Kinetic Energy of an object at the speed of light

  1. If you could fire a piece of lead at the earth that was 1cm3, at close to the speed of light, what would be the amount of enery released? What would be the effect on the planet with and without an atmosphere?

    thanks guys

  2. jcsd
  3. Can you pretend that you're talking to an idiot? :)

    I was hoping someone could do the calculations for me, and then translate that into something that I could grasp with my limited intellect... I really have no idea what a joule even is.

    I'm not a student, and the only reason for this question is personal curiosity.

    If the earth had no atmosphere, and the object hit the surface, what do you educated guys think would happen? Any guesses?
  4. As much as you want, depending how close you mean by "close". The question doesn't really make sense.
  5. DrGreg

    DrGreg 2,011
    Science Advisor
    Gold Member

    Kinetic energy is[tex]

    E = mc^2 \left( \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} - 1 \right)

    [/tex] where m is the mass of the lead, and v is its speed, and c is the speed of light. So it depends how fast you go: the closer to the speed of light, the larger the energy gets. If it were possible to reach the speed of light (it isn't), the energy would be infinite.
  6. Drakkith

    Staff: Mentor

    Well, for a 1 kg mass travelling at 0.9 c, 90% the speed of light, it would have kinetic energy equal to 1.163 x 10^17 joules. 2.1 x 10^17 joules is roughly what was released by the 50 megaton Tsar Bomba nuclear weapon. So 1kg of mass travelling at 0.9 c would have about 25 megatons worth of energy.

    0.9 c is about equal to 269,000,000 meters per second, or 269,000 km per its REALLY fast.
  7. Thanks Drakkith. The Tsar bomb reference was something that I could visualize. Ive watched the Tsar bomb video and am amazed every time I see it. I enjoy reading your posts, even though lots of things you talk about are way over my head.

    I guess another one of the things i was curious about was if a very tiny object could destroy the planet, if it was moving fast enough. Someone said earlier that at the speed of light, the object's KE would be infinite. So that means that any amount of mass could destroy the earth, if it were travelling at 1c? I realize this is impossible, but theoretically?
  8. Ryan_m_b

    Staff: Mentor

    I think you need to look up the word theoretically. It is an impossibility, you cannot get infinite energy. The statement barely makes any sense!
  9. Drakkith

    Staff: Mentor

    It not even theoretically possible. It is 100% impossible for anything with mass to reach c. But, theoretically, almost any amount of mass could be given a high enough velocity to destroy Earth. But that is only theoretically, and far from feasible.
  10. There is also the issue of energy transfer. While a 1 cc object may have enough kinetic energy to destroy the earth that doesn't mean that an impact will destroy the earth. It may just punch a hole straight through and keep going on the other side.

    I think determining what would actually happen would require either massive amounts of programing and computer simulation or building a gun that can fire a round a .99 c (pick your own velocity).
  11. You sure know how to make a guy feel stupid! Maybe the word I should have used was "hypothetically"? I barely graduated high school, and you guys humble me.

    Thanks, that was what I was getting at.

    Thanks mrspeedybob, you answered on of my questions from my OP.

    -Thanks for all of your replies, Ill do my best to ask questions that make sense. I'm just a normal guy that has an appreciation for science, even if I don't understand most of it.

  12. @ GammaR4yBurs : Why don't you just get into something real like start learning about physics and astronomy. Your curiousness about astronomy will help you very much.

    Its never late in life
  13. Ryan_m_b

    Staff: Mentor

    It wasn't my intention to make you feel bad. Even hypothetically doesn't make too much sense because if you break it down what you are asking is;

    "What do the laws of physics say about X (where X is something the breaks the laws of physics)".

    Don't worry, everyone learns this at some point.
    Last edited: Sep 11, 2011
  14. Thanks ryan, my questions were answered. Its just intimidating posting on this site, where questions have to be very specific for things to make sense. I have no desire to become a scientist of any sort, just some childish curiosities that I would like to hear experts opinions on. Again, thank you all for taking time to help me out!

  15. Drakkith

    Staff: Mentor

    Don't be afraid to ask a question, even if you think it is stupid!
  16. As noted, this can't happen...but if you get enough high energy radiation (no mass) that could also destroy just about everything on goes first and rather easily, but enough radiation (energy) to rip atoms apart is quite unlikely. Such fracturing of atoms is what happens in fission (nuclear) bombs.

    And with enough radiation energy earth could be pushed out of it's orbit if that energy exceeded gravitational attraction between earth and moon or earth and sun.

    Don't worry about feeling dopey here: we all learn from others and feel "dopey" from time to time...feeling dopey is also called "growth" if taken constuctively....and growth is usually uncomfortable.
  17. Isn't there an outside chance that a big glob of material ejected from a black hole could be going 99.999999% relative to earth, and impact hard enough to break the planet up?
  18. Ryan_m_b

    Staff: Mentor

    Nothing can be ejected from a black hole. However the more mass there is the more energy, same as increasing speed.
  19. Drakkith

    Staff: Mentor

    I don't think so. Anything with enough mass to be ejected from the accretion disc and pose a threat to a planet would probably be torn apart in the process.
  20. Hey gamma, check out the "boom table." Its a random list of things/events and their associated energy and TNT equivalent.

    For the smarter people, at the bottom it has the energy of all observable stars and the energy of the big bang. What do yall think of these values? They almost seem a little small considering how many stars are out there....Im guessing these are estimates lol.
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