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  • 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 counter intuitive, 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.

  • 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 got 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 moment 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 motionwhich is called kinetic energyis

  • 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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In my last video we performed an experiment in which two identical wood blocks were shot

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