Two identical, unlabeled boxes are transported to an orbiting space station. The astronauts know that one box is filled with a light sample of ants for an experiment, and the other is filled with heavy tools for repairs. How can the astronauts tell, without opening the boxes, which box has the tools

By applying force on each box

Explanation:

According to Newton second law of motion, the acceleration of object depends on force applied on the object and mass of the object.

F=ma

The box containing heavy tools for repair require greater force to accelerate them when compared to the box containing ants for an experiments.

The box with tools will be heavy to move.