a 645 N person is wearing stiletto shoes. If she lifts her left leg, and rocks back onto the heel under her right leg, the pressure the heel exerts on the floor is 9000000 PA. what is the diameter of the circular base of the heel in centimeters?

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a 645 N person is wearing stiletto shoes. If she lifts her left leg, and rocks back onto the heel under her right leg, the pressure the heel exerts on the floor is 9000000 PA. what is the diameter of the circular base of the heel in centimeters?

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quasarJose quasarJose · Answer 1 · 2025-03-27T14:03:08-04:00

Answer:

0.96cm

Explanation:

Given parameters:

Weight of person = 645N

Pressure of the heel = 9000000PA

Unknown

Diameter of the circular base = ?

Solution

Pressure is the force per unit area of a body.

Pressure = [tex]\frac{Force}{Area}[/tex]

To solve this problem, find the unknown area of the circle;

Pressure x Area = Force

Area = [tex]\frac{Force}{Pressure}[/tex]

Area = [tex]\frac{645}{9000000}[/tex] = 7.17 x 10⁻⁵m²

Note: 1Pa = 1Nm⁻²

Now;

Area of a circle = π r²

r = [tex]\frac{d}{2}[/tex]

Area = π x [tex]\frac{d^{2} }{4}[/tex]

d is the diameter

d² = 4 x Area x (1/π)

d² = 4 x 7.17 x 10⁻⁵ x (1/3.14) = 9.13 x 10⁻⁵

d = 0.0096m

To cm;

100cm = 1m

0.0096m; 0.0096 x 100= 0.96cm