Chemistry/Physics Problem...

[jamesbond007]

Hey guys! In my chemistry class, we are assigned this problem and I'm not sure how to go about setting up the equation. The problem reads: a 600lb man with 10" long shoes exerts exactly 1 atm of pressure. How wide are his shoes? (express answer in cm)

http://wine1.sb.fsu.edu/chm1045/notes/Gases/IdealGas/Gases04.htm

I'm currently reading this page as my teacher's notes aren't the greatest, but can't make sense of the problem at 12:19AM. 😛

Can anyone lend a helping hand?

Thanks!
~Travis

 

[hypn0tik]

Pressure = Force / Area.

Careful of units though. He is 600 pounds, one dimension of his shoe is given in inches while the pressure is given in atmospheres. They want the other dimension in centimeters. WTF?

Also, I'm going to assume rectangular shoe.

 

[zephyrprime]

Yeah, are the shoes rectangular?

anyway,

600lbs/(10"*width*2) = 1 atmosphere of pressure measured in lbs/in^2

Then just convert inches to cm. (2.54c, = 1 in)

The problem doesn't have anything to do with gas laws.

 

[jamesbond007]

yeah, I'm also assuming rectangular shoe as well. I figured 272.727kg as his weight.

So far I got 1atm=272.727/10n

That'd mean his shoe is 27.2727cm wide?

EDIT:

zephyrprime, with that, I got width=30, so that came out to 76.2, which isn't the right answer. =/ (nor is 27.272cm)

 

[jagec]

Tell them the question isn't well defined, since it doesn't mention the shape or loading of the shoes.

 

[hypn0tik]

Originally posted by: jagec
Tell them the question isn't well defined, since it doesn't mention the shape or loading of the shoes.

I'm willing to bet you have to assume uniform distribution of the load. Shape of the shoes it up for grabs, but if they gave you a length and want the width, it's probably rectangular in shape.

 

[jamesbond007]

Ok, I fixed an error from above.

I have 1atm = 272.727kg/(25.4*width)

I got 10.73728...cm, but it still is 'wrong' according to our answering system. (Blackboard) It says to round to the nearest 3 significant digits, but to be honest, I suck at those. I tried 10.7 and 10.737 and it's still wrong. =/

 

[hypn0tik]

Originally posted by: jamesbond007
Ok, I fixed an error from above.

I have 1atm = 272.727kg/(25.4*width)

I got 10.73728...cm, but it still is 'wrong' according to our answering system. (Blackboard) It says to round to the nearest 3 significant digits, but to be honest, I suck at those. I tried 10.7 and 10.737 and it's still wrong. =/

Convert everything to SI units.

Atmospheres into Pascals, pounds to kilograms, inches to meters.

You'll get your answer in meters, so convert that to cm.

 

[jamesbond007]

Originally posted by: hypn0tik

Originally posted by: jamesbond007
Ok, I fixed an error from above.

I have 1atm = 272.727kg/(25.4*width)

I got 10.73728...cm, but it still is 'wrong' according to our answering system. (Blackboard) It says to round to the nearest 3 significant digits, but to be honest, I suck at those. I tried 10.7 and 10.737 and it's still wrong. =/

Convert everything to SI units.

Atmospheres into Pascals, pounds to kilograms, inches to meters.

You'll get your answer in meters, so convert that to cm.

I converted 1atm into pascals and came up with 101325.010007 pascals...does that sound right? So I ran through 101325.010007=272.727/(.254*width) and it was .010596

So, I entered 1.059 and tried 1.06 and that still didn't work! :|

 

[Howard]

I get 10.374cm.

Usually when I work with Pascals, I write the unit down as N/m^2. If you write down all the units, it'll be easy to divide them out and manipulate them. So you have Newtons, meters, kg. Convert kg into Newtons and after you divide everything out you should have meters. Then multiply by 100 for cm.

 

[jamesbond007]

Originally posted by: Howard
I get 10.374cm.

Usually when I work with Pascals, I write the unit down as N/m^2. If you write down all the units, it'll be easy to divide them out and manipulate them. So you have Newtons, meters, kg. Convert kg into Newtons and after you divide everything out you should have meters. Then multiply by 100 for cm.

I tried entering 10.374 and 10.4 (since we have to work it out to 3 significant digits), but no dice. I guess we usually work with the basic metric system, for the most part, in class. (kg, cm or m, km, etc) My instructor hasn't mentioned anything about Pascals, so I don't know if we should have to go that far. I'm reading some posts in our Chemistry discussion board and no one has said they've got an answer that works. A lot of people have 10.x as an answer, but nothing has given them the points for the problem. Ah well, perhaps a visit to the professor will fix this mystery problem.

Thanks for the help everyone! 😀

 

[Howard]

Originally posted by: jamesbond007

Originally posted by: Howard
I get 10.374cm.

Usually when I work with Pascals, I write the unit down as N/m^2. If you write down all the units, it'll be easy to divide them out and manipulate them. So you have Newtons, meters, kg. Convert kg into Newtons and after you divide everything out you should have meters. Then multiply by 100 for cm.

I tried entering 10.374 and 10.4 (since we have to work it out to 3 significant digits), but no dice. I guess we usually work with the basic metric system, for the most part, in class. (kg, cm or m, km, etc) My instructor hasn't mentioned anything about Pascals, so I don't know if we should have to go that far. I'm reading some posts in our Chemistry discussion board and no one has said they've got an answer that works. A lot of people have 10.x as an answer, but nothing has given them the points for the problem. Ah well, perhaps a visit to the professor will fix this mystery problem.

Thanks for the help everyone! 😀

A Pascal is equivalent to a pressure of one Newton applied uniformly on an area of one square meter - i.e. 1 Pa = 1 N/m^2

If you change all the units to SI units (m, kg, N) everything is much easier to work with. If you still don't get the right answer, I would ask the prof.