# F=MA in the boxes

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1. Oct 2, 2015

### Physou

I suppose I make two boxes with cardboard, they have the same content : one weighs 10 kg of cardboard the second only 1 kg. I suppose the cardboard doesn't break when the boxes hit the ground : if I let fall the 10 kg box, will the content be more damaged when reaching the ground than in the 1 kg box ?

2. Oct 3, 2015

### Staff: Mentor

Both boxes will hit the ground at the same speed (assuming they're small enough that air resistance isn't important), so any difference in the damage to the contents will have to do with the details of how they were packed.

3. Oct 3, 2015

### Physou

Let's say : the content is tightly packed sort of eggs whose shells are so hard that they did not break when my 1 kg box hit the soil. Does it mean that they won't break either when I let fall my 10 kg box ?

4. Oct 3, 2015

### lightarrow

Let's say the box is of cylindrical shape with diameter which allows only eggs in a single row, and you are comparing boxes hitting the ground with the cylindre's axis vertical and in first case you have one egg only in the box, in the second case you have two or more.
If the egg doesn't break in the first case, I would say that in the second case, the egg closer to the ground could break, because of the other eggs' inertia (the more eggs in the box, the more probable it breaks). I'm not totally convinced however. When I'll finished to make some computations I'll tell you (or, more probably, someone else will have already answered to you).
If that really was your question, of course...
(and if it was, my compliments to you, it's really interesting).

--
lightarrow

5. Oct 3, 2015

### Physou

Thank you for seeing an interest in my question. I am asking this both as part of self teaching physics and as a professional exporter of fragile items. We know that employees at the posts throw the boxes; reinforcing the postal boxes is a solution that is limited by the higher postal cost caused by the higher weight of the cardboard.

Now I would rephrase my question : if 10 eggs in a cylindrical box weighing itself 1 kg don't break when the box falls, does it imply that the same 10 eggs packed the same way, but this time in a 10 kg ( reinforced ) box won't break either ? It seems to me that as the speeds ( of boxes and eggs ) is the same in the 2 experiments the impact on the eggs will also be the same whatever the weight. But I am confused : if I let the 10 kg box fall on one toe I could break it and not with the 1 kg box falling from the same distance. I mean where lies the difference between the eggs in the boxes and my toes ? Thank you very much for helping !

6. Oct 3, 2015

### Staff: Mentor

Now that is a very different question... All else being the same, a postal employee can throw a light box farther and faster than a heavier box, but is probably more likely to drop the heavier box in the first place.

The difference between your toes and the eggs in the box is that your toes are stopping the box from moving while the box is stopping the eggs from moving. Imagine an ant sitting on top of a box that we drop on your toes... The ant doesn't care how much the box weighs, but your toes do.

7. Oct 3, 2015

### Physou

Thank you , this is clear now !

8. Oct 3, 2015

### 256bits

The way to answer your question is for you to do throwing tests, crush tests, and dropping tests, on your box with the contents in it, so that you can be sure to some confidence that your fragile contents will remain intact under some chosen adverse conditions of manipulation. ( If you feel that the transport companies do a drop kick on boxes then test for that also )

Even with an IATA certified box used for the transport of dangerous goods, the box and its packing will receive certification through a series of tests that it must pass, so that the contents remain viable, wherein the condition of the box is secondary. A drop test is one such test.

For the 1 kg or the 10kg box, there is no answer to your question which one is better. Interior packing material is important, so that upon receiving a jarring shock, the packing material and the exterior of the box will absorb most of the energy. Dropping a box and it hitting the ground involves the box decelerating from a velocity to zero in a short period of time. ( Maybe the box bounces and tumbles, we don't know ). A larger box could be designed so that it might be able to accommodate more deflection of its sides or corners upon impact, thus extending the deceleration period so there would not be as much g-force upon the contents.

Just because a box is heavier does not automatically mean it is better or worse for the contents.

9. Oct 3, 2015

### Physou

If I have a 10 kg box with a content of tightly packed eggs ( or balls etc ) that can collide with each other ( despite the protective paper wrapping them ) and collide with the cardboard of the box, and if this box has higher energy when colliding with the ground than the 1 kg box ( is that true ? ), with the same content, why this would not affect the content itself : why should the energy be absorded only by the exterior of the boxes and by the packing material ? wouldn't the content absorb also a part of the energy ? but then since the heavier box has more energy to get absorbed , then the balls in this heavier box would collide more than in the 1 kg box, when taking a part of the energy of the hit ?

Last edited: Oct 3, 2015
10. Oct 3, 2015

### 256bits

One does not want the egg(s) to move around freely within the box, collide with themselves, nor collide with the sides of the box.

Ten 1 kg boxes have the same amount of kinetic energy as 1 10 kg box just before impact when dropped from a height.
You could tape 10 of the 1 kg boxes together and achieve the 10 kg box.

Put the egg(s) within the interior of the taped boxes. The egg(s) would have a better chance of surviving from a drop, as the exterior boxes will take most of the hit.

11. Oct 3, 2015

### CWatters

I have some experience designing and testing packaging for fragile items. Its quite an art and there is far more to it than can be covered here. Sometimes double packing can work well but packing should be "designed" just like any other product. You can't design packing without knowing about the product being packed and how it will be shipped.

12. Oct 3, 2015

### Mister T

Imagine an accelerometer packed within the boxes. All other things being equal, the higher the accelerometer reading the greater the chances of damage. If the same force is applied to each box, the heavier box will undergo the smaller acceleration.