Physic
posted by Timothy Tran .
Two boxes sit sidebyside 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.
and Calculate the contact force if the 5.09 N force is applied to the heavy box instead.

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. 
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

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 FF2=m1*a
This also means that the acceleration can be determined from
F=(m1+m2)*a