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We experimentally investigate the dynamics of a sphere rolling up a granularslope. During the rolling-up motion, the sphere experiences slipping andpenetration (groove formation) on the surface of the granular layer. The formerrelates to the stuck motion of the rolling sphere, and the latter causes energydissipation due to the deformation of the granular surface. To characterizethese phenomena, we measured the motion of a sphere rolling up a granular slopeof angle $\alpha$. The initial velocity $v_0$, initial angular velocity$\omega_0$, angle of slope $\alpha$, and density of the sphere $\rho_s$ werevaried. As a result, the penetration depth can be scaled solely by the densityratio between the sphere and granular layer. By considering the rotationalequation of motion, we estimate the friction due to the slips. Besides, byconsidering energy conservation, we define and estimate the friction due togroove formation. Moreover, the translational friction is proportional to thepenetration depth. Using these results, we can quantitatively predict thesphere's motion including stuck behavior.

Energy dissipation of a sphere rolling up a granular slope: slip and deformation of granular surface