Measurements of Stopping Force on Ball on Impact with Granular Medium

We present direct measurements of the deceleration vs. time of a 3.8 cm diameter brass ball plunging into a loose granular bed of 400 - 600 $\mu $m glass beads. Data were obtained using an accelerometer chip housed within the ball. As suggested by Durian and co-workers, the measured force on the ball is well described by a velocity dependent force $\alpha v^2$ plus a separate depth dependent force $\beta (z+z_0 )$. For impact velocities in the range 1.3 -- 5.1 m/s, a single set of parameters $(\alpha ,\beta ,z_0 )$ fits all the data well, with the exception of the first few ms after impact, when the ball is only partially submerged in the granular matter.