5.4 Harder questions on Pressure

5.4 Harder questions on Pressure

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

NOTE: convert from cm2 to m2 you need to divide by 10000

P = F / A

1) Ordinary shoe heel pressure: F = 40 kg = 400N, Area = 0.05 x 0.05 = 0.0025 m2

P = F / A

= 400 / 0.0025

= 160,000 Pa (N/m2)

2) An elephant: F = 500 kg = 5000N, Area = 0.1 x 0.1 x pi = 0.01 pi

P = F / A

= 5000 / 0.01pi

= 159,154 Pa

= 160,000 Pa (2 sf)

3) High-heeled shoe: F = 40 kg = 400N, Area = 0.5 cm2 = 0.00005 m2

P = F / A

= 400 / 0.00005

= 8,000,000 Pa

4000 kPa = 4,000,000 Pa

High-heeled shoe will do the damage!