Question

The contraction of the left ventricle (chamber) of the heart pumps blood to the body. Assuming that the inner surface of the left ventricle has an area of \({\bf{82}}\;{\bf{c}}{{\bf{m}}^{\bf{2}}}\) and the maximum pressure in the blood is 120 mm-Hg, estimate the force exerted by that ventricle at maximum pressure.

Short answer

The force exerted by that ventricle at maximum pressure is \(130.8\;{\rm{N}}\).

Step-by-step solution

Given Data

The area of inner surface of left ventricle is \(A = 82\;{\rm{c}}{{\rm{m}}^2}\).

The maximum pressure is \(P = 120\;{\rm{mm - Hg}}\).

Understanding the relation of force and pressure

In this problem, the relation of force with pressure and cross-sectional area will be used to find the force exerted by the ventricle at maximum pressure.

Calculating the force exerted by the ventricle

The relation to find force is given by,

\(F = PA\)

On plugging the values in the above relation.

\(\begin{array}{l}F = \left( {120\;{\rm{mm - Hg}} \times \frac{{133\;{\rm{N/}}{{\rm{m}}^2}}}{{1\;{\rm{mm - Hg}}}}} \right)\left( {82\;{\rm{c}}{{\rm{m}}^2} \times \frac{{1\;{{\rm{m}}^2}}}{{{{10}^4}\;{\rm{c}}{{\rm{m}}^2}}}} \right)\\F = 130.8\;{\rm{N}}\end{array}\)

Thus, the force exerted by that ventricle at maximum pressure is \(130.8\;{\rm{N}}\).