Question

1. An 8kg mass is observed traveling with a speed of .08*c.

What is its classical momentum?

What is the relativisitic momentum?

What is the difference between the two values?

Repeat the problem for a speed of .2*c and .8*c

Answer 1

0.08c:

classical momentum = m v = 8 * 0.08 * 3e8 = 1.92 x 10^8 Kg.m/s

relativistic momentum = 1/(1 - (v/c)^)^0.5 m v = 1/(1-0.08y2)y0.5 *8*0.08*3e8 = 1.93 x 10^8 Kg.m/s

difference = 1.92617e8 - 1.92e8 = 6.17 x 10^5 Kg.m/s

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0.2c:

classical momentum = m v = 8 * 0.2 * 3e8 = 4.8 x 10^8 Kg.m/s

relativistic momentum = 1/(1 - (v/c)^)^0.5 m v = 1/(1-0.2y2)y0.5 *8*0.2*3e8 = 4.90 x 10^8 Kg.m/s

difference = 4.89898e8 - 4.8e8 = 9.90 x 10^6 Kg.m/s

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0.8c:

classical momentum = m v = 8 * 0.8 * 3e8 = 1.92 x 10^9 Kg.m/s

relativistic momentum = 1/(1 - (v/c)^)^0.5 m v = 1/(1-0.8y2)y0.5 *8*0.8*3e8 = 3.2 x 10^9 Kg.m/s

difference = 3.2e9 - 1.92e9 = 1.28 x 10^9 Kg.m/s

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