Extra Credit Problem $2$: Ice Block on an Inclined Plane

A block of ice rests on a rough wooden incline. The coefficient of static friction between the ice and the wood is ${}_s=0\mathrm{.}25,$ and the coefficient of kinetic friction is ${}_k=0\mathrm{.}20.$ Assume the block starts at rest and the ice is initially at $0C.$

Determine whether a $2\mathrm{.}0$ kg block of ice will slide when the incline angle is $10.$

Will the block begin to slide if the incline angle is increased to $20?$ If so$,$ calculate the change in thermal energy from friction after the block travels $2$ m $.$

Assuming all the increased thermal energy goes into melting the ice, calculate the mass of ice melted due to friction. Give your answer in

milligram. $($Can you please detail how you solved this physics problem well$).$