Question

A woman walks into a carpet store wearing high-heeled shoes with a circular heel of diameter 0.987 cm. To the dismay of the store manager, she balances on one heel on an expensive carpet sample. If she has a mass of 53.0 kg, determine the pressure she exerts on the carpet sample.

Answer 1

To solve this problem it is necessary to apply the concepts related to the Pressure which describes the amount of Force made on an area unit.

Its mathematical expression can be defined as

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

Where,

F= Force

A = Area

Our values are given as

$d = 0.987*10^{-2}m$

With the diameter we can find the Area of the circular heel, that is

$A = \pi (\frac{0.987*10^{-2}}{2})^2$

$A = 7.6511*10^{-5}m^2$

To find the force by weight we need to apply the Newton's second Law

$F = mg$

$F = 53*9.8$

$F = 519.4N$

Finally the pressure would be

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

$P = \frac{519.4}{7.6511*10^{-5}}$

$P = 6788566.35Pa$

$P = 6.788MPa$

Therefore the pressure that she exerts on the carpet sample is 6.788Mpa