Minimum area of a shoe heel exerting pressure

[Molly1235]

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! :-)

 

[SteamKing]

We can't tell what you did unless you show us your calculations.

 

[haruspex]

... It will also help if you post the answer from the book.

 

[Molly1235]

... 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...

 

[haruspex]

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.

 

[arildno]

He outsmarted me at least, although that isn't too difficult in the general case. Damn!

 

[Molly1235]

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

 

[arildno]

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?