The spring of stiffness k is compressed and suddenly released, sending the particle of m...

The spring of stiffness k is compressed and suddenly released, sending the particle of mass m sliding along the track. Determine the minimum spring compression δ for which the particle will not lose contact with the loop-the-loop track. The sliding surface is smooth except for the rough portion of length s equal to R, where the coefficient of kinetic friction is μ_k.