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A tomato is travelling very fast towards a 1 cm thick steel plate.

Let's say this happened in a vacuum, so that the air resistance wouldn't rip the tomato apart before it even hit the steel plate.

Obviously the tomato would get destroyed too, but the question is whether there would be a hole in the steel plate, given enough speed.

I guess a more general way to phrase the question is: Can a soft object create a hole through a hard surface, as long as the soft object is traveling fast enough?

If yes, is there a limit to this concept? For example, could the tomato even penetrate a wall made of diamond, as long as it was traveling fast enough?

Edit: A comment on one of the answers used this video to show that tomatoes can't exist for very long in a vacuum. If this is correct, the situation needs to be that the tomato is stationary, the plate moves, and the tomato is put into the vacuum shortly before impact. I believe the impact scenario would be the same in that case?

Fiksdal
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    See https://en.wikipedia.org/wiki/Water_jet_cutter – DJohnM Mar 07 '16 at 05:37
  • @DJohnM Fascinating. – Fiksdal Mar 07 '16 at 05:43
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    If you make your tomato relativistically fast, it doesn't even matter that it's a tomato. It just becomes this giant stream of radiation hitting your target. – knzhou Mar 07 '16 at 06:30
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    Obbligatory reference. – Neil Mar 07 '16 at 11:34
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    @knzhou "very fast matter" and "radiation" aren't exactly the same thing. – Asher Mar 07 '16 at 13:40
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    The real key here is the idea of "strength" as the capacity to absorb "damage energy". A waterjet cutter goes through steel all day long, and not only is it softer than the tomato - it is a fluid. The matter in the water has enough energy that the steel it impacts cannot absorb it, and it breaks. – EngrStudent Mar 07 '16 at 13:54
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    @Asher but at relativistic speeds, one very quickly follows the other. Check out the what-if reference. – Carl Witthoft Mar 07 '16 at 15:28
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    force=mass*acceleration.Even for low mass given enough acceleration you can pierce almost anything. – Mihai Mar 07 '16 at 15:37
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    How thick is the steel plate? You can have a sheet of solid steel on the order of tinfoil thickness, and an ordinary person would be able to throw a tomato through it with just arm strength. ;) – Mason Wheeler Mar 07 '16 at 15:38
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    @Asher What do you call a He4 atom moving at relativistic velocities?

    I call it an alpha particle and two beta particles, which are two of the three kinds of things we normally call "radiation".

     – Monty Harder Mar 07 '16 at 15:48
  • @Mason Wheeler If it was that thin, would you call it a plate? Or a sheet, foil, etc? Nitpicking a little bit here, maybe? Fine, let's consider it 1 cm thick. – Fiksdal Mar 07 '16 at 18:08
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    @Fiksdal Yes, nitpicking, but nitpicking with a point: you have to define your expectations in order for the question to be meaningful. – Mason Wheeler Mar 07 '16 at 18:10
  • @Mason Wheeler Sure, point taken. I've added it to the question. – Fiksdal Mar 07 '16 at 18:17
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    Would a nuclear reaction caused by a tomato moving fast enough count as piercing? If not, then there's an upper bound of plate thickness, beyond which there would be only more and more complete nuclear fusion and obliteration of the tomato (and everything around it at increasing radius). – hyde Mar 08 '16 at 18:32
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    Related, if not duplicate. ![Is it possible to cut harder material with a less hard material?][1] [1]:http://physics.stackexchange.com/questions/137443/is-it-possible-to-cut-harder-material-with-a-less-hard-material# – Anubhav Goel Mar 11 '16 at 07:16

4 Answers4

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The notion of soft or hard object depends on the velocity of interaction. Water can be soft or hard as rock depending on how fast you fall in (or surf upon).

For a shock, the main thing that matter is momentum. In space, where relative speeds can be very high, a simple bolt can cause serious damage to the ISS, and simple flakes of paint cause deep scratches. So, yes, the tomato would create a hole (and evaporate in the shock).

