# Relativistic Error in Classical Formula for Kinetic Energy

Using the classical and relativistic expressions for kinetic energy, calculate the range of velocities for a particle of mass m such that we use the classical expression for kinetic energy to within an accuracy of 1%.

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#### Solution Preview

The classical formula for kinetic energy is

K_c = 1/2 mv^2

while the relativisitic formula is

K_r = (gamma - 1)mc^2,

where gamma = 1/sqrt(1 - v^2/c^2) is the Lorentz factor. We want to know what values of v does K_r differ from K_c by no more than 1%. We ...

#### Solution Summary

We compare the classical and relativistic formulas for the kinetic energy of a particle traveling at speed v, and determine the range of speeds v for which these formulas differ by less than 1%.

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