A lady weighting 115 lbs is using a pair of high heel shoes. The area where the foot feels the most stress has a circular pattern with a diameter of 2.25 in. What is the stress exerted on one foot?
a. 28.9 lbs/in^2
b. 51.1 lbs/in^2
c. 57.8 lbs/in^2
d. 103.0 lbs/in^2
If she is standing still on both feet
area = 2 * pi d^2/4 = 7.95 in^2 total area of both feet
we spread 115 pounds over that area so
115/7.95 = 14.5 pounds/in^2
BUT
if she puts the whole 115 pounds on one foot (like walking) 7.95/2 = 3.98 in^2
115 / 3.98 = 28.9 pounds/in^2
just looking at the choices, the units are lbs/in^2, as in pounds over the area. area of circle=pi*r^2. pi=3.14. the diameter is 2.25, so the radius is 2.25/2=1.125. plug that into area of circle=pi*r^2=3.14*1.125^2=3.974.
115 pounds / 3.974in^2=28.9 lbs/in^2
To find the stress exerted on one foot, we need to calculate the pressure exerted by the lady's weight on the circular area where the foot feels the most stress.
The formula to calculate pressure is:
Pressure = Force / Area
First, we need to calculate the force exerted by the lady's weight on one foot. We know that the lady weighs 115 lbs, so the force exerted on one foot is equal to her weight, which is 115 lbs.
Next, we need to calculate the area of the circular pattern where the foot feels the most stress. The diameter is given as 2.25 in, so the radius (r) of the circle is half the diameter, which is 2.25 / 2 = 1.125 in. The area of the circle can be calculated using the formula:
Area = π * (radius)^2
Substituting the radius value, we have:
Area = π * (1.125)^2
Area ≈ 3.977 in^2
Now, we can substitute the values of force (115 lbs) and area (3.977 in^2) into the pressure formula:
Pressure = 115 lbs / 3.977 in^2
Using a calculator to perform the division, we find:
Pressure ≈ 28.965 lbs/in^2
Therefore, the stress exerted on one foot is approximately 28.965 lbs/in^2.
Rounding this value to the nearest tenth, the correct answer is:
a. 28.9 lbs/in^2