Question

Each of the three plates has a mass of $10kg$. If the coefficients of static and kinetic friction at each surface of contact are ${\mu }_s=0.3$ and ${\mu }_k=0.2$, respectively $(g=10m{s}^{-2})$. Find the acceleration of block $B$.

Answer 1

a) $f_{1static}={\mu }_s{N}_1=0.3\times 10g=0.3\times \times 10=30N$

if $F=18<f_{1static},$ then block D doesn't slip on C.

b) Considering C

$f_{2static}={\mu }_s{N}_2={\mu }_s(10g+N_1)={\mu }_s(10g+10g)=0.3\times 20\times 10=60N$

Here, $f_2=100N>(f_{2static}+f)$ then blockC slips on B

Let acceleration of C and D is $a_2$ towards right then

$a_2=\frac{100-F-f_{2static}}{M_C+M_D}=\frac{100-18-0.2\times 20g}{10+10}=\frac{100-18-40}{20}=\frac{42}{20}=2.1m/s$

c) Consider block B,

$f_{2kinetic}=40N$

$f_3<f_{2kinetic}$

$f_{3static}={\mu }_3{N}_3=0.3(20g+10g)=0.3\times 30g=90N$

$f_{3static}>[f_{2kinetic}-(f_3=15N\left)\right]$

Hence, block B doesn't move.

Acceleration of B is zero.