In this problem we will observe how the momentum of an electron changes as its v

Question

In this problem we will observe how the momentum of an electron changes as its velocity approaches the speed of light. The mass of an electron is 9.109 x 10^-31 kg. First, what is the momentum of an electron which is moving at the speed of a car on a highway, say 25 m/s, in kilogram meters per second? What is the momentum of an electron moving at 16% of the speed of light, in kilogram meters per second? What is the momentum of an electron moving at 89% of the speed of light, in kilogram meters per second? What is the non-relativistic momentum of an electron moving at this speed (89% of the speed of light), in kilogram meters per second? When the electron is moving at 89% of the speed of light, how many times greater is the relativistic momentum than the non-relativistic momentum? Which of the following facts are true about the ratio of relativistic to non-relativistic momentum of an electron? What is the ratio of the relativistic momentum to the classical momentum of a rockctship moving at 99.6% of the speed of light, in kg. m/s?

Explanation / Answer

mass = 9.109 * 10^-31 kg

a) momentum = m v = 9.109 * 10^-31 * 25 = 2.27 * 10^-29 kg m/s

b) momentum = m v = 9.109 * 10^-31 * (0.16 * 3 * 10^8) = 4.37 * 10^-23 kg m/s

c) momentum = m v = 9.109 * 10^-31 * (0.89 * 3 * 10^8) * 1 / sqrt(1 - 0.89^2) = 5.33 * 10^-22 kgm/s

d) non realtivistic momentum = 9.109 * 10^-31 * (0.89 * 3 * 10^8) = 2.43 * 10^-22 kgm/s

e) ratio of relativisitc momentum to non relativistic momentum = 1 / sqrt( 1 - (v/c)^2)

= 1 / sqrt(1 - 0.89^2) = 2.19

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