Figure 1

(Color online) The vertical position $z$ of the bottom of a sphere vs time $t$, for typical conditions as labeled. The impact begins at $\{z=0,t=0\}$, and gravity points in the $-z$ direction. Only every $1∕100$ datum is shown. The inset shows the final penetration depth vs total drop distance, both scaled by the minimum penetration depth $d_0$. The small symbols represent data for four wooden spheres from Ref. 10. The large symbols represent additional runs, for which in this paper we report on impact dynamics (◇ is for the example in the main plot). The values of $d_0$ are 0.63 and 0.44 cm for the 1.99 and 1.49 in. diameter spheres, respectively.Reuse & Permissions

Figure 2

(Color online) Vertical components of position, velocity, and acceleration vs time, for all runs; red (orange) dots are for $D_b=1.99\mathrm{in}.$ (1.49 in.). To within measurement errors, the data collapse when lengths are scaled by $d$ and times are scaled by $d∕v_0$, where $d$ is the final penetration depth and $v_0$ is the impact speed. By construction, the scaled position data all decay from 0 to $-1$ with an initial slope of $-1$ (gray lines). Note that the acceleration is not constant (gray dashed line $ad∕v_0{}^2=1∕2$), but rather decreases with time. The data rule out the power-law forces consistent with Eq. (1), but are consistent with a modified Poncelet model.Reuse & Permissions

Figure 3

(Color online) Velocity and acceleration vs position, and acceleration vs velocity (inset), for all runs, scaled as in Fig. 2; red (orange) dots are for $D_b=1.99\mathrm{in}.$ (1.49 in.). Excellent fits to the modified Poncelet model are shown as solid purple curves. The various dashed curves represent the same power-law forces as in Fig. 2.Reuse & Permissions