# Why do the pieces of breaking objects scatter?

If I were to drop most objects to a level floor, they would land with a thud or bounce a few times without gaining any lateral velocity.

But a fragile object will not only break into two or more pieces, but the pieces will usually move laterally across the floor.

I suppose the center of mass of the system probably remains at the location where the object broke, but I don't see any reason for the pieces to behave any differently than a typical object that bounces or thuds. Or to put it another way, I can't determine a force that would provide the acceleration by which the pieces gained their lateral velocity.

Why does this happen?

• simple. the solid object is like a spring held together. when it "breaks" that is the spring being released. Commented Jan 8 at 15:20
• Idea for an experiment: pick up the fragments and drop them again, to see if they still spread out the second time.
– jpa
Commented Jan 9 at 9:56
• Basically collision with the pieces above. When you have an object below (floor) and above the piece "squeezing" it from both top and bottom it basically forces the piece to move in the only way it can - horizontally Commented Jan 9 at 22:45
• @slebetman This would be a nice slowmo experiment. Have a glass ball with layered colors. When dropped, see which layer flies far the most. I suppose the top layer would, relatively, stay put since there's nothing that "squeezes" it from the top. However, the bottom might still bump it up, so I'm not sure what we would get. Commented Jan 10 at 10:43
• There should really be a mention of thermal stresses and of the unstable equilibria baked into certain materials (especially glass) in manufacturing, which both can permit things shattering with more, not less, kinetic energy than they had before they broke, but I'm not confident enough in my knowledge to post an answer. Maybe I'll make a follow-up question if someone doesn't bring it up here.
– g s
Commented Jan 11 at 10:06

Generally, when an object collides with the floor there will be some sort of asymmetrical deformation of the object before it ultimately fails. This deformation puts a rather large amount of strain on the localized region of the object that can be considered as a sort of potential energy. When the object breaks, this energy is converted into kinetic energy, which sends part of the object flying. The part that goes flying will obviously be related to the part when the deformation caused a mechanical failure. There can, of course, be a sort of cascade of failures as well. To the degree that the system is conservative (i.e. we are ignoring things like sound waves, friction, etc.), the other pieces will tend to fly apart in a way that will conserve the linear momentum of the whole collection of parts. This gives the typical “scatter” effect that you observe.

• Such as buckling under its own inertia. The most symmetrical example I can think of that is easily available is when you shoot a lead pellet at a hard steel surface. It flattens and mushrooms quite symmetrically outward in all directions, yet all the motion was in the line of fire. Commented Jan 8 at 0:53
• @DKNguyen another example, perhaps more readily available in most of the world, is to drop an egg from quite a height onto a smooth floor. Dropped big end down it stays that way up and breaks really rather symmetrically. The shell is fragile, but the membrane is tough, so the shell isn't scattered as much as you'd think Commented Jan 8 at 9:35
• An easy visual analogy is bending a credit-card by standing it straight up and pushing onto the top. The credit-card will buckle to one side by the pressure and it will fly away to the side like a loaded spring. The downwards pressure is converted into stress and the stress is converted to lateral motion when the card flips away. Commented Jan 8 at 9:42
• "To the degree that the system is conservative" should be deleted because linear momentum is ALWAYS conserved. Energy may "leak" when we ignore sound waves, friction, etc..., but momentum is different. From an applied perspective, momentum would be useful for examining the linear momentum of the system in the $x$ and $y$ directions immediately before and after the collision. Any time we have to measure the change in momentum of the Earth, momentum is practically useless because Earth is big. Commented Jan 9 at 21:20
• Linear momentum is certainly not always conserved. Whenever a net external force is applied the linear momentum will not be conserved. This is because the change in momentum as a function of time is the definition of force. In fact, this is essential to the object breaking! The momentum changes because the floor applies a force on the object, leading to breakage. Commented Jan 9 at 21:27

What you describe is the shift from rigid body dynamics to fluid dynamics. Let's take your fragile object falling on earth to the grandest scale. A planetary collision. The planets don't bounce or land with a thud. They splash like a liquid. Everything behaves like a liquid at large scales (of time and space).

Every solid object that falls with a thud prefers to minimize energy by splashing like a liquid, to lower its center of mass, but its bonds prevent them. You have a spectrum of objects, from bouncing solids to splashing liquids, and the fragile object you are seeing is somewhere in between.

• I really like this answer for providing intuition. That said I think as it stands it kicks the explanation down the road to the next question: “why do liquids splash like they do with at times extreme lateral velocities for each droplet?”. Might be worth a quick discussion of the physics of splashing liquids for completeness. I’m guessing in a liquid the lateral acceleration comes from interaction between a liquid and a much more dense material (usually a solid), e.g. water on concrete will splash outward vigorously?
– bob
Commented Jan 9 at 4:42

Simple gravity and normal forces.

Reaction to deformation, as mentioned in Matt Hanson's answer, plays a huge part in it, but even an idealized instantaneous shattering without deformation will cause this scattering effect.

