BB moving at 0.01% the speed of light

[Afrobot]

I'm writing a book and in it there is a character who can accelerate objects to extreme speeds in one direction. His weapon of choice is a custom built gun that is similar to a BB gun. It fires 5mm tungsten rounds that weigh 1 gram (for simplicity). Normally the gun is just a non-lethal air powered gun, but when he uses it he can accelerate the load to 0.01% the speed of light. The problem is I don't know how much damage this would do. I want him to be able to blow people way to the point that they are just a stain on the side walk, to wreak tanks in a single shot, blow holes through steel walls, not to level a city. I am worried that 0.01% the speed of light might be over kill so my question is how much force would this (shooting a 1 gram 5 millimeter ball at 0.01% c) produce and what type of damage would it do. For example if this was shot at a 5 meter x 5 meter iron wall that is a centimeter thick. Also this would blow someone up right? I'm not well versed in high velocity impacts.

tl;dr: 1 gram 5 millimeter ball projectile moving at 0.01% the speed of light hits a 25 meter^2 iron wall that is 1 centimeter thick and the projectile hits the wall perpendicularly. How much damage does this do to the wall an the surroundings? How long could the ball travel without being evaporated or otherwise destroyed? If you were firing this how far away would you want to be from the impact site?

In;b4: Ignore Newtons third, there is no recoil (magic)

Fallow up question: How would this be effected if the character also had a power that could increase the strength of molecular bonds, causing the ball to be extremely durable to the point that it would survive the impact? or just durable enough to survive the travel?

 

[sophiecentaur]

The formula for Kinetic Energy is half m vsquared. That will tell you how many Joules of energy the bullet would have. (you need to change your units to m/s and kg, of course).
You could then relate this energy to, say, the equivalent mass of petrol (or any fuel) or how long a 100MW generator would drive an arc welder for that amount. The sums are pretty straightforward but I don't have a pencil with me at the moment.
It would be hard to calculate the actual amount of damage because different types of ordnance can have very different effects on different targets. I imagine the projectile could tend to penetrate rather than knock the wall over. You'd also need to consider the effect on the air it travels through - shock wave and ionisation.

increase the strength of molecular bonds

You'd be talking in terms of a different substance there; everything about the bullet would change and that's even more of a stretch than just the speed of the BB. Sounds like Matrix stuff.

 

[Afrobot]

sophiecentaur,
According to that the Kinetic energy would be 4.5 GJ, which is slightly more energy than a ton of tnt. I'll make it so that he can vary the power and his upper limit is 1%. Thanks for the reply, but I am curious about what happens to the air. I imagine that it would be compressed a lot causing it to reach high temperatures but beyond that I don't know. Why would increasing the intramolecular force of the atoms in the BB change so much (and what would change).

 

[sophiecentaur]

Sudden compression of the air will heat it and cause it to ionise - leaving a glowing trail and, of course, dissipating some of the bullet's energy. This would limit the range in air. (Did you see any of the Perseid meteors recently?) For shortish range, this would not be a problem. (No more than all the others)

Inter /intra molecular forces are determined by (or determine?) the actual Chemistry of the substance and the density, too. This can be done, as with metal alloys, by adding traces of other substances like carbon and chromium. Easy to do before the event but a bit difficult to adjust by turning a knob on the side of the gun(!) unless you were actually making the bullets in real time.

 

[Afrobot]

Thanks again. This discussion has lead to even more questions (as all good discussions do) that I shall research in my own time:
> Why do gases ionize at high temperatures?
>> Is the energy from the heat transferred to the electrons causing them to be more erratic?
> If you could control the electrons of a metal could you use them to restructure it and make the metal stronger?
>etc
I love science, because the more you learn the more there is to learn, and there are still so many unanswered questions. Its turtles all the way down.

 

[Aero51]

Thanks again. This discussion has lead to even more questions (as all good discussions do) that I shall research in my own time:
> Why do gases ionize at high temperatures?
>> Is the energy from the heat transferred to the electrons causing them to be more erratic?
> If you could control the electrons of a metal could you use them to restructure it and make the metal stronger?
>etc
I love science, because the more you learn the more there is to learn, and there are still so many unanswered questions. Its turtles all the way down.

This should answer your first two questions pertaining to hypersonic flow
http://ftp.rta.nato.int/public/PubFullText/RTO/EN/RTO-EN-AVT-116/EN-AVT-116-03.pdf