Suppose that you are part of an astronomy team observing a group of micrometeors

Question

Suppose that you are part of an astronomy team observing a group of micrometeors (m = 5.60 times 10^-2 kg) travelling through the solar system. You observe that the group of meteors travels a distance of 9.90 times 10^4 m in 1.30 times 10^-3 Answer the three questions below, using three significant digits. A. What is the rest energy (E_0) of the one of the micrometeors? B: What is the distance (Delta x_m) travelled as experienced by the micrometeors? C: Calculate the relativistic momentum (p) of one of the micrometeors.

Explanation / Answer

A) rest energy, E0 = m c^2 = 5.60 x 10^-2 x (3 x 10^8)^2

= 5.04 x 10^15 J

B) by length constarction, moving observer will experience short length by factor Y.

v = d / t = 9.90 x 10^4 / (1.30 x10^-3) = 7.615 x 10^7 m/s

v/c = (7.615 x 10^7) / (3 x 10^8) = 0.2538 c

Y = 1 / sqrt[1 - (v/c)^2 ] = 1 /sqrt[1 - 0.253^2] = 1.034

L = (9.90 x 10^4) / 1.034 = 9.57 x 10^4 m

C) p = Y m v

= 1.034 x 5.60 x 10^-2 x 7.615 x 10^7 = 4409389.6 kg m/s

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