V = 0 eeeee ell M X = 0 (6) in the figure above, the block of mass M has come to rest at a location to the right of the springis equibrum poston. The spring has a spring constant k, and the coefficients of kinetc and static friction between the block and the surface are , and „, respectively LOn the dot belon, which represents the block at rest and to the right of z - 0, draw and label the forces (not components) that act on the block. Each force must be represented by a distinct arrow starting on, and pointing away from, the dot

Given

In the figure above, the block of mass M has come to rest at a location to the right of the spring's equilibrium position. The spring has a spring constant k, and the coefficients of kinetic and static friction between the block and the surface area, and respectively.

(i) On the dot below, which represents the block at rest and to the right of z=0 draw and label the forces (not components) that act on the block. Each force must be represented by a distinct arrow starting on, and pointing away from the dot.

(ii) Derive an expression for the maximum displacement possible for the block that will allow the block to still remain at rest. Express your answer in terms of M. ${\mu }_k, {\mu }_s,$ and physical constants, as appropriate, as following below.

(i)

$$\begin{gathered} \mathrm{Here}, \\ N = mg = \mathrm{normal} \mathrm{reaction} \mathrm{force} \\ {F}_{R }= \mathrm{restoring} \mathrm{force} = -K x_{max} \\ {f}_s = \mathrm{limiting} \mathrm{frictional} \mathrm{force} = {\mu }_{s}N ={\mu }_{s}mg \end{gathered}$$