A Question regarding stress/cross sectional area

[FaroukYasser]

Homework Statement

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.

Homework Equations

Stress = Force/ Cross sectional area

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?

 

[Chestermiller]

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

 

[FaroukYasser]

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

 

[Chestermiller]

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