This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ASTRONOMY 294Z: The History of the Universe Professor Barbara Ryden SOLUTIONS TO PROBLEM SET # 5 1) [20 points] Einstein showed that mass ( M ) and energy ( E ) are interchange able: E = Mc 2 , where c is the speed of light. This implies, for instance, that 1 kilogram of matter is equivalent to an energy E = (1 kg) (3 10 8 m / sec) 2 = 9 10 16 kg m 2 / sec 2 . An energy of 1 kg m 2 / sec 2 is known as 1 joule, for short. The joule is not a unit of energy that is used much in everyday life. To give you a sense of scale, burning one gallon of gasoline releases 1 . 3 10 8 joules (130 million joules) of energy. Okay, enough background. Heres the question: If you were capable of converting mass to energy with 100% efficiency, how much mass M would you need to produce an energy E = 1 . 3 10 8 joules ? If E = Mc 2 , then M = E/c 2 . Thus, to produce E = 1 . 3 10 8 joules = 1 . 3 10 8 kg m 2 / sec 2 , the amount of mass required is M = E c 2 = 1 . 3 10 8 kg m 2 / sec 2 (3 10 8 m / sec) 2 = 1 . 44 10 9 kg . (1) This mass can also be written as 1.44 micrograms; its roughly equivalent toThis mass can also be written as 1....
View
Full
Document
 Winter '08
 RYDEN
 Astronomy

Click to edit the document details