Another Bee question

Got me a bee gun, yes I do.
I use my gun to shoot bees at you.

My ammo weighs 0.218 grams and is specially coated with a super-thin coating of frictionless polymer to eliminate drag without compromising the splattiness of the bee. My gun is powered by a scalar field generator which can accelerate the bee via a 300 mile circular accelerator to any speed (up to the speed of light–gotta keep it legal you know) I desire. There is negligible recoil when the bee leaves the muzzle.

So far I have fired bees into the ceiling, across town and I think I managed to lodge one squarely between a couple boulders on the moon. That last shot at the moon got me to wondering, because I fired it really fast at like .25 light speed to keep from having to lead a moving target too much, how much damage the bee did when it hit. I was pretty sure I saw a good sized puff of moon dust. But I didn’t worry too much about it.

Ok, questions:

  1. How much force did my moon bee deliver when it hit?
  2. How fast would I need to shoot a bee to stop an oncoming 3,500 kg school bus moving at 100 kmph?
  3. What are some significant practical applications of a bee fired at light speed? (could it damage a bus? Destroy the moon? Alter a planet’s trajectory?

I’ve got no idea on question 1.

On question 2, at no speed would the bee stop an ordinary school bus. Above a certain speed, it would just make a hole right through the bus, and come out the other side, like a bullet.

Question 3 assumes an impossibility. Since a bee has mass, it cannot travel at light speed.

  1. Let’s assume that the bee experienced a decleration from c to 0 of 0.1 sec. Rounding c to 3 x 10[sup]8[/sup] m/s, and knowing F=ma, we get

F =
0.218 g x c =
0.000218 Kg x (300,000,000 m/s)/0.1 s =
65,400 N

This is roughly the force of 15,000 lbs. in Earth gravity.

  1. I agree with Giles that you will just punch a bee-sized hole through the school bus. However, if we assume an indestructible bus, you would need the momentum of the bee to equal the momentum of the bus but in the opposite direction, due to conservation of momentum.

The momentum of the bus is

3500 Kg x 100 Km/hr =
3500 Kg x 100,000 m/hr =
3500 Kg x 100,000/3600 s =
97,222 Kgm/s

To determine the needed bee speed:
(97,222 Kgm/s)/.000218 Kg =
445,972,477 m/s

which is faster than c, so you aren’t going to stop anything much bigger than a Hummer.

1: From the Relativistic calculator, I get 6.425E+11 Joules. That converts to ~0.15 kilotons of TNT.

2: If the .25 light speed bee managed to not pass through the bus and instead decelerate quickly and spectacularly, the bus would not only stop but be converted to tiny bits by the same 150 tons of TNT equivalent in energy. In order for the bee to have the same relativistic momentum of the bus, you will need to send it hurtling toward the bus at 250,000,000 m/s, which will have about 20 times the kinetic energy of your 0.25c bee. This will vaporize your average bus.
Relativistic calculator to play around with other scenarios:

Wouldn’t your bee explode immediately after leaving your bee gun barrel and hitting air really hard? Frictionless polymer won’t reduce air compression in front of bee and heat and pressure from that, even at fraction of c, would be enough to vaporize poor insect.

  • sigh * ok, the polymer has a really really high specific heat. Like, nearly infinitely high. It’s really expensive polymer.

Éxactly. There is no way to have a bee, or pretty much any object, move through air at such speeds and not instantly vaporise.

Joules is energy; the OP asked for force. I suppose this could be more informative than the question actually asked.

The kinetic energy is a good point, although again, I was answering the question as asked, making an assumption that allowed it to actually be answered. When I worked for Ford analyzing barrier tests we always estimated damage as proportional to kinetic energy, and even a bee moving anywhere near c would pack a wallop of kinetic energy.