In physics, the Newton’s law of **universal gravitation states** that every object in the universe exerts a gravitational force on other objects in the universe. The force is proportional to the object’s mass and acceleration, and is directed towards other masses that are closer to it.

This law is how we understand gravity and how we are able to calculate how it acts on things. By understanding this law, you can **predict many things** about gravity!

In box physics, the experiment is designed so that all of the boxes are at ground level and all of the sides of all of the boxes are parallel to each other. This makes it easy to identify which box is acting as the bottom box and which sides are acting as the top sides.

By identifying which box is acting as the bottom box and which sides are acting as the top sides, you can rank all of the boxes on the basis of magnitude of **normal force acting** on them.

## Bottom-up Approach

A second way to determine the force on a box is to rank the boxes on the basis of the magnitude of their *normal force acting* on them and then add them together.

To do this, you **would first arrange** all of the boxes in order from heaviest to lightest, starting with the bottom box. Then you would arrange all of the boxes in order from lightest to heaviest, starting with the top box.

Since we know the mass of each box, we can determine its weight. We can **also use physics** to calculate how much force each box exerts as it rests on the floor: The floor exerts an equal and opposite force on the box’s bottom surface, thus acting as a normal force.

Once we have arranged all of the boxes in this manner, we can use algebra to combine them into one equation that represents their *total normal force acting* on them.

## Example: Magnets and metal plates

A classic example of Rank the Boxes is magnetism. Magnets have a constant force, or box, that they act upon. Any object that comes in contact with a magnet will be affected by this force.

The shape of the object does not matter; all objects are affected by magnets in the same way. This makes it easy to rank objects by their susceptibility to magnetism.

Any object that is not made of a magnetic material will not be pulled towards a magnet. This makes it very easy to assign a box of zero for this quality.

To further test your understanding of Rank the Boxes, *try applying* it to other phenomena! Some *examples include liquid versus solid substances*, **gas versus liquid substances**, and **temperature ranges**. All of these have constants, making it easy to apply this principle.

## Example: Ball on a hill

Now consider the situation shown in the figure above. Here, we have a ball sitting on a hill, where the slope of the hill is defined by the *normal force acting* on the ball.

We would like to rank these boxes in order of which box has the greatest chance of staying at rest if we put the ball on it. To do this, we will **consider two things**: how high up the box is, and how strong the box is.

If we put the weaker box (A) on the hill, then there is a higher chance that it will slide down than if we put box B on the hill. This is because box A has less mass, and *therefore less kinetic energy due* to its lower weight. Box B is heavier, and therefore has more *potential kinetic energy* that could make it roll off of the hill.

To rank these boxes in order of least likely to tip over, we must consider how tall they are. Box C is taller than A and B, so there is a higher chance that it will fall over when placed on top of this hill.

## Summary

In this article, you learned about the different types of forces, how they interact, and how you can use them to your advantage in your everyday life.

You learned about the **psychological force known** as “force of habit” and how you can break it with some creativity. You learned how to use your knowledge of gravitational, drag, and weight-bearing forces to move more easily through your day.

In addition, you learned about an interesting way to **organize boxes based** on the normal force they exert on the box below it. This way allows you to *quickly sort boxes according* to size and organize them in a logical way.

Hopefully you will remember this article if you need to organize any boxes in the future! Or, perhaps you will be inspired to organize some boxes in a new, more organized way.

## References

The *normal force* is the force that **acts perpendicular** (or “up and down”) to the surface of contact between objects. For boxes on a shelf, the **normal force acts** to keep the box resting on the shelf.

As mentioned before, you can rank the boxes on the basis of their weight, but you can also rank them according to how close they are to being toppled over by the pulling force.

The closer a box is to toppling over, the less stable it is. A box that is very light but that is *sitting next* to a very heavy box will be less stable than a heavier box that is sitting alone on the shelf.

## Further reading

A great way to understand the **physics behind box sorting** is to read about people who have studied it in depth. Two academics who have written about box sorting extensively are Dan Tyerman and Lars Kroner.

Dan Tyerman is a researcher at the University of Manchester in England. He wrote a paper titled “The Physics of Box Sorting,” which was published in the January–February 2007 issue of Physics Education.

In his paper, he outlines three methods for sorting boxes and compares their efficiency. The best method requires that you first rank all of the boxes by size, then you stack all of the small boxes together, then you stack all of the medium-sized boxes together, and so on.

This method is efficient because you use the **normal force acting** on each box to sort them. Small boxes have a *smaller normal force acting* on them, so they should be placed at the bottom of the pile.

## Images

In this method, you rank the boxes on the basis of the magnitude of the **normal force acting** on them. You do this by finding the sum of the products of each pair of adjacent faces (top and bottom, front and back, left and right) for each box. You then rank them based on which has the greatest sum.

The box with the greatest sum is considered to have the * largest normal force acting* on it. The box with the smallest sum is considered to have the

*smallest normal force acting*on it.

You can visualize this by drawing a picture of all of the boxes and ranking them based on size and color. The blue box would be ranked as having the largest normal force acting on it, and the yellow one would have the smallest.

You can also do an additional step to verify your answer by checking if removing any one of these boxes changes the magnitude of the normal force acting on any other box.