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.

The escape velocity from a massive object is the speed needed to reach an infinite distance from it and have just slowed to a stop, that is, to have just enough kinetic energy to climb out of the gravitational potential well and have none left. You can find the escape velocity by equating the total kinetic and gravitational potential energy to zero   E=12mv2esc−GmM/r=0E=12mvesc2−GmM/r=0 vesc=2GM/r−−−−−−√vesc=2GM/r   where GG is Newton's constant of gravitation, MM is the mass of the object from which the escape is happening, and rr is its radius. This is physics you have seen in the first part of the course, and you should be able to use it to find an escape velocity from any planet or satellite.  For the Earth, for example the escape velocity is about 11.2 km/s, and for the Moon it is 2.38 km/s.  A very important point about escape velocity: it does not depend on what is escaping.  A spaceship or a molecule must have this velocity or more away from the center of the planet to be free…

28. A neutron lives 900 s when at rest relative to an observer. How fast is the neutron moving relative to an observer who measures its life span to be 2065 s?

Suppose that you are traveling onboard a spacecraft that is moving with respect to the earth at a speed of 0.975c. You are breathing at a rate of 8.0 breaths per minute. As monitored on earth, what is your breathing rate?

In a nuclear reactor, mass is converted to energy via nuclear fission reactions. The conversion of mass to energy is calculated from Einstein's famous equation. (The speed of light is c = 3.0 × 108 m/s.) Consider a reactor generating 890 megawatts of power. Calculate the decrease of mass in one year of running.

General Physics II #3 #38