Suppose that you have found a way to convert the rest energy of any type of matter directly to usable energy with an efficiency of85.0%. How many liters of water would be sufficient fuel to very slowly push the Moon 2.90 mm away from the Earth? Thedensity of water is pwater = 1.00kg/liter, the Earth's mass is Mearth = 5.97 x 1024 kg, the Moon's mass isMmoon = 7.36 x 10²² kg, and the separation of the Earth and Moon is deM = 3.84 × 10% m.water:Liters

The expression for the gravitational force between the Earth and the Moon is…

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dx 4x 3. In so-called "natural units" (which is just a sneaky way to let us ignore a bunch of constants), the relativistic kinetic energy of a rigid body is given by the formula 1 КЕ — т V1 – v2 where m is the rest mass of the body and v is its relative speed. Alien scientists on a space station are observing an object falling into a black hole. As the object falls, it is disintegrating, losing mass at a rate of 3 (so its mass is changing at a rate of -3). How fast is the kinetic energy of the main part of the object changing when its mass is 20, its velocity is .7, and it is accelerating at a rate of .1 (remember that acceleration is the derivative of velocity with respect to time: a = dt 1Note that this formula does not make sense when v > 1. That is because in natural units, a speed of 1 corresponds to the speed of light, and nothing with positive rest mass can go that fast.
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The sun generates energy through nuclear fusion, which converts mass intoenergy. If the sun radiates 3.8 × 1026 W of power, calculate the rate at which the sun loses mass (i.e., kg/s). _________×109kg/s ? Compare the energy produced per kg of fuel for the combustion of coal, d-d fusion and d-t fusion.d-d: __________ ×107 MJ/kg?d-t: ___________×108 MJ/kg ? The age of the sun has been estimated at 4.6 billion years. If it has radiatedenergy at the same rate throughout its lifetime, 3.8×1026 W and if its current mass is1.989×1030 kg, what fraction of its original mass has been lost _____________% ?
Suppose astronomers found evidence of an earth-like planet 20 lightyears away. a) what may be two ethical considerations that one may consider when deciding if humans should travel to this planet? b) how fast would a spaceship need to travel if the roundtrip can no take longer than 40 years for the astronauts? c) how much time will the trip take according to the people on earth?
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…