Homework H$\mathrm{.}4.$H

Given: Blocks A and B $($having masses of $2m$ and $m,$ respectively$)$ are connected by an inextensible

cable and are able to slide along a rough horizontal surface $($with coefficient of kinetic friction of

${}_k).$ A constant force $F$ acts to the right on block A$,$ as shown in the figure. Initially, blocks A

and B are moving to the right with a speed of $v_1.$ Assume that the cable remains taut at all times.

Find: For this problem:

$($a$)$ Draw a free body diagram $($FBD$)$ of a system made up of blocks A and B$,$ and the cable. Using

this FBD$,$ determine the speed of the blocks after they have traveled a distance of $s$ to the

right.

$($b$)$ Draw a FBD of block B alone. Let $F_{AB}$ represent the cable tension. Using this FBD$,$ determine

the work done by $F_{AB}$ on block B after B has moved a distance of $s$ to the right.

Use the following parameters in your analysis: $m=10kg,{}_k=0\mathrm{.}1,F=150N,v_1=10\frac{m}{s}$ and

$s=3m.$