ASTRONOMY 294Z
The History of the Universe
Professor Barbara Ryden
Problem Set # 5
Due Tuesday, February 19
at class time
NAME (please print clearly):
SCORE (instructor use only):
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document1) [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.
Here’s the question:
If you were capable of
converting mass to energy with 100% eFciency, how much mass
M
would
you need to produce an energy
E
= 1
.
3
×
10
8
joules? [Hint: The number you
get should be much, much less than the mass of a gallon of gasoline; burning
gasoline is a sadly ineFcient way of producing energy.]
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '08
 RYDEN
 Astronomy, Energy, Mass, Kilogram, energy consumption

Click to edit the document details