Your initial premise is incorrect. In the general case, an object that doesn't break will, in fact, gain some lateral velocity. Sure, a spherical ball wouldn't gain any lateral velocity if the surface is exactly horizontal, but even then, only if its angular momentum is exactly zero. A rotating ball will most definitely gain some horizontal velocity.

Try dropping a box. Unless it lands exactly on a face, it will definitely gain some lateral velocity as it tilts about the point of impact before bouncing back up. The amount of velocity gained depends heavily on the tilt with which the box lands, but having its center mass remain on the exact same spot would be impossible unless under a mathematically exact scenario. The reason it doesn't look like it's moving across is that the gained horizontal velocity is not all that great to begin with and simple friction is able to overcome it quite quickly.

Now to the scattering itself. Imagine some ideal object that breaks in exactly two halves without any deformation at all. At the moment of impact, both halves will have their own center of mass away from the point of impact, which will cause them to naturally rotate away from each other.

With shattering, you also get the effect that the various fragments will want to continue to descend under gravity, but there will be other fragments below them that will impede such motion. Those various fragments will then be bouncing off each other, and all those surfaces will definitely not be "exactly horizontal".

The extreme example of this is a liquid "object". A water droplet that hits the floor will shatter and scatter, simply because it can't remain droplet-shaped at all.

Consider this loose assembly of falling objects, consisting of a wedge and two spherical objects.

Initially they are all co-moving in free-fall, but the wedge hits the floor first and stops or rebounds, and the following balls collide with the wedge and are directed sideways according to the angles of the wedge.

Now imagine something fragile like a glass hitting the floor. It breaks into random shaped pieces due to microscopic fault lines and imperfections in the glass, creating a random assortment of wedges and other shapes. Some of these random shapes stop or rebound while others continue their downward trajectory and the collisions result in random rebound trajectories for some the pieces. This is why a shattered glass does not form a perfectly circular debris zone and some pieces will be randomly much further away from the impact point than most other parts.

This effect works in conjunction with the pancake effect that others have alluded to. If a very soft ball of clay hits the floor, it tends to get compressed and naturally 'pancakes' or spreads out. The conversion from spherical shape to pancake shape requires a horizontal momentum component as the clay ball seeks to reach a lower potential energy.

An additional effect is the release of tensions introduced during the manufacture of the object. These tensions are like dropping a bunch of armed mousetraps, and they release the tension energy on impact. Imagine folding a long flexible and fairly elastic ruler into a hoop and joining the ends with a weak link. When the looped horizontally orientated ruler hits the floor, the link breaks and the ruler straightens out to its natural straight shape causing a sideways force.

All these effects can work together depending on the situation.

Edit: just thought of another factor, the spaghetti bullet factor.

When a dropped object hits the floor, it sometimes flexes before it breaks, and this flexing stores additional tension energy which is released in random horizontal directions when the object finally snaps during the impact. (The video is pretty cool ;-)

• I was just about writing a similar explanation, until I saw this one. Great schematics! In addition I think liquids like water splashes for the same reasons, because first layers who lands may also have micro-structure upon impacting new layers. And on direct hit water acts like "almost solid". So same mechanical model should fit at principle. Commented Jan 9 at 20:08

# Spherical Cow

Consider a spherical cow dropped from a height of 1 meter. Ok, maybe not a cow. Imagine a basketball dropped from 2 m. This will generally not shatter. But hopefully, you can imagine when it bounces. Hopefully, you can see that the ball does not remain rigidly spherical, but instead deforms into an oblate spheroid (it squashes outwards like a pumpkin). If, for some reason, at the point of maximum deformation, it lost all structural integrity and shattered, I hope it is clear why some of the pieces will fly out horizontally even though the motion of the whole was entirely vertical.

Just to spell it out precisely, the contact force when the ball touches the floor resists the forward motion of the ball. And yet, the momentum of the ball must go somewhere, and that "somewhere" is the molecular bonds which give the ball its shape. And thus, the geometry of the ball determines how the downward momentum of the ball is transformed into momentum in many other directions. You can think of the molecular bonds as countless tiny levers which convert motion in one direction into motion in another direction. If the object maintains its structural integrity, the levers' actions are reversible and the object bounces. But if it fails catastrophically, then all those levers contribute to the numerous new momentum vectors of the resulting pieces.

Lest you think that air pressure inside the ball is somehow responsible for this explosive state of affairs, just replace the basketball with a wiffle ball, or any other structure which does not maintain an internal gas pressure.

Objects are not completely homogeneous and therefore when an object encounters energy in the form of an impulse function, the less dense layers in the object break first. These breaking points act like "fault lines" similar to those found in Earthquakes. Since the fault lines of each fragment are at angles with respect to each other, the shearing forces at the angled fault lines will push some fragments outward laterally and some fragment inward laterally, thus the fragments scatter.