# A Question regarding stress/cross sectional area

1. May 14, 2014

### FaroukYasser

1. The problem statement, all variables and given/known data
A cylindrical rod has a spherical bubble in it. as illustrated in figure 4.2 (in the attachments)
The rod has a cross sectional area of 3.2 x 10^-6 m^2 and is stretched by forces of magnitude 1.9 x 10^3 N.
The maximum Stress that the cylinder can take is 9.5 x 10^8 Pascals.
2. Relevant equations
Stress = Force/ Cross sectional area

3. The attempt at a solution
Basically what I did was say:
Maximum stress = Force applied/Area
9.5 x 10^8 = 1.9 x 10^3 / Minimum area
Minimum area = 2 x 10^-6 m^2
So the maximum Cross sectional area of a rod is 2 x 10^-6 m^2

The right answer was on the other hand to do all this + subtract new area from old area so it becomes (3.2 - 2) x 10^-6 = 1.2 x 10^-6
This is the part I don't understand. Shouldn't the maximum cross section of the ball be the area of the new cylinder so that if it is more then the cylinder breaks???

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2. May 14, 2014

### Staff: Mentor

Hi Farouk,

I'd like to help with this, but I don't see the actual question that is being asked. What are they asking you to find?

Chet

3. May 15, 2014

### FaroukYasser

Sorry forgot to include it . It was: what is the maximum cross section of the ball.
Its really vague what is asked here :/

4. May 15, 2014

### Staff: Mentor

The bubble can't support any stress, so all the stress must be carried by the 2x10-6 m2 of rod material surrounding the bubble. That leaves 1.2x10-6 m2 cross sectional area available for the bubble.

Chet