Relativistic vs non-relativistic momentum

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To find the momentum of a 1g particle moving at half the speed of light, use the non-relativistic formula p=mv and the relativistic formula p=mv/(1-v^2/c^2)^(1/2). Comparing the two results typically involves determining which value is larger or smaller. A more precise approach includes calculating the ratio of classical to relativistic momentum or the percentage difference between them. For this scenario, the relativistic momentum is approximately 4.2% larger than the classical momentum. This analysis highlights the significance of relativistic effects at high velocities.
daisy7324
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The question ask to find the momentum of a particle with mass 1g moving with half speec of c and then compare the answer with the result using relativistic formula for momentum. Do I just use p=mv for non relativistic and p=mv/(1-v^2/c^2)^1/2 and put them equal to each other to find the relationship? Thanks:biggrin:
 
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Those are the right formulas. When asked to compare to quantities, usually you can answer that by stating which quantity is bigger, which is smaller etc. That's all they are asking for.
 
If you wanted to be more precise you could find the ratio of classical to relativistic momentum.
 
Or you could find the percentage difference between the two, e.g. "the relativistic momentum is 4.2% larger than the classical momentum."
 

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