Bullet Block Explained!

In my last video, we performed an experiment in which two identical wood blocks were shot with the same rifle, one through the center of mass and the other one slightly off to one side. Now, if you haven’t seen that video yet, then click here now and go and watch it. Or, if you are on a mobile device, click the link in the description.

So the question was: Compared to the block shot straight through its center, how high would the block shot to one side go? Now, 60 percent of you predicted that it wouldn’t go as high.

It didn’t seem as high.

Now check out the high speed footage.

Oh, no.

You can clearly see that both blocks...

What?

... go to the exact same height.

Oh, come on.

Nineteen percent said that it would go higher. And only 21 percent correctly predicted that both blocks would go to the exact same height. So most of us got it wrong the first time around and that includes Henry and me and Destin who has a lot of experience with this stuff.

I mean, I can’t tell you how many times I have hit wood with a rifle.

So even experienced and intelligent people get it wrong sometimes. In this case, I think the result was particularly counterintuitive because the spinning block clearly ended up with more energy than the other block. So I asked you guys to make me a video response and explain what is happening. And this is what I received.

If you imagine the bullet traveling through the center of the block, then... [multiple voices]

Whoa. That is a lot of video responses. And that is not even all of them. I have got to say I was blown away by all of the great video responses I received. You guys are awesome and really, really appreciate all the effort you went to. You know, some of you actually replicated the experiment, perhaps with different setups.

Oh, ah.

The experiment was featured on blog posts, including Scientific America and Wired. There is an interactive simulation you can try. The link is in the description. And someone even made a web comic. It is so incredible, you know, watching all of those video responses.

And I did watch all of them. That was my proudest moment making this YouTube channel, seeing all of you guys doing science and getting so involved and putting in so much effort. It just blows my mind. It is amazing. Thank you guys so much. Thank you, thank you. I can’t even put it into words how awesome it is. Whoo.

So what is the answer? How could two identical blocks shot with the same rifle end up with different amounts of energy? Well, some of you felt that the amount of rotational energy would be basically insignificant.

What if the amount of energy necessary to get that very small block rotating really is negligible in comparison to the amount of energy necessary to lift it into the air and resist gravity?

Well, we can calculate it because the spinning block was rotating at about 11 times per second. So you can calculate that its rotational energy would be equal to 50 percent of the gravitational potential energy when those blocks were at their peak. So the spinning block actually had 1.5 times the energy of the non-rotating block. And in my books, that is not negligible.

So what else could be causing this? Well, some of you actually measured the height difference using pixel counters and found that the blocks didn't go to exactly the same height. So this raises an important question, which is: How different would those heights have to be before you can think that there really is a difference there?

Well, given that the rotational energy is about 50 percent of the gravitational potential energy, you might expect the spinning block to go half as high. But looking at the video footage, you can clearly see it doesn’t go half as high. It goes basically to the same height. To know for sure, you would probably want to do the experiment a number of times. In science, you have got to repeat things and make sure what you saw is not just a fluke, that it will happen every time.

So, in fact, we did repeat the experiment a number of times and here are all of the blocks lined up side by side so you can compare their heights. The blocks clearly do not all go to the same height. So you might say: Derek, you were tricking us. You just picked the two that went the closest and used those.

It is true. I did do that. But the point is do the spinning blocks go systematically to a lower height than the non-spinning blocks? And I think from the video footage the answer is clearly no.

So why not? Well, another common response I saw was that air resistance must play a role, that the spinning block exposes a small surface area as it is traveling upwards and this means there is less air resistance impeding it.

So even with a lower velocity, it could make it to the same height as the non-spinning block. But you can do the calculation and find that the difference in air resistance would be, at most, about 0.6 percent of the weight of the block. In other words, negligible.

So what is the real answer? Well, there are a number of ways of approaching the problem and I saw you guys try almost all of them: force, torque, momentum, energy. But the easiest one of these is the law of conservation of momentum.

You see, when the bullet is fired out of the rifle, it has a certain amount of momentum entirely in the vertical direction. And when the bullet becomes lodged in the block, the bullet and block together must have that same momentum that the bullet had. Now, it doesn’t matter where on the block the bullet hits because the bullet had a certain momentum before it hit the block. The block and bullet together afterwards must have that amount of momentum upwards.

So this means regardless of whether the block is spinning or not, it must have the same upwards velocity so that it has the same momentum, so it will go to the same height regardless of whether it is spinning or not. It is simple conservation of momentum. Momentum is always, always conserved. It is something you can always rely on. And it is why you should think about it first.

But some of you may say: Ok, well, there is also angular momentum in the spinning block. But the point is: Angular momentum and linear momentum are independent and they are conserved independently. So you can simply think about the upward momentum of the bullet and that is going to have to be the upward momentum of those two blocks and it doesn’t matter that one is spinning, because they have the same total linear momentum upwards. So they have to go to the same height.

But if that is the case, why does the spinning block end up with this extra rotational energy? Well, the thing about energy is, it is a little bit tricky. Although total energy is conserved, the energy of motion—which is called kinetic energy—is not conserved.

So what happens is as the bullet strikes the wood, a lot of its kinetic energy is lost, heating up the wood, creating sound, and deforming that wood block. So it would be possible for the rotating block to end up with more energy of motion, more kinetic energy, if the bullet loses less energy deforming the wood and heating it up and creating that sound.

And this kind of makes a little bit of intuitive sense because if you imagine the bullet entering the block on the side, the block will be moving away from it faster because it is rotating. So that may mean that the bullet doesn’t penetrate in as far and so it wouldn’t lose as much energy as it is entering the wood, which explains why the block has extra energy allowing it to rotate and go the same height as the other block.

Let’s have a look at how far in the bullet went into each block. This is our first test. Here we go. This is the one where it went straight in.

There.

Yeah.

And we come over here to the opposite end.

This is where the bullet went in off center.

It is not going in here. See where my...?

Yeah, let’s see the other one.

Ok. It is all the way in. It is part way in.

So the bullet didn’t go as far into the spinning block.

Right.

So that was pretty convincing evidence. But just to be extra sure, we x-rayed both blocks and this is what we saw. I am going to overlay the blocks so we can see the difference in penetration depth.

Hang on. It looks like both blocks penetrated each block to the same depth. So does that mean our theory is wrong? Well, let’s think about how different the bullet depths should be. I mean, when the bullet strikes the block, it actually loses 97 percent of its original kinetic energy. And the amount of rotational energy the spinning block has only works out to about one percent of the original kinetic energy of the bullet.

So we would only expect a difference in depths of about one percent. And for our measurements, that would be about a tenth of a millimeter. That would be immeasurable and that is what we see. So although this answer is a little bit unsatisfying, at least it is the truth.

As an extra challenge, I want you guys to think about how we could perhaps modify this experiment so the difference in bullet depth would be measurable. You can leave your answers in the comments or make me another video response because I love those so much.

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