Question

Two blocks $A$ and $B$, attached to each other by a massless spring, are kept on a rough horizontal surface $(\mu=0.1)$ and pulled by a force $F=200\, N$ as shown in the figure. If at some instant, the $10\, kg$ mass has acceleration of $12\, m / s ^{2}$, what is the acceleration of $20\,kg$ mass (in $m / s ^{2}$ )?

Answer 1

$N_{1}=100$
$k x-\mu N_{1}=10 \times 12$
$k x-10=120$
$k x=130$ ...(i)
$N_{2}=200$
$200-k x-\mu N_{2}=20 a$
$200-130-(0.1 \times 200)=20 a$
$70-20=20 a$
$a=\frac{50}{20}=2.5\, m / s ^{-2}$