Question

In a laboratory an electron is given a kinetic energy of .400 MeV and sent to the right. A spacecraft moves to the right with a speed of .50c with respect to the laboratory. What would be the kinetic energy of the electron as measured by someone in the spacecraft's frame of reference? The mass of an electron is 9.11x10-31 kg and the mass energy of an electron is .511 MeV.

Answer 1

The kinetic energy of a particle is given by

where mc² is the rest mass energy. and is the Lorentz factor.

In the laboratory frame K=0.400MeV. Rest mass energy of electron is mc²=0.511MeV

Squaring both sides

The electron is moving at speed 0.82787c to the right laboratory frame of reference.

Let A represents the electron, B represents the spacecraft, C represent the laboratory. Velocity of electron (A) relative to the laboratory (C) is

Velocity of spacecraft (B) relative to the laboratory (C) is

Both velocities are to the right, so they are taken as positive. Velocity of laboratory (C) relative to the spacecraft (B) is

The velocity is negative because laboratory is moving to the left relative to the spacecraft.

Using Einstein's velocity addition rule, the velocity of electron (A) relative to spacecraft (B) is

The Lorentz factor of electron in spacecraft's frame is

The kinetic energy of electron relative to the spacecraft's frame is