Question

A block $A$ of mass $m_1$ rests on a rough horizontal surface. The coefficient of friction, between the block and the surface is $\mu$. A uniform plank $B$ of mass $m_2$ rests on $A.$ $B$ is prevented form moving by connecting it to a light rod and hinged at point $P$. the coefficient of friction between $A$ and $B$ is $\mu$. Find the acceleration of blocks $A$ and $C.$.

Answer 1

On mass $m_1$ forces acting in horizontal direction are :

(i) friction due to $m_2=\mu m_{2}g$ leftard

(ii) friction due to ground $=\mu (m_1+m_2)g$ leftward (As friction $=\mu N$)

(iii) Tension of staring (T) rightward.

So, $T-{\mu }_{1}g-2\mu m_{2}g=m_1\alpha \to \left(1\right)$

For $m_3$ mass : $m_{3}g-T=m_3\alpha \to \left(2\right)$

Adding equation $1$ and $2$ we get :

$m_{3}g-\mu m_{2}g=(m_1+m_3)\alpha$

$\Rightarrow \alpha =\frac{(m_3-\mu m_1-2\mu m_2)g}{m_1+m_3}$