Question

A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor?

Answer 1

Mass of girl, m = 50 kg

∴Force on the heel, F = mg = 50 x 9.8 = 490 N

Diameter, D = 1.0 cm = `1 xx 10^(-2)m`

`:. "Area A"  =(piD^2)/4 = (3.14xx(1xx10^(-2))^2)/4 = 7.85 xx 10^(-5) m^2`

`:. "Pressure", P = F/A = 490/(7.85xx10^(-5)) = 6.24xx10^6 "Pa"`

Answer 2

Mass of the girl, m = 50 kg

Diameter of the heel, d = 1 cm = 0.01 m

Radius of the heel = `r = d/2 = 0.005 m`

Area of the heel = `pir^2`

= π (0.005)²

= 7.85 × 10^–5 m²

Force exerted by the heel on the floor:

F = mg

= 50 × 9.8

= 490 N

Pressure exerted by the heel on the floor:

`P = "Force"/"Area"`

`= 490/(7.85xx10^(-5))`

= 6.24 × 10⁶ N m^–2

Therefore, the pressure exerted by the heel on the horizontal floor is  6.24 × 10⁶ Nm^–2.