Contact Area of Particle-Plane Impact

June 8, 2016July 31, 2018

A particle of radius R impacts a wall with some velocity, $V_{impact}$ . The penetration length is defined as $\delta$ . The contact area radius is defined by $a$ .

Using Pythagorean Theore parparimpact m, the contact radius is defined by:

$a^2 + (R - \delta)^2 = R^2$

$a^2 = R^2 - (R-\delta)^2$

$a^2 = R^2 - (R^2 -2R \delta + \delta^2)$

$a^2 = 2R \delta - \delta^2$

If $\delta$ is small then $\delta^2$ is even smaller and we may omit it. Therefore, $a^2 = 2R \delta$ and the cross sectional area is defined by: $A_0 = \pi a^2 = 2 \pi R \delta$ .