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 1.50cm² and the woman’s mass is 55.0kg. Express the pressure in Pa.

1. 2.22×10³ Pa
2. 3.67×10³ Pa
3. 4.41×10³ Pa
4. 6.18×10³ Pa

Answer 1

The pressure exerted by the woman's heel is 3.6 × 10³ Pa, calculated using the force of gravity on her mass and the area of the heel.

Step-by-step explanation:

To calculate the pressure exerted on the floor by a woman's high-heeled shoe, we use the formula for pressure:

Pressure (P) = Force (F) / Area (A)

First, we need to convert the woman’s mass from kilograms to newtons to find the force, which is weight in this context. We do this using the gravitational constant (9.8 m/s2):

F = mass × gravity = 55.0 kg × 9.8 m/s2 = 539 N

Now convert the area of the heel to meters squared (m2):

1.50 cm2 = 1.50 × 10-4 m2

Now, calculate the pressure:

P = 539 N / 1.50 × 10-4 m2 = 3.593 × 103 N/m2 = 3.593 × 103 Pa

So, the pressure exerted by the heel is approximately 3.6 × 103 Pa, which is option 2, 3.67 × 103 Pa, since it's the nearest value provided in the options.