Frazer does Physics: 5.4 Pressure

October 23, 2011

Recall and use the relationship between pressure, force and area:

$Pressure=\frac{force}{area}$

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

NB: 1N/m² = 1Pa

Using the Formula

Calculate the pressure generated by an ordinary shoe heel (person of mass 40kg, heel 5cm x 5cm), an elephant (of mass 500kg, foot of 20cm diameter) and a high-heeled shoe (person of mass 40kg, heel area 0.5cm²). Which ones will damage a wooden floor that starts to yield at a pressure of 4000 kPa?

1. Ordinary shoe heel

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

$F=40kg\times 10N/kg=400N$

$A=0.05m\times 0.05m=0.0025m^{2}$

$p=400/0.0025$

$p=160,000N/m^{2}$

$p=160kPa$

2. Elephant

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

$F=500kg\times 10N/kg=5000N$
$A=\pi r^{2}=\pi 0.1^{2}=0.01\pi$
$p=5000/0.01\pi$
$p=159,154.9Pa$
$p\approx 159kPa$

3. High-heeled shoe

$p=\frac{F}{A}$
$F=40kg\times 10N/kg=400N$

$A=0.5cm^{2}=0.00005m^{2}$
$p=400/0.00005$
$p=8,000,000Pa$
$p=8,000kPa$
$p=8MPa$

Clearly one can see that the high-heeled show will do the most damage to the floor.

Frazer does Physics

October 23, 2011

5.4 Pressure

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