Question

Find the maximum force that should act on the $1\text{kg}$ body for the system to accelerate together with $2{\text{m/s}}^2$. Take $g=10{\text{m/s}}^2$.

• A. $4\text{N}$
• B. $5\text{N}$
• C. $7\text{N}$
• D. $9\text{N}$

Answer 1

The correct option is D $9\text{N}$


From FBD of the system of blocks, we can write
$F-f=(m_1+m_2)a_s$ where $a_s$ is the acceleration of the system.
For $F=F_{max}$, friction will have limiting value
$f={\mu }_{1}N={\mu }_1(m_1+m_2)g$

Then, $F_{\text{max}}=(m_1+m_2)({\mu }_{1}g+a_s)$
$m_1=1\text{kg};m_2=2\text{kg};{\mu }_1=0.1;a_s={\text{2 m/s}}^2$

Hence, $F_{\text{max}}=(2+1)(0.1\times 10+2)$
$=3\times 3=9\text{N}$