2. 130 points] In the following problem, c stands for the speed of light, which
ID: 2032515 • Letter: 2
Question
2. 130 points] In the following problem, c stands for the speed of light, which you may take to be 3.00 x 10 m/s. A particle has a mass of 2.00 kg. This particle is observed in two reference frames, a lab and a rocket. The rocket has a velocity relative to the lab of 0.800 c in the +x direction. In the lab the particle is observed to have a velocity with an x component of 0.600 c, a y component of 0.000 c, and a z component of 0.000 c. (a) Calculate the x, y, and z components of the particle's momentum, as observed in the lab. Calculate the total energy of the particle, as observed in the lab. Now consider measurements made in the rocket reference frame. (b) Calculate the x, y, and z components of the particle's velocity, as observed in the rocket. Give your answers as multiples of c. (c) Based on your velocity from part b, calculate the x, y, and z components of the particle's momentum, as observed in the rocket. Also based on your answer from b, calculate the total energy of the particle, as observed in the rocket. (d) Consider an alternative to part c for calculating momentum and energy as observed in the rocket. Based on the momentum and energy of the particle as observed in the lab (your answer to part a), use the Lorentz transformation to calculate the momentum (x, y, and z components) and energy as observed in the rocket. Note: there are many zeros among the answers to this problem, but make sure to quickly show the calculations that lead to these zeros.Explanation / Answer
a) As the velocity in y and z direction is zero, the particles will not have momentum in either of these directions.
P = m*v
P = 2*0.6c
P = 2*0.6*3E8
P = 3.6E8 kgm/s
Energy will be kinetic energy
E = 1/2mv2
E = 1/2m(p2 / m2)
E = 1/2*p2 / m
E = p2 / 2m
E = 3.24e16 joules.
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