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.

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 F-F2=m1*a

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

To calculate the contact force between the boxes when a horizontal force is applied, we need to consider Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.

1. When the 5.09 N force is applied to the lighter box:
- Since the boxes are in contact, the force applied to the lighter box will also be exerted on the heavier box due to the interaction between them.
- The contact force between the boxes will be equal in magnitude and opposite in direction to the applied force, so it will also be 5.09 N.

2. When the 5.09 N force is applied to the heavier box:
- In this case, the force will act in the same direction as the applied force on the heavier box, so the contact force between the boxes will be the same as the applied force, which is 5.09 N.

Therefore, regardless of which box the 5.09 N force is applied to, the contact force between the boxes will be 5.09 N.