1. Calculate the energy needed to accelerate a spaceship of mass 10,000 kg to a speed of 0.3c for intergalactic space exploration. Compare this with a projected annual energy usage on Earth of 1021 J.
2. Derive Equation for the relativistic kinetic energy and show all the steps, especially the integration by parts.
3. A test automobile of mass 1000 kg moving at high speed crashes into a wall. The average temperature of the car is measured to rise by 0.5°C after the wreck. What is the change in mass of the car? Where does this change in mass come from? (Assume the average tions useful for producing energy through nuclear fusion.
(a) Assume the deuterium (2H) and tritium (3H) nuclei are at rest and use the atomic mass units of the masses in Appendix 8 to calculate the mass- energy imbalance in this reaction. This amount of energy is given up when this nuclear reaction occurs.
(b) What percentage of the initial rest energy is given up?