Community
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Fabrice NEYRET
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    Is it (tomato-steel collision strong enough to puncture the later) implied to happen in vacuum? – Mindwin Remember Monica Mar 07 '16 at 14:21
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    Well for the tomato to be travelling fast enough it's presumably in a zero-drag environment as there's absolutely no chance a tomato at Earth-atmosphere terminal velocity could pierce steel: so I'd suggest that yes, it's implied to happen in a vacuum. – Jon Story Mar 07 '16 at 16:43
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    This all reminds me of the Columbia debris impact tests that NASA conducted after the Space Shuttle Columbia was damaged by a piece of foam during launch and subsequently broke apart on reentry. Video of lab impact test: https://www.youtube.com/watch?v=IgQ3ekcvyRA – Paul T. Mar 07 '16 at 18:31
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    In any case, there would be no tomato left, and there probably won't be a clean tomato-shaped hole either (like what you tend to see in cartoons). What would happen is a crater (as mentioned in other answers) that, with sufficient momentum, can end up deep enough to reach the other side of the plate. Of course, if the plate is really 1 cm thick (I was thinking of a meter-thick plate myself), the tomato might actually be able to pierce it properly (tomato-shaped hole and all). – January First-of-May Mar 07 '16 at 20:51
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    Is there an7ything to back this claim at all? Water cutters are a different case as that's like throwing a million tomatoes, rather than one. – Tomáš Zato Mar 08 '16 at 11:50
  • @TomášZato: I'm thinking the same. especially, because a watter cutter is something different. Water has a pretty high tollerance against preassure. so the water itself wouldn't actually "squeeze". It would try to escape, but by the force of a water cutter it just happens pretty limited. While a tomato would have some potential of squeezing. No physician over here and my understanding of pressure resistance related to this might be wrong. But I'd assume water cutter working with oxygen instead of water, would escalate quiet differently before force is even strong enough to make the oxygen cut. – Zaibis Mar 09 '16 at 12:34
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At high speeds the structure of the material becomes far less important than it is at low speeds. At high enough speeds, the issue is not whether the tomato can retain structure during the impact (it wont), but rather the issue becomes one of sheer mass.

The issue is easiest to see in the tomato's reference frame, where one treats the tomato as holding still, and the plate is moving towards it at a high velocity. At impact, we have a momentum problem to solve. If the plate "wants" to retain structural integrity it needs to deal with the fact that there is mass in front of it which needs to be dealt with. It needs to either:

  • Let the mass pass through it, which is very hard given the subatomic forces involved with two masses passing through each other. The result would be catastrophic for the structural integrity of the plate. (I don't think this can happen at realistic speeds, but at relativistic speeds, it might do the job)
  • Accelerate the mass forward to the velocity of the plate. This requires a huge amount of force applied to the tomato. The rest of the plate (the part not hitting the tomato) "wants" to keep going at the same velocity. Thus, the outside parts of the plate will not slow down until the information that the impact occurred reaches them (at the speed of sound). The plate has to accelerate the mass of the tomato fast enough to get it up to speed before the difference in velocity of the far edges of the plate and the impacted region is enough to tear the metal apart. Mass is mass. It doesn't matter if its squishy mass like a tomato, or hard mass like rock, if you need to accelerate it, you need a force. That force is proportional to the acceleration needed. Naturally, the faster the plate is going, the higher the acceleration needed will be to keep the whole plate together while the shockwave propagates through the metal.
  • Deflect the mass elsewhere, to decrease how much one actually needs to accelerate the mass. If you threw the tomato at a knife edge, it would be much harder for the tomato to break the knife because the tomato's mass doesn't need to move very much to go around the knife. There are still shockwaves, like before, but their effect is mitigated because the shape of the object decreases the determental effects. Of course, at the subatomic level, you'll still see forces that could probably break the knife in half, but we can ignore that line of reasoning because you've chosen a plate. If you think accelerating the tomato to plate speeds in a fraction of a second is a lot of force, just consider how hard it would be to accelerate it sideways even further. In fact, if your plate was perfect (made of unobtanium), it would have to push the tomato sideways at infinite speed to get the tomato mass out of the way. With realistic materials, the plate will react, such as bending, which avoids this absurd infinite case.

In the end, we rely on effects like this for a lot of our ballistic missile defense systems. The whole point of a kinetic kill vehicle is to simply put a mass in the way of the incoming ballistic missile, and let the missile deal with the question of how to deal with all that mass in its way. Ignoring the guidance challenges of an intercept at those velocities, we could fling tomatoes at the incoming missiles and knock them out of the sky.

Cort Ammon
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As Anubhav mentioned in his comment, tomato would break into pieces before it hits the plate. However, to answer the logic of the question such event is possible.

A ping pong ball can rip a huge hole on the ping pong racket if it is fast enough. https://www.youtube.com/watch?v=acRnKnsddwc

Update:

It would make a hole, if you make enough assumptions. As you put it, if we think unimaginably fast (99% of light speed), it would behave basically as light. Since laser cutters can cut through steel plates, I would assume it could.

Yield strength of steel is 215 Mpa, and if you assume a tomato is .2 kg and the impact area is 1 cm^3, then you would need 1075 m/s. (Speed of light is 300.000.000 m/s) These are simple assumptions and basic calculations. I would believe there might be some mistakes.

