We study the statics of an elastic sphere held in a rigid groove by gravity
and friction, as determined by contact mechanics. As a function of the gro
ove's opening angle and its tilt with respect to the vertical, we identify
two regimes of static equilibrium for the ball. At large opening angle or s
mall tilt, the ball rolls at both contacts as it is loaded. This is an anal
og of the "elastic" regime in the mechanics of granular media. At small ope
ning angle or large tilt, the ball rolls at one contact and slides at the o
ther as it is loaded, analogously with the "plastic" regime in the mechanic
s of granular media. In the elastic regime, the stress indeterminacy is res
olved by the kinetics of the response to loading.