Question

In the figure shown above, find the interaction force between the $3kg$ and $4kg$ block.

Answer 1

Let interaction b/w 2kg, 3kg block $=T_1$

and interaction b/w 3kg, 4kg blcok $=T_2$

since there is no friction, the whole system will move with same acceleration let say 'a' to the right

Applying force balance on each block

$N_1-20=0\Rightarrow N_1=20N$

$45-T_1=2a$ ...(1)

$N_2-30=0\Rightarrow N_2=30N$

$T_1-T_2=3a$ ...(2)

$N_3-40=0\Rightarrow N_3=40N$

$T_2-9=4a$ ...(3)

adding eqn. (1) (2) and (3)

we get,

$45-9=9a$

$\Rightarrow 9a=36$

$\Rightarrow a=4$

Now, from eqn. (3)

$T_2-9=4a$

$T_2-9=4\times 4$

$\Rightarrow T_2=16+9=25N$

hence interaction b/w 2kg and 4kg blcok is 25N