The famous equation " E = mc2" applies to ideal particles , such as light which i suppose has negligible mass , but how does same gets applicable to body with masses as it would be difficult to achieve speed of light to them !
e = mc2 for heavy weights !
As mass increases, doesn't the equation tend towards infinity faster? I don't recall ever coming across a mass problem with the equation.
| sanju wrote: |
| The famous equation " E = mc2" applies to ideal particles , such as light which i suppose has negligible mass , but how does same gets applicable to body with masses as it would be difficult to achieve speed of light to them ! |
Mass-energy equivalence is not the way to consider this particular problem. What you need is Lorentz Factor in Special Relativity to calculate relativistic mass.
http://en.wikipedia.org/wiki/Introduction_to_special_relativity
PS - according to this, of course, nothing with positive mass can attain the speed of light (c).
| sanju wrote: |
| The famous equation " E = mc2" applies to ideal particles , such as light which i suppose has negligible mass.... |
Just the opposite, in fact, on many counts.
Light particles do not have "negligible mass", they have no mass - zero, not "almost zero", exactly zero.
E = mc² does not apply to just "ideal" particles, it applies to all bodies with mass, from an electron to an entire city bus to a whole galaxy to the entire universe. It does not apply to light particles, because they have no mass (it may seem to - since they have zero mass, m = 0 so E = 0, so it looks like it can apply... but it doesn't, as i will shortly explain).
E = mc² tells you how much energy you would get if you could convert all of the mass of something to energy (or vice versa). Let's say you have a mass of 50 kg. If i were to convert your entire body to energy, i would have 15 gigajoules (14989622900 J) of energy.
E = mc² only applies to stationary bodies. This is why it doesn't apply to light particles... because light particles are never stationary, they are always moving at the speed of light.
If the body is moving, then you have to use:
E = √((p² × c²) + (m² × c⁴))
Where:
E = energy
p = momentum
m = mass
c = speed of light
As you can see, when momentum (p) is 0 - as it is for stationary particles - this reduces back down to E = mc².
For light particles, the second term is always 0 because the mass (m) is zero. So the energy of a light particle is E = pc.
| Indi wrote: | ||
Just the opposite, in fact, on many counts. Light particles do not have "negligible mass", they have no mass - zero, not "almost zero", exactly zero. E = mc² does not apply to just "ideal" particles, it applies to all bodies with mass, from an electron to an entire city bus to a whole galaxy to the entire universe. It does not apply to light particles, because they have no mass (it may seem to - since they have zero mass, m = 0 so E = 0, so it looks like it can apply... but it doesn't, as i will shortly explain). E = mc² tells you how much energy you would get if you could convert all of the mass of something to energy (or vice versa). Let's say you have a mass of 50 kg. If i were to convert your entire body to energy, i would have 15 gigajoules (14989622900 J) of energy. E = mc² only applies to stationary bodies. This is why it doesn't apply to light particles... because light particles are never stationary, they are always moving at the speed of light. If the body is moving, then you have to use: E = √((p² × c²) + (m² × c⁴)) Where: E = energy p = momentum m = mass c = speed of light As you can see, when momentum (p) is 0 - as it is for stationary particles - this reduces back down to E = mc². For light particles, the second term is always 0 because the mass (m) is zero. So the energy of a light particle is E = pc. |
You described the law nicely. But is it not tough to believe this law specially for high masses partials? Specially if all the energy move to kinetic energy?
Nope, there is no problem applying E = √((p²c²) + (m²c⁴)) to large masses at all. It is routinely applied to planets, stars, galaxies... and even the entire universe. It applies equally well to things that are not moving at all (when it simplifies to E = mc²), to things moving very slowly, to things moving almost at the speed of light, and even to things moving at the speed of light (when it simplifies to E = pc).
For example, i could take our galaxy - about 10¹¹ solar masses - and tell you that if we took it and turned it into a ping pong ball - about 3 kg - how fast that ping pong ball would be travelling (assuming that the galaxy was stationary, and no energy was lost). It would just be:
Mc² = √(p²c² + m²c⁴)
where M is the mass of the galaxy, p is the momentum of the ping pong ball, and m is the mass of the ping pong ball. To solve:
M²c⁴ = p²c² + m²c⁴
p²c² = M²c⁴ - m²c⁴
p = c√(M² - m²)
That gives p, the momentum of the ping pong ball. You could use the classic, Newtonian formula for momentum, but at the speed you're probably going to get, you may want to use the relativistic formula or you'll get a speed faster than light.
Even though we're dealing with things as massive as galaxies and as light as ping pong balls... and things going really fast and things standing still... there are no problems. (You can even plug in numbers and solve this, if you're masochistic. It will probably make your calculator snort, though.)
For example, i could take our galaxy - about 10¹¹ solar masses - and tell you that if we took it and turned it into a ping pong ball - about 3 kg - how fast that ping pong ball would be travelling (assuming that the galaxy was stationary, and no energy was lost). It would just be:
Mc² = √(p²c² + m²c⁴)
where M is the mass of the galaxy, p is the momentum of the ping pong ball, and m is the mass of the ping pong ball. To solve:
M²c⁴ = p²c² + m²c⁴
p²c² = M²c⁴ - m²c⁴
p = c√(M² - m²)
That gives p, the momentum of the ping pong ball. You could use the classic, Newtonian formula for momentum, but at the speed you're probably going to get, you may want to use the relativistic formula or you'll get a speed faster than light.
Even though we're dealing with things as massive as galaxies and as light as ping pong balls... and things going really fast and things standing still... there are no problems. (You can even plug in numbers and solve this, if you're masochistic. It will probably make your calculator snort, though.)
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