How to solve

Problem $4[30$ pts$]$: Both the interface between B and the ground and the boundary between A and $B$ have static and kinetic friction coefficients ${}_S$ and ${}_k$ respectively. What the largest force $P$ such that A does not slip? How quickly can the blocks be pushed $8$ meters?

$m_A=5kg,m_B=8kg$

${}_s=0\mathrm{.}4,{}_k=0\mathrm{.}25$

$=36\mathrm{.}87,$

Please write final answers here

$\backslash$table$[[($a$)$ Maximum force $P,25\mathrm{.}11$ N$],[($b$)$ Time to push the block $8$ meters,$2\mathrm{.}25$ secs$]]$

Approach

draw FBD &K

bor both use EOM

In the workspace below, demonstrate the problem$-$solving process including approach, governing equations and diagrams as needed. You must include your governing equations and