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I was watching this video on YouTube, which showed several slow-motion shots of bullets impacting Prince Rupert's drops. One thing I noticed is that there's a noticeable delay between when the bullet strikes the drop, and when the drop recoils backwards.

It's most noticeable in the first shot, which starts at about 1m48s and lasts until about 1m55s.

I took a few screen shots to illustrate my point. These were taken at equalish (done by hand) intervals. I added the purple line. Note that the rightmost edge of the drop stays roughly flush to the line for frames 1-5, but then moves a few pixels in frame 6. It's even more striking in the video: the drop seems to hold almost still, and then suddenly lurch backwards.

delayed reaction to Rupert's Drop being hit by bullet

One thing I did notice: the tip of the drop breaks off (without shattering the whole drop, as explained at 2m16s) just before the drop moves backwards. I'm guessing it has something to do with a shock wave traveling through the drop, reaching the tip, and then... something? If that's the case, then why does the drop move back as soon as the tip breaks? I would expect it to be further delayed by the time it takes for the shock wave to move back up.

What exactly is going on here?

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2 Answers 2

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There is no delay:

  • The slow-motion video is being played at a non-constant frame rate.

That becomes clear in the way the swirl of fumes from the gun accelerate at around 1:51 in the video.


Old take (wrong)

The hit made the glass drop rotate as well as recoil.

That's especially noticeable from the way the strings holding the drop become increasingly less tight from frame to frame.

The key point, as you guessed, is the tip breaking off. Energy is released and the tip shoots downwards and to the left: conservation of moment leads to the remaining of the drop being pushed upwards and to the right, and to the bend in the drop crossing your magenta line.

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  • $\begingroup$ I don't think it's conservation of momentum. The tip that goes bottom-left does so at roughly the same speed as the rest of the drop, despite being far less massive, so momentum is going to the right after the split. That actually makes sense -- a bullet did just hit it, after all -- but it doesn't answer the question of why the momentum didn't seem to move to the right immediately, or what force acted on it to accelerate it after the split. $\endgroup$
    – yshavit
    Sep 20, 2017 at 5:13
  • $\begingroup$ @yshavit, I took a better look at the video and updated my answer. $\endgroup$
    – stafusa
    Sep 20, 2017 at 7:38
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    $\begingroup$ Oh my gosh! You're right! Wow, great catch. That also explains why there isn't a delay on subsequent shots in that same video (and in the followup video). $\endgroup$
    – yshavit
    Sep 20, 2017 at 14:14
  • $\begingroup$ It becomes even more clear when you look at the time counter in the bottom left corner. (Although this still doesn't necessarily exclude all acceleration - I still argue that there should be some acceleration coming from the fumes.) $\endgroup$
    – mivkov
    Sep 21, 2017 at 13:31
  • $\begingroup$ @Mladen, I also believe the fumes should have some effect, but given the much larger mass of the bullet, I'd say it's negligible. $\endgroup$
    – stafusa
    Sep 21, 2017 at 13:39
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I can't really say what exactly it is, I'd need to experiment a bit first, but I have a few suggestions:

First thing to consider is that rigid bodies are never perfectly rigid, at least not on an atomic level. A decent approximation for a rigid body (or a crystal if you will) is atoms being in a grid, held together by interatomic forces. The atoms will never be perfectly still and in place, but vibrate as if held together by springs. (Approximating the interatomic forces by a harmonic oscillator for a solid body is actually a popular concept.)

What does it mean for our case? Well, imagine pushing a relaxed spring. First the spring will contract a bit due to its inertia, but then move as a whole (and start expanding back and then oscillating while moving in the direction of the push.) Same thing is to be expected here: The distances between the atoms first contract, "absorbing" the shock if you will, and only then the object as a whole will start to move. So this is one cause of the delay.

Secondly, you observed an accelerated motion. Accelerated motion always means that there is a force acting on the object. Always. But the acceleration only is apparent after the bullet and the drop are not in contact anymore. Sure, while they were in contact, the force came from the bulled, which changed the drop's momentum ( it's motion ) according to $\vec{F} = d\vec{p}/dt $ . But after they lose contact, there can be no more transfer in momentum, yet the drop seems to accelerate. So how can this be?

Again, accelerated motion always means that there is a force acting on the object. So we need another source for the force. Maybe one we can't see?

My best guess is that the acceleration comes from the hot air and gas coming out of the pistol/gun (couldn't find the technical term for this gas leaving the gun), which partly are slower than the bullet itself (some appear to be faster, see around 1:46 in the video you linked). You can also see some black smoke passing the drop around 1:52, just around the time when the main acceleration seems to start.

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  • $\begingroup$ I would appreciate a comment on the downvote? $\endgroup$
    – mivkov
    Sep 19, 2017 at 20:49

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