A 3.0-kg and a 5.0-kg box rest side-by-side on a perfectly smooth, level floor. A horizontal force of 32 N is applied to the 3.0-kg box pushing it against the 5.0-kg box, and, as a result, both boxes slide along the floor. How hard do the two boxes push against each other?

12 N against each other

Explanation:

Step 1: calculate the common acceleration of the two boxes when they join together

F = ma; m = (3 + 5) kg and F = 32N

a = F/m

a = 32/8 = 4 m/s²

Step 2: calculate the impact force of 3 kg box on 5 kg box

F = ma

F = 3 X 4 = 12N

Step 3: Calculate the force of 5kg box when it accelerate on 4 m/s²

F = ma

F = 5 X 4 = 20 N

Step 4: calculate the opposing force of 5kg box

F = 32N - 20N = 12N

Therefore, each box exerts a force of 12N to the other in opposite direction.

Newton's third law of motion, "action and reaction are equal and opposite"