As shown in Figure $28,$ a uniform sphere of mass $m=7kg$ and radius $r$ rolls without slip toward a large crate with mass $M=60kg$ that rests on top of a rubber mat nailed into the ground. The coefficient of friction between the crate and mat is given by $.$ A spring with stiffness $k$ is attached to the crate at a height $h=0\mathrm{.}8m$ above the mat, and the crate's mass center $G$ is located a distance $d=0\mathrm{.}5m$ from either of its supports A and $B.$ The sphere makes contact with the spring with a speed of $v=4\frac{m}{s}.$ Find the spring stiffness $k$ so that the crate just barely tips without slipping, and solve for the minimum frictional coefficient $$ needed to keep the crate from slipping when it tips.