Two boxes sit side-by-side on a smooth horizontal surface. The lighter box has a mass of 5.91 kg, the heavier box has a mass of 7.67 kg. Calculate the contact force between these boxes when a horizontal force of 5.09 N is applied to the light box.

Question

and Calculate the contact force if the 5.09 N force is applied to the heavy box instead.

Answer 1

They would accelerate initially at the same acceleration, a m/s/s.
Total mass, M = m1+m2 = 5.91 + 7.67 kg
Force, F = 5.09 N.
Acceleration, a = F/M
The contact force is the force required to set the farther block in motion at the calculated acceleration a.
The force is in turn equal to ma, where m is the mass of the farther block.

Answer 2

Thanks for your help but I'm still a bit confuse. By using F=ma, we are solving for acceleration, but how would I conduct that into finding the horizontal force? Thank you very much for you help

Answer 3

If the two blocks move together, their acceration will be the same. The force is mass of the block * acceleration, hence
F=ma.
Schematically, it is:
External force, F -> block1 -> block2

The external force F is applied on block1. Block1 in turn applies a force F2 to block2. Both of them move in tandem with an acceleration of a.

Thus F2=m2*a
and net force on block1 is F-F2=m1*a

This also means that the acceleration can be determined from
F=(m1+m2)*a