The total cross-sectional area of the load-bearing calcified...

The total cross-sectional area of the load-bearing calcified portion of the two forearm bones (radius and ulna) is approximately $2.4 \mathrm{~cm}^{2}$. During a car crash, the forearm is slammed against the dashboard. The arm comes to rest from an initial speed of $80 \mathrm{~km} / \mathrm{h}$ in $5.0 \mathrm{~ms}$. If the arm has an effective mass of $3.0 \mathrm{~kg}$ and bone material can withstand a maximum compressional stress of $16 \times 10^{7} \mathrm{~Pa}$, is the arm likely to withstand the crash?

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Key Concepts

Material Strength

Material strength signifies the maximum stress a material can endure before failing. In engineering and biomechanics, comparing the calculated stress with a material's strength is crucial to ensure that structures such as bones or engineered components can survive impact forces without breaking.

Deceleration and Impact Force

Deceleration is the rate at which an object’s velocity decreases. In collision events, a high deceleration over a short time results in significant forces acting on the object. Using Newton's second law (F = ma), these forces can be calculated, which is critical in assessing potential damage during impacts.

Impulse-Momentum Theorem

This theorem states that the change in an object's momentum is equal to the impulse applied to it, which is the product of the force and the time period over which it acts. It is fundamental in understanding how forces are transmitted during a rapid deceleration, such as in crash scenarios, by relating momentum loss to impact forces.

Stress Calculation

Stress is defined as the force applied per unit area. It is a key concept in determining how different materials or structures respond to external loads. In biomechanics and material science, calculating stress helps in evaluating whether a structure can withstand the applied load without failure.

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