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Determine the ratio of the relativistic kinetic energy to the nonrelativistic kinetic energy (1/2mv2) when a...

Determine the ratio of the relativistic kinetic energy to the nonrelativistic kinetic energy (1/2mv2) when a particle has a speed of (a) 1.83 × 10-3c. and (b) 0.817c.

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Answer #1

a)

v = 1.83 x 10-3 c

v/c = 0.00183

relativistic kinetic energy is given as

KEr = mc2 (1/sqrt(1 - (v/c)2) - 1)

Non-relativistic kinetic energy is given as

KE= (0.5) mv2

Ratio is given as

Ratio = KEr /KE= (mc2)(1/sqrt(1 - (v/c)2) - 1) ) /((0.5) mv2 )

Ratio = KEr /KE= (2)(c/v)2 (1/sqrt(1 - (v/c)2) - 1) )

Ratio = KEr /KE= (2)(1/0.00183)2 (1/sqrt(1 - (0.00183)2) - 1) )

Ratio = 1

b)

v = 0.817 c

v/c = 0.817

relativistic kinetic energy is given as

KEr = mc2 (1/sqrt(1 - (v/c)2) - 1)

Non-relativistic kinetic energy is given as

KE= (0.5) mv2

Ratio is given as

Ratio = KEr /KE= (mc2)(1/sqrt(1 - (v/c)2) - 1) ) /((0.5) mv2 )

Ratio = KEr /KE= (2)(c/v)2 (1/sqrt(1 - (v/c)2) - 1) )

Ratio = KEr /KE= (2)(1/0.817)2 (1/sqrt(1 - (0.817)2) - 1) )

Ratio = 2.2

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