A square $4-$kg$-$box lies on the righthand side of a bigger $11\mathrm{.}0-$kg rectangular box. Both objects start from

rest. The only friction occurs on the interface between the boxes. The coefficient of kinetic friction between

the two is $0\mathrm{.}25.$ The rectangular box is $3$ meters in length. A constant horizontal force pulls on the square

box to the left. It takes $2$ s for the square box to get to the other side of the rectangular box. Note though,

the rectangular box may also move during this time.

$($a$)$ Draw a free$-$body diagram for both objects and label each

force using the notation used in this course.

$($b$)$ Symbolically write out Newton$$s $2$nd law for both objects.

Don$$t put in numbers, only use the variables and notation

used in this course.

$($c$)$ Identify all Newton$$s $3$rd law force pairs.

$($d$)$ Use sign sensemaking to determine the direction of accelera$-$

tion of the rectangular box. Explain why you believe it will be

in that direction.

Now input numbers and find the following quantities.

$($e$)$ What is the magnitude of the force applied to the top box?

$($f$)$ How far does the bottom box travel? $($Hint: use a non$-$moving$/$non$-$accelerating reference frame,

i$.$e$.$ static origin on the right side of the table for both blocks.$)$

$($g$)$ What is the final velocity of the top and bottom block?