Caleb M. answered • 05/31/14
Tutor
5.0
(102)
Mathematics Tutor
Pressure is the ratio of force and area. Meaning, pressure is the force per area. Therefore, we have
Pressure = Force / Area
We know the sub's window is a circular window. A circle has area A= Pi* r^2. So we have
Pressure = Force / ( Pi * r^2 )
We know the window can withstand 30,000N of force, this gives us
Pressure = 30000 / (Pi * 0.5^2) = 38,197.2
The units are the units of force, N, divided by the units of area, m^2. So our answer has units of N/m^2 or Pascals. Rounding appropriately, our answer is 38,200 Pa or 38.2 kPa. This is about the pressure required from a long-duration blast needed to cause most buildings to collapse.
Caleb M.
No one claimed that the numbers in the problem were realistic! But as for the final sentence, it was for general interest. I do not claim to it's exact accuracy but would be willing to believe it. This information was taken from WolframAlpha upon entering 38.2 kPa which then gave:
'1.1 x long-duration blast overpressure level needed to cause most buildings to collapse'
I could have easily misinterpreted the information. However, it is more lively the 30,000N is unrealistic. This force is on par with the force of a baseball bat hitting a ball. I would be willing to bet a major league swinger could not shatter a sub window with a bat - or one would hope. Meaning the 30,000N is far too low for a real submarine window. But all this is what makes 'real world' problems fun! Thank you for your input.
Report
05/31/14
Peter H.
05/31/14