Consider a collision in which a stationary particle with mass M is bombarded by a particle with mass m, speed v0, and total energy (including rest energy) Em. (a) Use the Lorentz transformation to write the velocities vm and vM of particles m and M in terms of the speed vcm of the center of momentum. (b) Use the fact that the total momentum in the center-of-momentum frame is zero to obtain an expression for vcm in terms of m, M, and v0. (c) Combine the results of parts (a) and (b) to obtain Equ. Ea2 = 2Mc2 Em + (Mc2)2 + (mc2)2 for the total energy in the center-of-momentum frame.
Consider a collision in which a stationary particle with mass M is bombarded by a particle with mass m, speed v0, and total energy (including rest energy) Em. (a) Use the Lorentz transformation to write the velocities vm and vM of particles m and M in terms of the speed vcm of the center of momentum. (b) Use the fact that the total momentum in the center-of-momentum frame is zero to obtain an expression for vcm in terms of m, M, and v0. (c) Combine the results of parts (a) and (b) to obtain Equ. Ea2 = 2Mc2 Em + (Mc2)2 + (mc2)2 for the total energy in the center-of-momentum frame.
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Consider a collision in which a stationary particle with mass M is bombarded by a particle with mass m, speed v0, and total energy (including rest energy) Em. (a) Use the Lorentz transformation to write the velocities vm and vM of particles m and M in terms of the speed vcm of the center of momentum. (b) Use the fact that the total momentum in the center-of-momentum frame is zero to obtain an expression for vcm in terms of m, M, and v0. (c) Combine the results of parts (a) and (b) to obtain Equ. Ea2 = 2Mc2 Em + (Mc2)2 + (mc2)2 for the total energy in the center-of-momentum frame.
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