Question

As a woman walks, her entire weight is momentarily placed on one heel of her high-heeled shoes. Calculate the pressure exerted on the floor by the heel if it has an area of 1.60 cm2 and the woman's mass is 54.0 kg. Express the force in N/m2 and lb/in2. (In the early days of commercial flight, women were not allowed to wear high-heeled shoes because aircraft floors were too thin to resist such large pressures.)

Answer 1

P = 3.3075 x 10⁶ N/m² = 479.71 lb/in²

Step-by-step explanation:

In order to find the pressure , we first need to find the force exerted by the lady. The force must be equal to the weight of the lady:

Force = F = Weight = mg

F = mg = (54 kg)(9.8 m/s²)

F = 529.2 N

Now, we convert area to S.I unit:

Area = A = (1.6 cm²)(1 m/100 cm)²

A = 1.6 x 10⁻⁴ m²

Now, the pressure can be calculated as:

Pressure = P = F/A

P = 529.2 N/1.6 x 10⁻⁴ m²

P = 3.3075 x 10⁶ N/m²

Now, we convert this into lb/in²:

P = (3.3075 x 10⁶ N/m²)[(0.000145038 lb/in²)/(1 N/m²)

P = 479.71 lb/in²