We report on craters formed by balls dropped into dry, non-cohesive, granular media. By explicit variation of ball density $\rho_{ b}$, diameter $D_{ b}$, and drop height $H$, the crater diameter is confirmed to scale as the 1/4 power of the energy of the ball at impact: $D_{ c}\sim(\rho_{ b}{ D_{ b}}^{ 3}H)^{ 1/4}$. Against expectation, a different scaling law is discovered for the crater depth: $d\sim({ \rho_{ b}}^{ 3/2}{ D_{ b}}^{ 2}H)^{ 1/3}$. The scaling with properties of the medium is also established. The crater depth has significance for granular mechanics in that it relates to the stopping force on the ball.
Categories: cond-mat.soft