Impact Force

Overview

Engineering reference data for Impact Force in dynamics.

Key Formulas

Newton's Second Law

$F = ma$

Force = mass × acceleration.

Kinetic Energy

$E_k = \frac{1}{2}mv^2$

Energy of motion.

Momentum

$p = mv$

Mass × velocity.

Work

$W = Fd\cos\theta$

Force × displacement × cos(angle).

Variables

Examples and Applications

Car Crash Impact Analysis

Consider a 2000 kg vehicle traveling at 60 km/h (16.7 m/s) colliding with a rigid barrier:

• Crumple zone deformation: 0.5 m
• Average impact force calculation: $F_{\text{avg}} = \frac{1}{2} m v^2 / s = \frac{1}{2} \times 2000 \, \text{kg} \times (16.7 \, \text{m/s})^2 / 0.5 \, \text{m} = 558 \, \text{kN}$

Comparative analysis:

• Vehicle weight: $F_w = mg = 2000 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 19.6 \, \text{kN}$
• Impact force ratio: $558 \, \text{kN} / 19.6 \, \text{kN} \approx 28.5g$

Safety note: The NHTSA maximum chest acceleration limit is 60g for durations >3 milliseconds.

Falling Object Impact

The kinetic energy at ground impact equals potential energy:

$E = F_{\text{weight}} h = m a_g h$

Where $a_g = 9.81 \, \text{m/s}^2$ (standard gravity).

Equivalence insight: A 90 km/h vehicle collision compares to a 32 m vertical drop.

Practical example - Person falling from a table:

• Mass: 90 kg
• Fall height: 1.2 m
• Impact deformation: 2 cm (0.02 m)
• Energy: $E = 90 \times 9.81 \times 1.2 = 1059 \, \text{J}$
• Average force: $F_{\text{avg}} = 1059 / 0.02 = 53 \, \text{kN}$

Key Engineering Insight

The deformation distance ($s$) is the critical variable controlling impact forces. Doubling the crumple zone reduces peak forces by approximately half for the same impact energy. This principle informs automotive safety design, protective equipment, and packaging engineering.

References

• Original Source