▪ (c)-Show that Lorentz force density (p(Ē + Ủ × B), — and velocity 4-vector are perpendicular.<

Spacecraft Alpha moving at 0.60c with respect to the earth. If spacecraft Beta has a speed of 0.20c with respect to the earth in the same direction as Alpha. Calculate the speed of Alpha as measured from spacecraft Beta

4. Bob is moving away from Alice with speed of 0.5c. Carlos is moving away from Alice and to Bob with speed of 0.8c. What is the speed of Carlos as measured by perpendicular Bob?

2. An alternative derivation of the mass-energy formula E, = moc² also given by Einstein, is based on the principle that the location of the center of mass (CM) of an isolated system cannot be changed by any process that occurs inside the system. The Figure below shows a rigid box of length L that rests on a frictionless surface; the mass M of the box is equally divided between its two ends. A burst of electromagnetic radiation of energy E, is emitted by one end of the box. According to classical physics, the radiation has the momentum p = "0%c , and when it is emitted, the box recoils with the speed v z Eo/ so that the total momentum of Mc the system remains zero. After a time t z L/c the radiation reaches the other end of the box and is absorbed there, which brings the box to a stop after having moved the distance S. If the CM of the box is to remain in its original place, the radiation must have transferred mass from one end to the other. Show that this amount of mass is m, = c2.