles to a surface:

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

Pressure is measured in pascals ($\text{Pa}$), where $1\text{ Pa} = 1\text{ N/m}^2$.

Part (b): Calculating the pressure at the cutting edge

First convert the contact area into square metres. Since $1\text{ m}^2 = 10\,000\text{ cm}^2$:

$0.03\text{ cm}^2 = \frac{0.03}{10\,000}\text{ m}^2 = 3\times10^{-6}\text{ m}^2$

Now substitute into $p = F/A$:

$p = \frac{45\text{ N}}{3\times10^{-6}\text{ m}^2} = 1.5\times10^{7}\text{ Pa}$

This huge value (about 150 times atmospheric pressure) shows just how large a pressure a small force can produce when it acts over a tiny area.

Part (c): Why sharpening increases the pressure

The force the woodworker applies is unchanged. What changes is the area of contact: a sharpened edge comes to a very thin line, so the same force is now squeezed into a much smaller area than a blunt edge would give. Because $p = F/A$, reducing the area (with the force fixed) increases the pressure produced at the edge. This much greater pressure is what allows the blade to push into, and separate, the fibres of the wood, a blunt edge spreads the same force over a wider area, producing a much lower pressure that tends to crush rather than cut the wood.

Final answers

• (a) $p = F/A$; pressure is measured in pascals ($\text{Pa}$)
• (b) Pressure at the edge $=$ $1.5\times10^{7}\text{ Pa}$
• (c) A sharpened edge has a much smaller contact area, so for the same force the pressure produced is much greater, letting the blade cut into the wood more easily