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Two Bullets

Science brain teasers require understanding of the physical or biological world and the laws that govern it.


Puzzle ID:#3610
Fun:*** (2.71)
Difficulty:** (1.24)
Submitted By:bobbrt*****




A piece of firewood is standing on end. Which is more likely to knock the piece of wood over - a lead bullet fired from a gun or a rubber bullet of the same mass travelling at the same speed (and hitting the same spot)?
Assume that the rubber bullet does not disintegrate on impact.

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Apr 21, 2002

Good one..
I knew the answer but i didn;t know how to explain it scientifically.
Apr 27, 2002

Very good description!!
Jun 04, 2002

Is that Newton's 3rd law? For every action there is an equal and opposite re-action?
Jun 15, 2002

I though that was Newton's first law?
Jul 09, 2002

I'm with AbdulAziz, I knew the answer, just not how to explain it!
Feb 19, 2003

Newton's first law is INERTIA
Dec 30, 2003

This is good teaser. I've tried to explain the concept to my dad but he didn't believe me.
Sep 21, 2005

You learn something new every day

Good one
Jan 01, 2006

for this to be true the bullet would have to hit straight on and not at an angle.

here's an example that is fairly common knowledge. you take a bat or other large object and try to break a wooden board is the board easier to break hitting straight on or at an angle?
of course its easier to break hitting straight on. when it hits at an angle not all of the energy is transfered straight into the board its deflected instead of absorbed.
Jun 16, 2008

The problem with your reasoning is that the rubber bullet ricochets off of the wood not because the wood has to absorb more energy, but because energy is REFLECTED by the wood. Newton's 3rd law still illustrates why the wood is more likely to be knocked over, but the rubber bullet, if it has the same mass and momentum, hits the wood with the same amount of energy as the lead bullet. The difference is that more of the kinetic energy is transformed into potential energy and back.
Aug 03, 2008

I agree with tangled brain. Your reasoning is basically sound, but the terminology is incorrect.

The just-ricocheted rubber bullet will have have MORE kinetic energy than the just-embedded lead bullet. However, the rubber bullet will impart more momentum to the log.

How does this work? It's because kinetic energy is a scalar quantity and momentum is a vector. Vectors have direction. The momentum of the just-struck log will have more momentum than the rubber bullet started with, because the richoeted bullet has negative momentum.

Mathematically, it looks like this:

Let's say the bullet weighs .007 kg and strikes a 10kg log at 300 meters/second.

The initial kinetic energy of the bullet is 1/2 (mass * velocity^2)... 315 joules in this case.

The initial momentum of the bullet is mass * velocity... 2.1 kg-m/s in this case.

The collision of the rubber bullet, according to the riddle, is elastic. BOTH momentum and energy must be convserved. This leaves only ONE possible solution for the resulting bullet and log velocities:

Rubber bullet after collision:

. . . . . Mass = .007 kg

. . . Velocity = -299.58 m/s (yep, that's a negative velocity. Velocity is a vector)

Kinetic energy = 314.119 joules (it kept almost all of it)

. . . Momentum = -2.0971 kg-m/s (note, once again, a negative number)

Log after collision:

. . . . . Mass = 10 kg

. . . Velocity = .4197 m/s

Kinetic energy = .88074 joules

. . . Momentum = 4.1971 kg-m/s

Add the two momentums (to double-check) and you get the initial momentum: 4.1971 + (-2.0971) = 2.1

By comparison, the lead bullet does NOT experience an elastic collision. It couldn't have, because it's been embedded in the log. So we need calculate only the velocity of the bullet-log system.

Bullet and log together:

Mass = 10kg + .007kg = 10.007kg

Momentum = 2.1 kg-m/s (exactly the same as the bullet's prior to embedding)

Velocity = 2.1 / 10.007 = .2099 m/s

Q.E.D., the lead bullet imparts only about half as much momentum as the rubber bullet.

You might be wondering...

The kinetic energy of the log-bullet system is very low: 1/2 [10.007kg * (2.099m/s)^2] = .22044 joules. Where's the missing energy? Lead bullets are designed to deliver a large amount of energy to the interior of a target, and that's exactly what it did. It tore a whole in the log, sending dust and tiny splinters in all directions (net momentum = zero, but lots of kinetic energy); these splinters in turn ripped apart other sections of the log, and after a second or two it all decayed to the microscopic level where it is now measured as heat energy.

[Note for the curious: A large amount of destructive kinetic energy translates to a very small amount of heat energy. It would take about 15 bullets to raise the average temperature of a 10kg log by only one degree centigrade.]
Jan 22, 2009

The author sort of slides over the point that the "bullets" are the same mass. Of course, this means that the rubber bullet it 3 or 4 times the size of the lead bullet.
Oct 14, 2016

"Bullet" is too generic a term, as not every bullet will "embed" itself in the firewood. A hollow-point bullet, designed for expansion, will simply mushroom on impact and knock the wood over without penetration. A frangible bullet with enough mass will disintegrate upon impact, but will still impart enough inertia on the wood to knock it over.

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