Question

Block A of mass $35$ kg is resting on a frictionless floor. Another block B of mass $7$ kg is resting on it as shown in the figure. The coefficient of friction between the block is $0.5$ while kinetic friction is $0.4$. If a force of $100$N is applied to block B, what is the acceleration of the block A? :($g=10m{s}^{-2}$).

Answer 1

static friction force

$f_s=\underset{–}{<}\mu \times N$

$N=mg=7\times 10=70N$

$f_s\underset{–}{<}{\mu }_s\times 70$

$f_s\underset{–}{<}0.5\times 70$

$f_s\underset{–}{<}35N$

hence force applied is greater

$f_k={\mu }_k\times 70$

$f_k=0.4\times 70$

$f_k=28N$

${f_1=f}_k=28N$

$a=\frac{f_1}{35}=\frac{28}{35}=0.8m/s^2$