Question

SP6 Ann measures the (relativistic) momentum of a tiny particle to be 3.2 x 103 kg mls. The mass of the particle is 8 x 10-3g, and it is moving in the-x-direction a. Find the total energy of the particle according to Ann b. Find the difference of the particle's total energy and its rest energy, and compare it to the kinetic energy of the particle calculated non-relativistically. . Write the components of the momentum 4-vector of the particle according to Ann. d. Bob moves past Ann in the +x-direction at a speed of 0.6c, and measures the energy of the same particle. Compute the energy of the particle according to Bob in two ways: i using velocity addition ii. using a lorentz transformation of the 4-vector momentum components measured by Ann

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Answer 1

Total relative energy of the particle is E = squareroot p^2c^2 + m^2 c^4 = squareroot 3. 2 times 10^3)^2 + (8 times 10^6)^2 times (3 times 10^8) = squareroot 9. 22 times 10^23 + 5. 18 times 10^23 = 1. 2 times 10^12 required difference between the total energy and rest energy is, E_x = squareroot p^2 c^2 + m^2 c^4 - mc^2 = [1. 2 times 10^12 - (8 times 106-6) (3 times 110^8)^2] j = 4. 8 times 10^11 j which is the relative kinetic energy \r\n the non- relative kinetic energy is given by E_k non relative = 1/2 mv^2 velocity v can be calculated from p = mv/squareroot 1 - v^2/c62 = 3. 2 times 10^3 or v/squareroot 1 - v^2/c^2 = 3. 2 times 10^3/8 times 10^-6 = 4 times 10^8 = 4/3 c rightarrow E_k Nonrelativistic = 1/2 mv^2