Question

stress and biomechanics
in the physical world, stress is pressure or tension that is placed on something. biomechanical engineering is a field that studies mechanical stress. in one branch of this field, engineers apply their understanding of statics, dynamics, and fluid flow to solve difficult problems of the heart and blood vessels. think of your heart as a pump and your blood vessels as pipelines. the pump and pipelines need to be in good working order so blood can carry nutrients and oxygen to cells of your body.
imagine that youre a biomechanical engineer. you want to determine how much pressure, or stress, a certain membrane can withstand before bursting. the membrane could belong to a blood vessel or even the human heart. the membrane acts like a balloon thats being inflated: just enough air will sufficiently inflate the balloon. too much air will cause the skin of the balloon to tear, popping the balloon. in this task, you will assign some numbers to this situation to further your understanding of mechanical stress.
part a
one kind of stress is called pressure. pressure is calculated as force divided by area. force is a push or a pull. it is measured in units such as pounds or newtons. area is measured in units such as square inches or square meters. the equation for calculating pressure is $p = \frac{f}{a}$ where $p$ is pressure, $f$ is force, and $a$ is area.
use the equation to calculate the average pressure on the membrane below. express your answer in units of pounds per square inch (psi).
$f = 60$ lb.
$a = 24$ sq.in.
part b
heres another kind of pressure problem. a force of 22 pounds presses on a membrane. the average pressure on the membrane is 2.75 pounds per square inch (psi). what is the area of the membrane in square inches? the equation for calculating pressure is $p = \frac{f}{a}$ where $p$ is pressure, $f$ is force, and $a$ is area.
$f = 22$ lb.
$a = ?$ sq.in.

Explanation:

Step1: Identify values for Part A

Given $F = 60$ lb and $A=24$ sq.in.

Step2: Substitute values into pressure formula

$P=\frac{F}{A}=\frac{60}{24}$

Step3: Calculate pressure for Part A

$P = 2.5$ psi

Step4: Identify values for Part B

Given $F = 22$ lb and $P = 2.75$ psi.

Step5: Rearrange pressure formula for area

$A=\frac{F}{P}$

Step6: Substitute values into area - formula for Part B

$A=\frac{22}{2.75}$

Step7: Calculate area for Part B

$A = 8$ sq.in.

Answer:

Part A: 2.5 psi
Part B: 8 sq.in.