Question

Two boxes sit side by side on a smooth horizontal surface. The lighter box 5.2 kg, the heavier box has a mass of 7.4kg (a) find the contact force between these boxes when a horizontal force of 5.0 N is applied to the light box. (Hint: you need to calculate acceleration first)

Answer 1

OK.  So you're pushing on the small box, and on the other side of it, the small
box is pushing on the big box. So you're actually pushing both of them.

-- The total mass that you're pushing is (5.2 + 7.4) = 12.6 kg.

-- You're pushing it with 5.0N of force.

-- Acceleration of the whole thing = (force)/(mass) = 5/12.6 = 0.397 m/s² (rounded)

-- Both boxes accelerate at the same rate. So the box farther away from you ...
the big one, with 7.4 kg of mass, accelerates at the same rate.

The force on it to make it accelerate is (mass) x (acceleration) =

                                                              (7.4 kg) x (5/12.6 m/s²) =  2.936 N.

The only force on the big box comes from the small box, pushing it from behind. 
So that same  2.936N  must be the contact force between the boxes.