Help me find my error in a relativistic kinetic energy calculation

In summary, the conversation discusses the energy needed to accelerate a 50,000,000 kg asteroid to relativistic speeds using a hypothetical particle accelerator. The total kinetic energy of the asteroid is calculated to be 1.44 E+36 Joules due to relativistic effects. The energy needed to accelerate the asteroid is shown to be several orders of magnitude lower, around 4.5 E+24 Joules, and the conversation discusses the potential mistake in this calculation, which is determined to be the omission of the Lorentz factor. The importance of the Lorentz factor in calculating the kinetic energy at relativistic speeds is emphasized.
  • #1
Serenityseeker22
4
1
Hi everyone.
Given: an asteroid with the mass of 50,000,000 kg, which is moving with the velocity of oh-my-god particle -- 99.99999999999999999999951% of c.
Due to relativistic effects, its total kinetic energy will be 1.44 E+36 Joules (Lorentz factor = 3.2 E+11).
A hypothetical particle accelerator accelerates bodies 40,000,000 times faster than the most powerful real accelerator.
The energy needed to accelerate such asteroid to this speed is several orders of magnitude lower than the total kinetic energy, or around 4.5 E+24 Joules
I know that there's some mistake, but can't see it yet.
 
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  • #2
We can't see your mistake either, unless you show us the details of your calculations. :frown:
 
  • #3
What I'm trying to say is that the energy needed to accelerate the asteroid is much lesser, than the total kinetic energy this asteroid distributes. It violates some laws of physics, I'm sure of it, but I don't know what exactly and how.

My calculations:

Lorentz factor --
9e74c1f95dd3e0bb0fbb32ae1be1ed4a0c29c6a2

oh-my-god particle's speed -- 99.99999999999999999999951% of light speed
light speed -- 299,792,458 m/s
Relativistic kinetic energy --
rke2.gif

mass -- 50,000,000 kg
Lorentz factor calculation

v2 / c2 = (0.9999999999999999999999951 * 299,792,458)2 / 299,792,458 2 = 0,9999999999999999999999902

Thus, Lorentz factor equals -- 1 / √(1-0,9999999999999999999999902 ) = 319 438 282 499,97

Total kinetic energy equals 50,000,000 * 299,792,4582*(319 438 282 499,97-1), or rougly 1.435 E+36 Joules

To accelerate an asteroid to such speed, I used the same formula sans the Lorentz factor. So, energy needed to accelerate this rock by a hypothetical particle accelerator is 4.5 E+24 Joules
Where's my mistake?
 

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  • #4
Serenityseeker22 said:
I used the same formula sans the Lorentz factor.
What same formula? Show your work. And why ever would you remove the Lorentz factor?
 
  • #5
Serenityseeker22 said:
To accelerate an asteroid to such speed, I used the same formula sans the Lorentz factor. So, energy needed to accelerate this rock by a hypothetical particle accelerator is 4.5 E+24 Joules
Where did that ##4.5\times{10}^{24}## number come from? How did you calculate it? Show your work.

You can simplify the calculations some by setting ##c=1## to get rid of the factors of 299792458. This is equivalent to choosing to measure distances in units of light-seconds instead of meters (the speed of light is one light-second per second) so doesn't change the physics. You can always convert back to Joules when you're done.

Don't use a hand calculator for problems like this one. You have so many decimal places in some of your numbers that roundoff errors will kill your accuracy. Instead, you can use one of the many online arbitrary precision calculators - google for "online infinite precision calculator".
 
  • #6
Nugatory said:
Where did that ##4.5\times{10}^{24}## number come from? How did you calculate it? Show your work.

You can simplify the calculations some by setting ##c=1## to get rid of the factors of 299792458. This is equivalent to choosing to measure distances in units of light-seconds instead of meters (the speed of light is one light-second per second) so doesn't change the physics. You can always convert back to Joules when you're done.

Don't use a hand calculator for problems like this one. You have so many decimal places in some of your numbers that roundoff errors will kill your accuracy. Instead, you can use one of the many online arbitrary precision calculators - google for "online infinite precision calculator".
Same formula,KE=M*C2 just without Lorentz factor, because I thought it's only relevant when the body moves with relativistic speeds, not when it gets accelerated. Of course I might be wrong, and I probably am, that's why I'm asking.
 
  • #7
Serenityseeker22 said:
when the body moves with relativistic speeds, not when it gets accelerated.
As you accelerate to relativistic speed the body moves with relativistic speed. You need the Lorentz factor.
 
  • #8
Dale said:
As you accelerate to relativistic speed the body moves with relativistic speed. You need the Lorentz factor.
That's what I needed to hear, thank you very much.
 
  • Like
Likes Dale
  • #9
Serenityseeker22 said:
KE=M*C2
KE=MC^2 never tells you kinetic energy. It always tells you rest energy.
 
  • #10
Of course, the kinetic energy is equal to the energy it takes to accelerate the mass from rest.
 

1. What is the formula for relativistic kinetic energy?

The formula for relativistic kinetic energy is E = (mc^2)/√(1-(v^2/c^2)), where E is the kinetic energy, m is the mass of the object, c is the speed of light, and v is the velocity of the object.

2. How do I know if my calculation for relativistic kinetic energy is correct?

You can compare your calculation to the formula and also double check your units to make sure they are consistent. Additionally, you can use online calculators or consult with a fellow scientist for verification.

3. What are some common errors in relativistic kinetic energy calculations?

Some common errors include using the wrong formula, incorrect unit conversions, and improper use of the values for mass and velocity. It is also important to ensure that the values used are consistent with the units used in the formula.

4. How can I check for numerical errors in my relativistic kinetic energy calculation?

You can check for numerical errors by plugging in different values for mass and velocity and seeing if the results are consistent with what is expected. You can also use a calculator with a high precision to reduce rounding errors.

5. What should I do if I am unable to find my error in the relativistic kinetic energy calculation?

If you are unable to find your error, it is always helpful to consult with a fellow scientist or an expert in the field. They may be able to offer insights or identify any potential errors that you may have missed. It is also important to double check your calculations and make sure all values and units are correct.

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