Question

When you stifle a sneeze, you can damage delicate tissues because the pressure of the air that is not allowed to escape may rise by up to 45 kPa.

If this extra pressure acts on the inside ofyour 8.4-mm-diameter eardrum, what is the outward force?

answer in N's

Answer 1

Concepts and reason

The concept used to solve this problem is force and pressure. Initially, calculate the area of the eardrum by using the area of circle. Finally, calculate the outward force on the eardrum by using the relation between pressure and force.

Fundamentals

The pressure is given by the following expression:

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

Here, F is the force acting on a surface and A is the area.

The area of a circle is given by the following expression:

$A = \frac{{\pi {d^2}}}{4}$

Substitute 8.4 mm for d in the above expression.

$\begin{array}{c}\\A = \frac{{\pi {{\left( {8.4{\rm{ mm}}} \right)}^2}}}{4}{\left( {\frac{{1{\rm{ m}}}}{{1000{\rm{ mm}}}}} \right)^2}\\\\ = 5.54 \times {10^{ - 5}}{\rm{ }}{{\rm{m}}^2}\\\end{array}$

The pressure is given by the following expression:

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

Rearrange the above expression for F.

$F = PA$

Substitute 45 kPa for P and $5.54 \times {10^{ - 5}}{\rm{ }}{{\rm{m}}^2}$for A in the above expression.

$\begin{array}{c}\\F = \left( {45{\rm{ kPa}}} \right)\left( {\frac{{1000{\rm{ Pa}}}}{{1{\rm{ kPa}}}}} \right)\left( {5.54 \times {{10}^{ - 5}}{\rm{ }}{{\rm{m}}^2}} \right)\\\\ = 2.49{\rm{ N}}\\\end{array}$

Ans:

The outward force is 2.49 N.