Decelerative motion of a sphere rolling up a granular slope

Vehicles are sometimes getting stuck by the wheels spinning out on loose sand surfaces. To understand the fundamental aspect of spinning out occurrence, we carry out a set of simplified experiments. Previous studies investigated the dynamics of the sphere rolling down/on a granular surface. However, the decelerative dynamics of the sphere rolling up a granular slope have not been examined. Here, we experimentally investigate the dynamics of the sphere rolling up a granular slope to characterize its decelerative motion both in rolling and translational directions [Fukumoto et al., Phys. Rev. E 109, 014903 (2024)]. In this experiment, the radius of the spheres is 6.35 mm. The typical glass bead size is 0.8 mm. We vary the slope α (0°<α<20°), the density of the sphere ρ_s ( ρ_s=930, 1400, 2600, 3900, and 7900 kg/m³ ), and the initial velocity v₀ (0.2 m/s < v₀< 0.7 m/s) with which the sphere enters the granular slope. In some cases, when the translational motion halts, rolling remains. Namely, we can observe the stuck occurrence in this experiment. According to the experimental results, the dynamics of the translational and rolling motions show constant deceleration. Based on this observation, we estimate the friction coefficients in rolling and translational motions. As a result, the rolling friction coefficient can be regarded as a constant value. The translational friction coefficient is proportional to the sinking depth of the sphere, and this relation can be applied to the case of vehicles rolling on a terrain.