# Why do whips hurt so much?

What exactly is the mechanism that makes a whip deliver such a strong impact? Elasticity, torque, or pressure? Just hitting something with a plank doesn't deal nearly as much damage. What's the difference?

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I think it has to do with something similar to what Prathyush stated: impulse. For a whip to be effective, you have to pull back after the tip is launched outwards. – user25886 Jun 16 '13 at 22:55

The reason, a Whip hurts so much is that the tip of whip moves extremely fast, causing the skin to tear.

The reasoning behind this is easy to analyze from momentum conservation. Lets take a convenient approximation, that the mass per unit length($\rho$) does not vary through the length of the whip. This is not how real whips are, but it will not effect the conclusion very much.

Initially the whole length of whip moves, say with velocity v, if you observe the motion of the whip closely, then you will see that as time elapses, the initial momentum is concentrated on a smaller and smaller section of the whip, while the rest is almost static.

Now if the whip length is l then intial momentum is $\rho l v$. If we look at a snap shot at some later time, and say we observe that $l_0$ is the length of the whip currently in motion.

Then by momentum conservation, $\rho v_0 l_0 = \rho v l$. This implies that the velocity of the moving end, $v_0 =\frac{v l}{l_o}$

as time elapses $l_0 \to 0$, $v_0 \to \infty$. The tip is moving at a very large speed, therefore it is capable is piercing. A thin tip makes the effect more dramatic(due to smaller $\rho$) but does not change the essential mechanism.

You may enjoy this video

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Why would a high velocity matter if the mass is relatively low. And what factors limit the speed from 'going to infinity.' The tip must cap out at some relatively low speed, that, while fast, is not nearly as fast as infinity. – user24082 Jun 16 '13 at 7:48
And also, what factor allows the momentum to transfer to the tip? It's clear that it occurs, but I see no reason why it should occur in that way. – user24082 Jun 16 '13 at 7:49
@tony there will be effects due to fluid mechanics which will be hard to analyze, and but effects like air drag, viscosity will be important. then there will be effects due to tension and so on, which will cause the tip to slow down and not allow it to reach infinity. In the extreme and unlikely cases the whip could snap into 2.(which can happen with noodles for instance, its only a matter of scales) – Prathyush Jun 16 '13 at 11:02
@tony I dont quite understand the intention behind comment 2, perhaps you should clarify. Momentum conservation is the reason. one end of the whip is held constant, and the other is set in motion. so end result is the static end gets larger and larger while the moving end gets smaller and smaller. – Prathyush Jun 16 '13 at 23:02

The speed of the tip of the whip can exceed the speed of sound. From Wiki:

The crack a whip makes is produced when a section of the whip moves faster than the speed of sound creating a small sonic boom. The creation of the sonic boom was confirmed by high-speed shadow photography in 1927.1

There are at least three "modes of motion" that can produce the necessary speed in a whip to cause it to crack. The three are: a half wave, a full wave and a loop. These names are indicative of the shape of the bends in the whip as it is thrown. In all three, the initial motion is applied to the handle, and the resultant shape moves down the whip's body to the tip. The high speed of the tip is explained by the law of the conservation of momentum. Since momentum is a vector, it has a direction, and does not pass through any bend that reverses the direction of movement in the body of the whip − such as the one that occurs when a half wave shape moves down a whip.

When a whip is thrown, the initial motion of the handle adds some amount of kinetic energy to the body of the whip. If the whip is going to crack, the handle movement must also produce one of the modes of motion that create a reversal of direction in the whip's movement. As the reversal of direction moves down the whip, the momentum and the kinetic energy in the whip, are concentrated in the segment of the whip between the tip and the moving bend. As the bend approaches the tip, the mass of the moving part approaches zero while the energy remains relatively constant. Since the momentum is the product of the mass and speed of the moving object, the smaller the mass, the higher the speed. Hence the end of the whip moves extremely fast, easily reaching the speed of sound.

Many published popular science explanations capitalize on the fact that the general shape of a whip is tapered: thick at the handle and very narrow at the tip, hence the decrease of the mass. While tapering does contribute the decreasing mass, it is not a deciding factor. Even "flat" un-tapered whips will crack. The actual decrease of the mass of the moving part occurs simply because the whip ends: the closer the moving bend is to the tip, the less mass is in the part that's moving in the given direction.

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I don't think it's that important that the edge of the whip moves so fast, since it has vanishing mass. In fact, I don't think a whip hurts more than an equivalently thin, long stick. – jjj Jun 12 '13 at 15:47
Is that true jjj? I'm still really confused, Wiki didn't help me much. Moving the whip forward gives it some initial Kinetic Energy, and momentum. It's then moved in an opposite direction creating some kind of bend, now, some force is applied so I'm not positive why momentum has to be conserved, but if it is, then I what I understand is that the kinetic energy and any deformational energy of the whip moves towards the tip? The problem I then have is, how would one calculate the actual speed of the tip? It's limited by existing energy, and the elasticity, correct? – user24082 Jun 12 '13 at 18:01
And I suppose the only thing that could make it hurt more than a thin long stick is if the energy is somehow being squeezed towards the tip, which is what Wiki is saying, but I'm not sure the mechanism that causes it. – user24082 Jun 12 '13 at 19:57
paint not proportional to energy. – raindrop Jun 17 '13 at 0:07

Just hitting something with a plank doesn't deal nearly as much damage.

Generally, a plank can be much more damaging than a whip. Whips may look cooler, but that seems to be about it.

http://en.wikipedia.org/wiki/Whip#As_practical_weapons

Differences in pain need not reflect the amount of damage done (if we can even define that properly). Soft-tissue bruising, abrasions, lacerations, fractures, etc. probably all cause pain, but possibly (I don't know), the pain levels are not in that order. I would think that whips are good at bruising and lacerations, whereas planks potentially cover a more wide range of damage. (There is a lot of stuff on the internet about surprisingly painful paper cuts, which might also be related somehow.)

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It doesn't actualy hurt here is an article about the type of whips jockeys use: http://www.guardian.co.uk/sport/2011/oct/18/jockeys-whip-didnt-hurt But I think you mean why does it seem to hurt. As @Alfred said this is because it exeeds th speed of sound. Sounds are traveling vibrations in the form of pressure waves in an elastic medium. In gases, sound travels longitudinally at different speeds, mostly depending on the molecular mass and temperature of the gas, and pressure has little effect. wiki says: Some common whips such as the bullwhip or sparewhip are able to move faster than sound: the tip of the whip breaks the sound barrier and causes a sharp crack—literally a sonic boom. Sonic booms generate enormous amounts of sound energy, sounding much like an explosion. This is exactly the situation of the whip.

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## protected by Qmechanic♦Aug 17 '13 at 21:54

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