pressure and high heels

We deviated from the script a little this week to look at how choice of shoes can affect the pressure put on the ground beneath your feet.  If we know the size of the force (F) and the area over which the force is applied (A), then we can calculate pressure using

$P = \displaystyle {F \over A}$

So when we start talking about shoes, we need to figure out the surface area of the footwear.  Luckily, Caitlin had flat-soled shoes on and volunteered to provide data for our calculation.  Here is the outline of her shoe, it’s drawn on graph paper so that the area can be calculated quickly by counting the large squares.  Each large square is 1 square centimetre – we counted the approximate area by considering only whole squares inside the black outline of the shoe.

Assuming a mass of 50kg, the pressure when wearing the flat shoes is

$P = \displaystyle {{(50 \times 9.8)N} \over {0.0306m^2}} = 16000Nm^{-2}$

The red shaded area of our photo shows the reduction in area when heels are worn.  With heeled shoes, the area is reduced to approximately 1 square cm per shoe.  The change in the pressure is staggering:

$P = \displaystyle {{(50 \times 9.8)N} \over {(0.0002)m^2}} = 2450000Nm^{-2}$

The Science Babe has made a video on this topic.  Good physics in here, although I’m not sure she can claim the equation shown above is Newton’s 2nd law.   What do you think?