Question

A 645 N person is wearing stiletto shoes. If she lifts her left leg, and rocks back onto the heel under her right leg, the pressure the heel exerts on the floor is 9000000 PA. what is the diameter of the circular base of the heel in centimeters?

Answer 1

The pressure by definition

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

so, the area of the base of the heel

$$A=\frac{F}{P}=\frac{645\:\rm N}{9000000\:\rm Pa}=7.17\times 10^{-5}\:\rm m^2.$$

The diameter of the base of the heel

$$A=\pi d^2/4,\quad d=\sqrt{4A/\pi},$$

$$d=\sqrt{4\times 7.17\times 10^{-5}/\pi}=0.0096\:\rm m=0.96\:\rm cm.$$