Chapter 30 answers:
Exercises:
1. In 1929, Edwin Hubble inadvertently discovered that the universe is expanding, confirming the earlier predictions
of Einstein's General Relativity. Relativity theory says that space itself is expanding, carrying all galaxies with it. Now if
the universe is currently expanding, it was smaller in the past. This means that all matter and energy was more and
more densely packed and thus hotter and hotter as one looks further back in time. Therefore our universe has cooled since
the beginning of time, according to the theory. The current temperature of the universe according to Big Bang
proponents of the 1940's and 1950's (Gamow, Alpher, Hermann) was somewhat less than 10 degrees celcius above
absolute zero (<10K). The problem was that no one had ever taken the universe's temperature! In 1965 this
was done by accident at Bell Labs by radio astronomers Arno Penzias and Robert Wilson (page 725)
Link: Penzias&Wilson They detected a signal with a temperature of about 3K. Since then, this measurement has been
refined by many experiments including the Cosmic Background Explorer
(COBE) sattelite.
4. The universe is expanding and therefore cooling as a whole. ( see #1 above).
6. I guess this one had a bit of algebra in it. If you can do one like this on the final exam, it'll surely be worth extra credit! Let t = time interval measured in our reference frame. Let to = the time interval ticked off by the other clock as we measure it. Since the other clock ticks half as fast, to = (1/2)t. Okay.. here goes:
Equation #1:
Square both sides and cross multiply to get: Equation #2:
your time are slightly (but indetectably) different than those of the trucker stopped by the side of the road!
23. In the famous equation E = mc2, E = energy, m=mass, and c=the speed of light (300,000 kilometers per second).
the c-squared factor is actually a coefficient (like in the algebra equation y = 2x in which 2 is the coefficient). This
coefficient relates energy to mass just as the 2 in the example relates y and x. Therefore energy and mass are
interchangeable like x and y! Matter can be converted to energy, and vice-versa. It may seem strange to learn
that a single grain of sand, if converted completely into energy according to the above formula, would produce enough
energy to power a medium-sized city for an hour. But a description of ice would seem equally strange to a tribal native of
Papua New Guinea who had never before seen it. Obviously, matter and energy seem different just as do
water and ice. But their interchangeability is the basis for the modern nuclear power industry and other technologies.
Matter and energy are different forms of matter-energy just as water and ice are different forms of H2O. ,
24. Yes. The ship can rotate on an axis to provide false gravity. Newton's first law says that any object continues
moving in a straight line unless a force acts upon it. An astronaut in a rotating drum-shaped craft would feel a constant
force from the local 'floor' (the inner side of the drum) since the drum's inner surface is constantly exerting a force on his
body to prevent him from moving in a straight line. Examples of this effect are the Starship 2000 rides at county fairs &
the Spinnaker at Six Flags theme parks as well as the tug you feel toward the right hand car door when you take a
sharp left turn.
28. This is because the bending effect is extremely small. It is so small that the first successful measurement of it
involved the bending of a beam of starlight around the sun in 1919 (there have been plenty of others since). For
comparison, the sun's gravity near the surface would be.. let me grab my calculator... mmm about 30 times that near the
surface of the earth. In other words, Elvis (in 1977) would have weighed about 30x(260 lbs) = 7800 lbs on the surface of
the sun. Even with all that gravity, the sun only caused the starlight beam to bend by 5 ten thousandths of a degree
as it grazed by the sun during the 1919 eclipse.
Problems:
problem 1.
Let's use Equation #1 again:
plug in v = .99c and to = 5 minutes:
c2 cancels and we get: t = 5/[sqrt(1-.98)] ((take the square root of (1-.98))
t = 35 minutes
problem 2.
Important: the book contains an error in the given formula on page 746. Instead, use the
correct version on page 732!
The everyday velocity of a car is about 27 m/s (60 m.p.h.)
when we substitute 27 m/s into both v1 and v2 (two cars approaching head-on), we get
V = 53.99999999999956 m/s compared with
V = 54 m/s for just ignoring relativity and adding v1 + v2.
This obviously won't help you avoid speeding tickets.
Problem #3
Plug in the values into the same formula we used above. this time v1= .8c, v2 = .5c and you should get .93c as
your answer or 93% the speed of light.