Answer
(a) The force of static friction on the packing case is 88 N directed northward.
(b) The force of static friction on the packing case is 78.4 N directed southward.
Work Step by Step
We can use $\mu_s$ to find the maximum possible acceleration of the packing case.
$mg~\mu_s = ma$
$a = g~\mu_s = (9.80~m/s^2)(0.30)$
$a = 2.94~m/s^2$
(a) When the truck's acceleration is $2.20~m/s^2$ northward, the force of static friction on the packing case can accelerate the packing case $2.20~m/s^2$.
$F_f = ma = (40.0~kg)(2.20~m/s^2)$
$F_f = 88~N$
The force of static friction on the packing case is 88 N directed northward.
(b) When the truck's acceleration is $3.40~m/s^2$ southward, the force of static friction on the packing case cannot accelerate the packing case. Therefore, the packing case will slide northward relative to the truck, and the force of kinetic friction will exert a force on the packing case directed southward.
$F_f = mg~\mu_k = (40.0~kg)(9.80~m/s^2)(0.20)$
$F_f = 78.4~N$
The force of static friction on the packing case is 78.4 N directed southward.
