Final answer:
The box will move across the floor if the applied force exceeds the force of friction, which depends on the coefficient of friction and the box's weight.
Step-by-step explanation:
To determine if the box will move across the floor, it is necessary to consider the friction between the box and the floor, as well as the applied force. When the box is pushed and slides, it experiences friction that acts in the opposite direction to the movement, slowing it down. If the applied force exceeds the maximum static friction force, which is the product of the coefficient of static friction and the box's weight (normal force), then the box will move. Otherwise, it will remain stationary. In the scenario described where a box slows down as it slides, this indicates that kinetic friction is at play, reducing the box's speed until it comes to a stop unless additional force is applied.
Regarding box A and box B, Box A is subject to a greater force, which means it will have a greater acceleration if the masses are equal. Therefore, it will travel faster over the same distance. When a force is applied over a distance, work is done, and kinetic energy increases. However, the transfer of energy is affected by friction, which does work in the opposite direction. Without friction, as in the case with Box A and B, the entire force contributes to increasing the box's kinetic energy, resulting in higher speed.
Therefore, friction is a significant factor that affects whether a box moves or not after a force is applied. We must compare the applied force to the force of friction determined by the coefficient of friction and the box's weight.