How many apples can I fit in a box using close packing of spheres?

[trillianK]

1. How many apples can you put into a box in the following dimensions:
Width: 1.25 meters
Length: 3 meters
Hight: 2.1 meters



2. Close packing of spheres



3. All I could find is the efficiency of close packing of spheres in face-centered cubic, which is 0.74048.

Is there an equation that takes into consideration the radius (I measured a few apples and it's about 3-4 cm) of the spheres (or the distance between the centers of two spheres, to be more precise) and the volume of the box to give the maximal number of spheres in the box?

Can I use all of that considering the fact that apples are not regular spheres? Am I thinking in the right direction?

I'm sorry if all of this sounds a bit silly, I come from a completely different walk of life and this is my only physics course.

Thanks for helping :)

 

[willem2]

I think calculating the volume of the box and using the maximum packing density for spheres of the same size will be enough. You could try how much apples fit in a smaller box, but I think you'd need hundreds of apples to get a reasonable estimate.

Of course with real world apples:
- you can fit in far more apples than you think.
- the apples at the bottom of the box will only be useful for applejuice.

 

[tomcue]

Hello! I can provide some insight into your question about how many apples can fit in a box using close packing of spheres. Close packing of spheres is a mathematical concept that describes the most efficient way to arrange spheres without leaving any gaps between them. This concept is often used in physics and other fields to study the arrangement of particles in a given space.

To answer your first question, the number of apples you can fit in a box using close packing of spheres will depend on the size of the apples and the size of the box. The efficiency of close packing, as you mentioned, is 0.74048, which means that in a face-centered cubic arrangement, about 74% of the space is occupied by the spheres. However, this efficiency may vary depending on the size and shape of the spheres.

To calculate the maximum number of spheres that can fit in a given space, we can use the formula for the volume of a sphere (V = 4/3 * π * r^3) and the volume of the box (V = L * W * H). By dividing the volume of the box by the volume of a sphere, we can determine the maximum number of spheres that can fit in the box.

However, as you mentioned, apples are not perfect spheres and may have irregular shapes and sizes. This can affect the efficiency of close packing and the maximum number of apples that can fit in the box. To get a more accurate estimation, you can measure the average size of the apples and use that to calculate the maximum number of apples that can fit in the box.

In conclusion, while close packing of spheres can give us a general idea of how many apples can fit in a box, the actual number may vary depending on the size and shape of the apples. I hope this helps and good luck with your physics course!