Minimum area of a shoe heel exerting pressure

In summary: No, you haven't.But:Is that area the area under a SINGLE shoe?In summary, the smallest area of the sole of a heel that a lady of mass 60kg could wear without permanently damaging the floor is 8.4 x 10^-5 m^2.
  • #1
Molly1235
77
4

Homework Statement



The floor on a dance hall can take a pressure of 3.5 MPa before getting damaged. A lady of mass 60kg wears high heeled shoes. What is the smallest area of the sole of a heel she could wear such that it won't permanently damage the floor?

Homework Equations



Area = Force/Pressure

The Attempt at a Solution



3.5 MPa = 3500000 Pa

Force (weight) = 60 x 9.8 = 588N

But I don't know where to go from there...I tried just dividing Force by Pressure but got a different answer to that in the book. Thanks in advance to anyone that can help! :-)
 
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  • #2
We can't tell what you did unless you show us your calculations.
 
  • #3
... It will also help if you post the answer from the book.
 
  • #4
haruspex said:
... It will also help if you post the answer from the book.

The book said 8.4 x 10^-5 m^2, but I did 588 (force) / 3500000 (pressure) = 1.68 x 10^-4.

I'm feeling there's a step I'm missing but I'm not sure...
 
  • #5
Molly1235 said:
The book said 8.4 x 10^-5 m^2, but I did 588 (force) / 3500000 (pressure) = 1.68 x 10^-4.

I'm feeling there's a step I'm missing but I'm not sure...
You may have noticed that your answer is exactly twice that given in the book (as I suspected).
Why do you think that might be? Btw, I agree with your answer. Whoever wrote the book has outsmarted him/herself.
 
  • #6
He outsmarted me at least, although that isn't too difficult in the general case. Damn! :biggrin:
 
  • #7
haruspex said:
You may have noticed that your answer is exactly twice that given in the book (as I suspected).
Why do you think that might be? Btw, I agree with your answer. Whoever wrote the book has outsmarted him/herself.

Ah ok, so you don't think I've gone wrong? I was a little confused haha
 
  • #8
Molly1235 said:
Ah ok, so you don't think I've gone wrong? I was a little confused haha
No, you haven't.
But:
Is that area the area under a SINGLE shoe?
 

FAQ: Minimum area of a shoe heel exerting pressure

1. What is the minimum area of a shoe heel that exerts pressure?

The minimum area of a shoe heel that exerts pressure varies depending on factors such as the weight of the person wearing the shoe and the type of surface they are walking on. Generally, the smaller the area, the greater the pressure exerted.

2. How is the minimum area of a shoe heel determined?

The minimum area of a shoe heel is determined through a combination of mathematical calculations and experimental testing. This involves measuring the force applied by the heel on a surface and dividing it by the area of the heel in contact with the surface.

3. Why is the minimum area of a shoe heel important?

The minimum area of a shoe heel is important because it affects the stability and balance of a person while walking or standing. A smaller heel area can increase the pressure on a surface, making it more difficult for the person to maintain their balance and potentially leading to slips or falls.

4. How does the material of the shoe heel affect the minimum area?

The material of the shoe heel can have a significant impact on the minimum area required to exert pressure. Softer materials, such as rubber, tend to have a larger area in contact with the surface, while harder materials, such as metal, can exert greater pressure with a smaller area due to their stiffness.

5. Is there a standard minimum area for shoe heels?

There is no specific standard for the minimum area of a shoe heel. However, some industries, such as construction, may have regulations or guidelines for the minimum heel area on safety footwear to ensure proper stability and balance for workers.

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