The heel on a pair of women’s shoes tapers from a radius of 1.75 cm down to a radius of 0.50 cm at the bottom. If 50% of the weight of a 600 N woman is supported by each heel, find the stress on each heel. Submit your answer in MPa.
whats the answer
To find the stress on each heel, we need to first determine the force supported by each heel.
Given that 50% of the weight of a 600 N woman is supported by each heel, each heel will support a force equal to half of the woman's weight.
Therefore, the force supported by each heel is:
Force per heel = 0.5 * 600 N = 300 N
Next, we can calculate the area of the bottom of each heel. The shape of the heel resembles a smaller circle on top of a larger circle, both with different radii.
The formula for the area of a circle is:
Area = π * radius^2
The area of the larger circle with a radius of 1.75 cm is:
Area of larger circle = π * (1.75 cm)^2
The area of the smaller circle with a radius of 0.50 cm is:
Area of smaller circle = π * (0.50 cm)^2
Now, to find the area of the heel, we subtract the area of the smaller circle from the area of the larger circle:
Area of the heel = Area of larger circle - Area of smaller circle
Finally, we can calculate the stress on each heel using the formula:
Stress = Force / Area
Let's plug in the values:
Stress = 300 N / (Area of the heel)
To convert the answer to MPa (megapascals), we divide the stress value by 1,000,000.
Therefore, the stress on each heel in MPa is:
Stress = (300 N / Area of the heel) / 1,000,000