Two blocks of masses m and 2m are placed in contact on a smooth . . .

Questions : Two blocks of masses m and 2m are placed in contact on a smooth horizontal surface. Two forces of magnitudes 10 N and 16 N respectively are applied on system as shown in figure. Normal contact force between the blocks is _____

Doubt by Divya

Solution : 

F₁=+10 N
F₂=-16 N

Net Force on the system 
F=F₁+F₂
F=10-16
F=-6 N [Towards Left]

(m₁+m₂)a=-6
(m+2m)a=-6
(3m)×a=-6
a=-6/3m 
a=-2/m — (1) 

-ve sign shows that the acceleration is acting towards the left side.

Let the normal contact force between the two given blocks be N

Considering the first block only 

F₁+N = m₁(a)
+10+(-N)=m(-2/m)
10-N=-2
10+2=N
12=N
N=12 N 

If we consider the second block only 

F₂+N = m₂(a)
-16+N=2m(-2/m)
-16+N=-4
-16+4=-N
-12=-N
N=12 N 

Hence, the normal contact force between the block is 12 N.