Minimum area of a shoe heel exerting pressure

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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! :-)
 

Answers and Replies

  • #2
SteamKing
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We can't tell what you did unless you show us your calculations.
 
  • #3
haruspex
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... It will also help if you post the answer from the book.
 
  • #4
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... 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
haruspex
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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
arildno
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He outsmarted me at least, although that isn't too difficult in the general case. Damn! :biggrin:
 
  • #7
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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
arildno
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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?
 

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