Finding the Velocity of an Asteroid with a Given Mass and Kinetic Energy

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SUMMARY

The discussion focuses on calculating the speed of a 2500 kg asteroid with a relativistic kinetic energy of 1e+20 J using the equation KE=(mc^2/sqrt(1-v^2/c^2)-mc^2. The user initially calculated a speed of 216480727.3 m/s, which raised concerns about the units and the expected format of the answer in terms of the speed of light (c). The confusion stems from the difference between relativistic speeds and classical interpretations, emphasizing the need for careful algebraic manipulation in relativistic physics.

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  • Understanding of relativistic kinetic energy equations
  • Familiarity with the speed of light (c) as a constant
  • Basic algebra skills for manipulating equations
  • Knowledge of mass-energy equivalence (E=mc^2)
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  • Review the derivation of the relativistic kinetic energy formula
  • Learn how to express velocities as fractions of the speed of light (c)
  • Practice solving similar problems involving relativistic speeds
  • Explore the implications of relativistic effects on mass and energy
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Students studying physics, particularly those focusing on relativity, astrophysics enthusiasts, and educators looking for examples of relativistic calculations.

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Homework Statement



An asteroid of mass 2500 kg has a (relativistic) kinetic energy of 1e+20 J. What is the speed of the asteroid?

Homework Equations



KE=(mc^2/sqrt(1-v^2/c^2)-mc^2

The Attempt at a Solution



I tried plugging in my values to this equation and got 216480727.3. the answer is in terms of c. I am not sure if I am doing something wrong or if I am in the wrong units because in all my problems where I am given a velocity its always a small value times c such as .9c and I got a large number. There is another problem like this where I am solving for the velocity I can't figure out either.
 
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sklotz said:

Homework Statement



An asteroid of mass 2500 kg has a (relativistic) kinetic energy of 1e+20 J. What is the speed of the asteroid?

Homework Equations



KE=(mc^2/sqrt(1-v^2/c^2)-mc^2

The Attempt at a Solution



I tried plugging in my values to this equation and got 216480727.3. the answer is in terms of c. I am not sure if I am doing something wrong or if I am in the wrong units because in all my problems where I am given a velocity its always a small value times c such as .9c and I got a large number. There is another problem like this where I am solving for the velocity I can't figure out either.

Show us the mathematical steps you used to arrive at this result. This seems to be an algebra issue.
 

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