Kinetic Energy

Reference data and engineering information about kinetic energy for dynamics applications.

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Overview

Engineering reference data for Kinetic Energy in dynamics.

Key Formulas

Kinetic Energy

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

Energy of motion.

Work

$W = Fd\cos\theta$

Force × displacement × cos(angle).

Variables

Symbol	Description	Unit
$F$	Force	N
$m$	Mass	kg
$a$	Acceleration	m/s²
$v$	Velocity	m/s
$E_k$	Kinetic energy	J

Worked Examples

Example: Kinetic Energy in a Car

The kinetic energy of a vehicle increases with the square of its speed. This relationship has critical implications for vehicle safety.

A car with a mass of 1000 kg traveling at 70 km/h has a kinetic energy of: $E_t = \frac{1}{2} \times 1000\ \text{kg} \times \left(\frac{70\ \text{km/h} \times 1000\ \text{m/km}}{3600\ \text{s/h}}\right)^2 = 189,043\ \text{J}$
The same car at 90 km/h has a kinetic energy of: $E_t = \frac{1}{2} \times 1000\ \text{kg} \times \left(\frac{90\ \text{km/h} \times 1000\ \text{m/km}}{3600\ \text{s/h}}\right)^2 = 312,500\ \text{J}$

Key Insight: A speed increase of 28% results in a 65% increase in kinetic energy. This energy must be absorbed by the vehicle's safety structure in a crash. Survivability in a crash at 70 km/h does not imply survivability at 90 km/h.

Example: Object on a Conveyor Belt

A steel cube weighing 500 lb moves at 9 ft/s. Its mass is: $m = \frac{500\ \text{lb}}{32.1740\ \text{ft/s}^2} = 15.54\ \text{slugs}$

Its translational kinetic energy is: $E_t = \frac{1}{2} \times 15.54\ \text{slugs} \times (9\ \text{ft/s})^2 = 629\ \text{ft·lb}$

Example: Flywheel

A flywheel with moment of inertia $I = 0.15\ \text{kg·m}^2$ spins at 1000 rpm.

First, convert rotational speed to angular velocity ( $\omega$ ): $\omega = 1000\ \frac{\text{rev}}{\text{min}} \times \frac{0.01667\ \text{min}}{\text{s}} \times 2\pi\ \frac{\text{rad}}{\text{rev}} = 104\ \text{rad/s}$