Question

The blocks A and B have masses of $2$ and $6kg$ respectively are kept on a rough horizontal surface of $\mu -0.2$ If a horizontal force of $6N$ pushes them calculate :
(a) the acceleration of the system
(b) the force that the 2kg block exerts on the other block

Answer 1

(a) Acceleration of the system

$m_1+m_2=m=2+6=8kg$

$\mu =0.2$

$f=\mu mg=0.2\times 8\times 9.8=15.68N$

$F=6N$

Now, $F-f=ma$

$6-15.68=(8)(a)

$\Rightarrow a=-1.21m/s^2$

There will be no acceleration because the applied force is less than the static friction force.

(b) force that the 2kg block exerts on the other block

$=Appliedforce-frictionalforceof2kgblock$

$=6-\left(0.2\right)\left(2\right)\left(9.8\right)=6-3.92=2.08N$

$\Rightarrow$ A force of $2.08N$ is applied on the other block.