Penetration of spheres into loose granular media

We study the penetration of steel spheres dropped vertically into a container of loosely packed, small glass beads. We find that the penetration depth of the spheres increases linearly with the incident momentum of the projectile, but with a zero-momentum intercept which can be either positive or negative. This behavior can be understood by modeling the granular medium as a fluid with a yield stress and an effective viscosity. We derive the scaling behavior of the viscosity and find agreement with our experimental results. We also explain the zero-momentum intercept in terms of the rheology of the granular medium.