Question

If ${\mu }_s\text{and}{\mu }_k$ represent the coefficients of static and kinetic friction with appropriate suffixes for the two bodies shown, find the acceleration of the system. Take $g=10m/s^2$.

• A. $\text{Zero}$
• B. $4.2m/s^2$
• C. $5.2m/s^2$
• D. $10m/s^2$

Answer 1

The correct option is C $5.2m/s^2$

The given system can be shown in the FBDs as


So, we have from the above condition
$f_{1max}={\mu }_{s1}\left(5g\right)=0.6\times 50=30N$
$f_{2max}={\mu }_{s2}\left(2g\right)=0.5\times 20=10N$
and, applied force $=13g=130N$

$\because$ the applied force > Total friction force of the system, the system will acclerate
$\therefore$ we have
$f_{k1}={\mu }_{k1}\left(5g\right)=\left(0.4\right)\left(5g\right)=20N$
$f_{k2}={\mu }_{k2}\left(2g\right)=\left(0.3\right)\left(2g\right)=6N$

So, from force equations: Taking the $5kg$ and $2kg$ masses as a system, we get
$13g-T_2=13a$
$\frac{T_2-f_{k_1}-f_{k2}=(5+2)a}{13g-20-6=20a}$
$\Rightarrow a=\frac{130-26}{20}=5.2m/s^2$