Question

Find the acceleration of the two bodies if the system is shown, is initially at rest. Take $g=10{\text{m/s}}^2$.

• A. $a_A=a_B=2{\text{m/s}}^2$
• B. $a_A=a_B=1{\text{m/s}}^2$
• C. $a_A=a_B=4{\text{m/s}}^2$
• D. $a_A=a_B=3{\text{m/s}}^2$

Answer 1

The correct option is A $a_A=a_B=2{\text{m/s}}^2$

The FBDs of the blocks are as shown

From the FBDs we have
$N_1=10g=100\text{N}$
$f_{\text{max}}=\mu N_1=0.5\times 100=50\text{N}$
$N_2=N_1+20g=100+200=300\text{N}$
Assuming the block to move together with common acceleration, then
$a_c=\frac{F}{m_A+m_B}=\frac{60}{10+20}=2{\text{m/s}}^2$

From the FBD of block $B$ we have
$f=m_B{a}_c=20a_c=20\times 2=40\text{N}$
Since, $f<f_{\text{max}}$, it means our assumption is right.
Hence, the blocks will move together with
$a_c=2{\text{m/s}}^2$