Question

A 54.0-kg woman wearing high-heeled shoes is invited into a home in which the kitchen has vinyl floor covering. The heel on each shoe is circular and has a radius of 0.460 cm. (a) If the woman balances on one heel, what pressure does she exert on the floor?

Answer 1

To calculate the pressure exerted by the woman on the floor, we can use the formula: Pressure = Force/Area. After substituting the given values, we find that the woman exerts a pressure of 8.00 x 10^6 Pa on the floor.

Step-by-step explanation:

To calculate the pressure exerted by the woman on the floor, we can use the formula:

Pressure = Force/Area

Force = Weight = mass x acceleration due to gravity

Area = pi x radius^2

Substituting the given values, we have:

Mass = 54.0 kg

Radius = 0.460 cm = 0.0046 m

Area = pi x 0.0046^2 = 6.62 x 10^-5 m^2

Weight = 54.0 kg x 9.8 m/s^2 = 529.2 N

Pressure = 529.2 N / 6.62 x 10^-5 m^2

Pressure = 8.00 x 10^6 Pa

Therefore, the woman exerts a pressure of 8.00 x 10^6 Pa on the floor.

Answer 2

Pressure = (total force on an area) / (the area of the area)

Force = the woman's weight

Weight = (mass) x (gravity) .

Weight = (54 kg) x (9.8 m/s²)

Weight = 529.2 Newtons

Area of a circle = (π) x (radius)²

Area of the bottom of the heel = (π) x (0.46 cm)²

Area of the bottom of the heel = 0.665 cm² = 0.0000665 m²

Pressure = (force) / (area)

Pressure = (529.2 N) / (6.65 x 10⁻⁵ m²)

Pressure = 7,960,756 N/m²

Pressure = 7.96 x 10⁶ Pascals

Pressure = almost 79 atmospheres !

This is why many places don't allow spikey heels to be walked in across their floors. (Really. I'm not making this up.)