This simple calculation shows us that the tomato should travel faster than a bullet. (Speed of bullet is approx. 400 m/s)

Mert Karakaya
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    There seems to still be debate as to whether it's possible for the tomato to reach that speed, but the YouTube video with the ping pong ball answers exactly what I wanted to know. – Fiksdal Mar 07 '16 at 11:47
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    @Fiksdal I have seen really firm tomatoes (as firm as an apple), but it is highly debatable if it will hold its structural abilities to pierce through a steel plate. In this case there are many other questions such as, would the plate bend or be dented rather than pierced through. This requires some calculation and investigation since steel is not as brittle as wood. – Mert Karakaya Mar 07 '16 at 12:19
  • Well, the point here is not really whether a tomato could travel that fast. For the sake of discussion, you could imagine the tomato being stationary, and the steel moving towards it. I understand that the impact scenario would be the same. If you believe it wouldn't make a hole, what if it was traveling insanely, immensely, unimaginably fast? – Fiksdal Mar 07 '16 at 12:24
  • @Fiksdal I updated my answer, check it out. – Mert Karakaya Mar 07 '16 at 12:39
  • Great answer, the only thing I'm unsure about is your assumption that it's impossible to accelerate a tomato that fast in a vacuum. See Moyli's comment on Anubhav Dev's answer. – Fiksdal Mar 07 '16 at 12:53
  • @Fiksdal I urge you to read my answer again. I have not said that it is impossible to accelerate in any part of the answer. In fact it is possible, but as I mentioned, there are a lot of assumptions to be made. If all the assumption conditions are met I can't see why not this experiment could be reality. – Mert Karakaya Mar 07 '16 at 13:03
  • What I meant is the idea that the tomato would "break apart" before it could reach such speeds. Why would it, if you accelerated it very slowly in a vacuum? – Fiksdal Mar 07 '16 at 13:05
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    It would start breaking apart as soon as it is in a vacuum. https://www.youtube.com/watch?v=92CuA6IKRvQ In order to accelarate it to such speeds, it would take a lot of time and a lot of space to actually conduct such experiment. Let alone the required force input for a long time. If you look at this at macro scale, even the smallest meteor can cause huge craters (eg on the Moon) due to high speeds (72000 m/s). Thus possible but not viable. – Mert Karakaya Mar 07 '16 at 13:09
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    If you move the tomato at 0.99c then you will nuclear reaction as soon as you hit air and a crater instead of a hole. – ratchet freak Mar 07 '16 at 13:16
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    @ratchetfreak I know exactly, but keep in mind that there is no other particles/objects other than the tomato and the steel plate. Thus you can not easily create such reaction without activated air particles around. Assumptions are ridiculous thus real word physics don't really make sense. You would have to investigate the questions under the assumptions. – Mert Karakaya Mar 07 '16 at 13:21
  • @ratchetfreak But there is not supposed to be any air involved in this scenario, right? – Fiksdal Mar 07 '16 at 13:23
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    @Fiksdal well you wouldn't have a plate after the fusion reaction between the carbon in the tomato and the iron in the steel. – ratchet freak Mar 07 '16 at 13:24
  • @ratchetfreak Right. – Fiksdal Mar 07 '16 at 13:27
  • @MertKarakaya True, from that video it appears that tomatoes can't exist for very long in a vacuum. So the situation needs to be that the tomato is stationary, the plate moves, and the tomato is put into the vacuum shortly before impact. – Fiksdal Mar 07 '16 at 13:41
  • @MertKarakaya I've edited the question to take into account that video. – Fiksdal Mar 07 '16 at 13:49
  • "Since laser cutters can cut through steel plates, I would assume it could" - you must be kidding. Laser cutters have nothing to do with that, it's not kinetic energy they're based on. – Tomáš Zato Mar 08 '16 at 11:53
  • @TomášZato Well, you must be kidding as well. Did you read the entire statement which says 99% of the light speed. At that speed, tomato would basically behave as energy. That's why, I gave the example of laser cutters. I don't really think you get the point of this question. He is asking if it is theoretically possible. – Mert Karakaya Mar 08 '16 at 11:56
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Yes, because even just a water (a big drop of water) would do this.

It has been written, in many sources (here for instance), that at high impact speeds the water (or even gas) is as hard as a concrete or glass. Mostly it is about crashing into water at high velocity, but water crashing into something would probably not make any difference.

Nightrider
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  • it is about crashing into water at high velocity is the same thing as water crashing into something. And have a look at https://en.wikipedia.org/wiki/Water_jet_cutter – stackErr Mar 08 '16 at 16:07