As a woman walks, her entire weight is momentarily supported on the heel of one shoe. Calculate the pressure exerted on the floor by a high-heel shoe worn by a 50-kg woman if the heel has an area of 2.0cm^2. Express the pressure in newtons per square meter and atmospheres.
I am using the formula :
P= F/A => F=mg A= 3.14(r^2)
M-50 kg
g=9.8 m/sec^2
r^2- (2cm^2)^2
I have the answer in my book so I know I'm not getting the formula right and I don't know why. Can someone please help me.
Thank you!
Heel pressure = (weight)/(heel area)
The heel area must be expressed as 2*10^-4 m^2. The heel pressure is M*g/2*10^-4 m^2
The dimensions wil be Pascals if M is in kg and g is 9.8 m/s^2.
I get it now! lol Thank you!
(50 kg)(9.8 m/sec^2)
____________________
(2.0m *10^-4)
=>
2.45 * 10^6 N-m or Pa
98
To calculate the pressure exerted on the floor by a high-heel shoe, you're on the right track with the formula P = F / A, where P is the pressure, F is the force, and A is the area.
First, let's find the force (F) exerted on the floor by the woman's shoe. The force can be calculated using the formula F = m * g, where m is the mass and g is the acceleration due to gravity.
Given:
m = 50 kg (mass of the woman)
g = 9.8 m/s^2 (acceleration due to gravity)
F = 50 kg * 9.8 m/s^2 = 490 N
Now, let's find the area (A) of the heel. You mentioned that the heel has an area of 2.0 cm^2. However, it's important to convert this area to square meters for consistency. Recall that 1 cm = 0.01 m, so 1 cm^2 = (0.01 m)^2 = 0.0001 m^2.
A = 2.0 cm^2 * 0.0001 m^2/cm^2 = 0.0002 m^2
Now, we can substitute the values of F and A into the formula P = F / A to find the pressure (P) in newtons per square meter (N/m^2):
P = 490 N / 0.0002 m^2 = 2,450,000 N/m^2 (or Pascal, Pa)
To convert the pressure to atmospheres, you need to know that 1 atmosphere is equal to 101,325 Pa. So, to express the pressure in atmospheres, divide the pressure (in Pa) by 101,325:
P (in atmospheres) = 2,450,000 N/m^2 / 101,325 N/m^2/atm ≈ 24.17 atm.
Therefore, the pressure exerted on the floor by the high-heel shoe worn by the 50 kg woman is approximately 2,450,000 N/m^2 (or Pa) and 24.17 atm.