Question

Block B of ass 2 kg rests on a block A of mass 10 kg. All surfaces are rough with value of coefficient of friction as shown in the figure. Find the minimum force F that should be applied on block A to cause relative motion between A and B.(g=10 m/s${}^2$)

Answer 1

$m_A=10kg{m}_B=2kg{\left(f_s\right)}_{ma{x}_1}={\mu }_s{m}_{B}g=0.25\times 2\times 10=5N{\left(f_s\right)}_{ma{x}_2}={\mu }_s(m_A+m_B)g=0.2\times 12\times 10=24N$

We apply force F such that A will not move with respect to ground

f at A wrt ground =F

Now if we apply F, on A and if A doesnot move by frictional force b/w A & B, F will be applied on it.

$F\ge {\left(f_s\right)}_{ma{x}_1}F\ge 5N$

We will obtain relative motion between A & B.