Physics question: does it hurt more to stub your toe on a more dense object?

[Alexis Voltaire]

Apropos of nothing, a question of density and impact damage that's been bugging me for a while. Thought of trying to submit it to an ask-a-question online site, but I've seen physics discussions on this forum before and I thought this would produce more interesting and quicker results.

The Question

Short version:
If an object (A) is in motion, and strikes a stationary object (B) resulting in damage to object A but not to object B, would a higher density in object B result in more damage to object A?

Long version:
I work in a steel fabrication shop. Over the course of several years I've smacked various parts of my body into stationary steel objects, and I've become convinced that steel hurts more and produces worse bruises than other objects (say wooden furniture) struck in the same way. Could this be a result of steel having greater density?

Logic seems to argue that the when striking a stationary object (say, stubbing your toe) the only factor that would affect damage is deformation of the stationary object to absorb impact energy. However, I've never caused permanent damage to anything wooden by stubbing my toe on it, and although I think wood does deform and rebound to absorb impact it doesn't seem to be enough to correlate to how much less it seems to hurt than something metal. And I know mild steel does absorb and rebound impact force. (although probably not as much)

From a physics standpoint, I know (?) that a more dense object will cause greater impact damage when striking something stationary, which is why hammer heads are made of steel. So if you changed perspective to imagine that *I'm* being hit *by* the steel, not the other way around, it makes sense that steel would hurt more.

Thoughts?

[Drew P]

Depends on the piece being hit; how is it in it's space? Free standing? Solidly connected to another object?
I walked into the side edge(the side where the locking mechanism is) of a door (in the middle of the night with no lights on), it was a slow pace, but the door didn't budge.....my small toe did.  Had a bruise along the side of my foot and up the ankle, broken of course.
Now, I've walked into doorways, wood and steel, both seem the same no matter what they're attached to. Brick wall attachment is more resistant to movement, though.

[Siliconous Skumins]

Simplistic answer:

Yes. Density is a factor up to a point where the the given body being hit is a human one. Foam sponge, Aerogel and cotton wool balls, all hurt a hell of a lot less than dropping a solid steel sledge hammer on your foot.... 


Slightly more complex answer:

Yes density is a factor, but past a certain threshold it no longer makes a difference in regards to contact damage, but still affects the mass of the object - larger mass requiring more energy to be moved = greater impact force against human body. At this threshold the SHAPE of the impactor is more important, sharp or pointed edges concentrating the force in a smaller area will cause much more damage but to a highly confined area of the human skin.

Wood tends to be quite lightweight and flexible, so during a collision with say a chair, the chair will move aside relatively easy.This reduces the forces transmitted to the skin, and as a result relatively little bruising occurs. Large wooden objects also tend to have much more rounded edges than metal objects, partly for aesthetic reasons, and partly due to the material properties not being suitable for forming sharp edges. This also helps spread the load over the skin impact area and reduces the concentration of forces.

Metal objects such as a safe or metal table will usually be heavier than wood due to having a higher density, and typically they will also have much more sharp edges and points due to the material being near ideal for forming into a sharp edge. Large metal objects will require a MUCH greater force in an impact to accelerate at the same speed as a wood item, this results in much higher forces being transmitted through the skin of the human body. Sharper angles and corners combined with a material the does not easily flex will result in a highly concentrated area of force on the human skin, causing significant bruising and damage.


Regardless of density, if an object is fixed in place, then this will also effect impact forces experienced in the human body. If an object is unable to move or flex, then the human body will experience very high impact and deceleration forces. This can result in significant damage to the human body.


The impacted are of the human body will also effect the resulting damage incurred during an impact with a stationary object, fleshy / fatty areas being more flexable and stretchy than thinner areas of skin covering hard bone, such as the hips, knees, elbow, etc. If the skin covering is sufficiently thin, and the impact forces are high enough, then the transmitted impact forces through the human body can be enough to overcome the bone's natural ability to flex slightly, and result in fracture or breakage of the bone.

[Peter Brassbeard]

Density would not directly impact how hard the hit was.  Hardness, and for harder objects total mass, are relevant.  It comes down to how much impact energy is deposited where.  Light or soft objects absorb the impact better.

[Alexis Voltaire]

Slightly more complex answer:

[SNIP]

Ah, thank you, I think this answers my question.

[Prof Marvel]

Elastic vs Inelastic collisions.

The "lighter" material in your words is actually more elastic or flexible.
The "denser" material is less elastic.

the "flexing" allows the force to be dissipated, vs the toe being badly squished.

note that concrete is even less elastic than steel, and tus ought to hurt more, but there is the "law of diminishing returns as the threshold of pain is exceeded" .

yhs
prof mumbls

[J. Wilhelm]

As stated above rigidity and shape will be dominant in determining damage to your toe.

Just a comment. While your soft foot hitting a hard immobile surface seems to be perfectly symmetric with a hard object in motion hitting your foot, also in motion, it is not quite that way.

The reason being that when the hard object is perfectly stationary and remains rigid you become 100% of the source of energy that hurts your toe. Energy doesn't flow into the dense, rigid object, because the object literally bounces back that energy at you. It doesn't matter what the rigid immobile object is made of, in the end the energy/momentum/force of impact will be the same provided the dense object remains perfectly rigid and immobile.

In the case of the dense object hitting your foot, a heavy material implies a momentum (and energy) as a function of mass and velocity - the head of a hammer is made heavy just for the sake of increasing the net energy/momentum by way of mass in a compact package to concentrate the energy to a small area - which increases the force of impact.  But the other part of the hammer is the hammer head; the hammer is an energy focusing mechanism. You can achieve the same amount of energy/momentum/impact force simply by increasing the size of the hammer and keeping the size of the hammer head the same if you want to - but it's impractical.  Compactness is the name of the game when using steel.

[J. Wilhelm]

Elastic vs Inelastic collisions.

The "lighter" material in your words is actually more elastic or flexible.
The "denser" material is less elastic.

the "flexing" allows the force to be dissipated, vs the toe being badly squished.

note that concrete is even less elastic than steel, and tus ought to hurt more, but there is the "law of diminishing returns as the threshold of pain is exceeded" .

yhs
prof mumbls

One must keep in mind, however that elastic objects can return 100% of the  energy being given to them, like a spring (nearly) does, and only a minute amount of energy is dissipated as heat... In the case of the "hammer to the toe" you don't have have an elastic, but rather a plastic deformation.  The toe absorbs the impact energy but does NOT return that energy, which in the end is what disrupts the living tissue. Plastic deformation = permanent energy absorption. If your toe was 100% elastic it wouldn't get hurt at all!!