Question

(I) The femur in the human leg has a minimum effective cross-section of about \({\bf{3}}{\bf{.0}}\;{\bf{c}}{{\bf{m}}^{\bf{2}}}\left( {{\bf{ = 3}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 4}}}}\;{{\bf{m}}^{\bf{2}}}} \right)\). How much compressive force can it withstand before breaking?

Short answer

The femur can withstand \(51 \times {10^3}\;{\rm{N}}\) force before breaking.

Step-by-step solution

Concepts

For this problem, you should use the relation between the compressive strength, force, and area, which is\({\bf{compressive}}\;{\bf{strength}} = \frac{F}{A}\).

Explanation

The cross-sectional area of the bone is \(A = 3.0 \times {10^{ - 4}}\;{{\rm{m}}^{\rm{2}}}\).

You know that the compressive strength of the bone is \(170 \times {10^6}\;{\rm{N/}}{{\rm{m}}^{\rm{2}}}\).

Suppose the bone can withstand F force before breaking.

Calculation

You know that

\(\begin{array}{c}\frac{F}{A} = {\rm{compressive}}\;{\rm{strength}}\\\frac{F}{{3.0 \times {{10}^{ - 4}}\;{m^2}}} = 170 \times {10^6}\;{\rm{N/}}{{\rm{m}}^{\rm{2}}}\\F = 51 \times {10^3}\;{\rm{N}}\end{array}\).

Hence, the femur bone can withstand \(51 \times {10^3}\;{\rm{N}}\) force before breaking.