Review
Chapters 9-14
Classical Relativity
A Reference System
Reference system : the set of objects that are
not moving relative to each other and that can
be therefore used as the basis for detecting and
describing motion.
Galileo asked if observers could decide
whose description was “correct”. He
concluded that they couldn’t. In fact,
each observer’s description was correct!
Galilean Principle of Relativity
The laws of physics are the same for all
inertial reference systems.
Questions
1. Alice in Wonderland begins with Alice falling down a deep,
deep rabbit hole. As she falls, she notices that the hole is lined
with shelves and grabs a jar of orange marmalade. She is afraid
to drop the jar for it might hit somebody on the head. What
would really happen to the jar if Alice had dropped it? Describe
its motion from Alice’s reference system and from the reference
system of someone sitting on the shelf.
You wake up in a windowless room on a train, which
rides along particularly smooth tracks. Imagine that you
have a collection of objects and measuring devices in
your room. What experiment could you do to determine
whether the train is stopped at the train station or
moving horizontally at a constant velocity?
Assume that you are riding in a windowless train on perfectly
smooth tracks. Imagine that you have a collection of objects and
measuring devices in the train. What experiment could you do to
determine whether the train is moving horizontally at a constant
velocity or is speeding up?
Accelerating Reference System
Forces that arise in accelerating
reference systems are called inertial
forces.
Another common label for these forces
is fictitious forces.
Special Theory of Relativity
Postulates of the Special Theory
of Relativity
The idea of an absolute frame of reference was gone with
the idea of stationary ether.
First Postulate
All laws of nature are the same in all uniformly
moving frames of reference.
Second Postulate
The speed of light in the free space has the
same measured value for all observers,
regardless of the motion of the source or
the motion of the observer; that is, the
speed of light is a constant.
Simultaneity
Two events that are simultaneous in one
frame of reference need not be
simultaneous in a frame of reference
moving relative to the first frame.
This non simultaneity of events in one
frame that are simultaneous in another is
a purely relativistic effect – a
consequence of light always having the
same speed for all observers.
Two side-by side observers at rest
relative to each other share the same
reference frame. Both would agree on
measurements of space and time
intervals between given events, so we
say they share the same realm of
spacetime.
Time Dilation
Lorentz Factor, g
g
1
v
1
2
c
2
If you are moving in a spaceship at a high speed relative
to the Earth, would you notice a difference in your pulse
rate? In the pulse rate of people back on the Earth?
Will observers A and B agree on measurements of time if
A moves at half the speed of light relative to B? If both A
and B move together at half the speed of light relative to
the Earth?
Space travelers on the way to colonize a planet orbiting
a distant star decide to cook a “three-minute-egg”.
Would a clock on Earth record the cooking time as less
than, equal to or greater than 3 minutes? Why?
In an experiment to measure the lifetime of muons moving
through the laboratory, scientists obtained an average value of 8
microseconds before a muon decayed into an electron and two
neutrinos. If the muons were at rest in the laboratory, would they
have a longer, a shorter, or the same average life? Why?
Length Contraction
L  L0 1  v / c
2
2
E  mc
2
Peter volunteers to serve on the first mission to visit Alpha
Centauri. Even traveling of 80% of the speed of light, the
round-trip will take a minimum of 10 years. When Peter
returns from the trip, how will his biological age compare with
that of his twin brother Paul, who will remain on Earth?
Is it physically possible for a 30-year-old college professor to
be a natural parent of 40-year-old student?
Is it possible for length contraction to occur without time
dilation? Explain.
Suppose the meter stick zips by you at a speed only slightly
less than the speed of light. If you measure the length of the
meter stick as it goes by, would you determine it to be longer
than, shorter than, or equal to 1 meter long? Why?
General Theory of Relativity
The principle of equivalence states that
observations made in an accelerated
reference system are indistinguishable from
observations made in a Newtonian
gravitational field.
An astronaut awakes in her closed capsule, which actually sits
on the moon. Can she tell whether her weight is the result of
gravitation or acceleration motion? Explain.
You wake up at night in your berth on a train to find yourself
“pulled” to one side of the train. You naturally assume that the
train is rounding a curve but you are puzzled that you don’t
hear any sounds of motion. Offer another possible
explanation that involves only gravity, not acceleration in
your frame of reference.
Bending of Light by Gravity
According to the principle of equivalence, if
light is deflected by acceleration, it must be
deflected by gravity.
Gravity and Time
According to Einstein’s general theory of
relativity, gravitation causes time to slow
down.
The Atomic Hypothesis
1. The ideal gas model accounts very well for the
behavior of gases at standard temperature and pressure.
Would the ideal gas model begin to fail for very large
pressures or for very small pressures? Explain your
answer.
2. A cube and a spherical ball are made of the same
material and have the same mass. Which exerts the
larger pressure on the floor?
1. You may apply enough force to the head of a pushpin to
push it into a plaster wall with you thumb. However, it
is not a good idea to try to do this with a needle. Use the
concept of pressure to explain the difference between
these two situations.
2. If you screw the cup of empty plastic drinking bottle on
tightly while walking in the mountains, why are the
sides of the bottle caved in when you return to the
valley?
1. Your right rear tire has to support a weight of 3000 N.
Normally, the contact area of your tire with the road is 200
square cm. If the pressure in your tire is suddenly reduced
from 32 pounds per square inch to 16 pounds per square inch,
what must be the new contact area to support the car?
2. Use the microscopic model of gas to explain why the pressure
in a tire increases as you add more air.
1. If the average speed of a perfume molecule is 500 meters
per second, why does it take several minutes before you
smell the perfume from a bottle opened across the room?
2. What happens to the average speed of the molecules of a
gas as it is heated?
States of Matter
Vdisplaced
V0

0
 fluid
The fraction of object submerged is given by
the ration of the object’s density to that of
the fluid.
Pascal’s Principle
A change in pressure at any point in
an enclosed fluid at rest is
transmitted undiminished to all
points in the fluid.
1. What shape would you expect a drop of water to take if it
were suspended in the air in the space shuttle?
2. If you fill a glass with water so the water is level with the top
of the glass, you can carefully drop several pennies into the
glass without spilling any water. How do you explain this?
3. Are you ears going to hurt more swimming 12 feet down in
your swimming pool or 12 feet down in the middle of Lake
Superior? Explain.
1. Fresh water has a density of 1000 kg per cubic meter at
4C and 998 kg per cubic meter at 20C. In which
temperature water would you feel the greater pressure at
the depth of 10 meters? Why?
2. Salt water is denser than fresh water. Would a scuba diver
have to go deeper in salt water or in fresh water to reach
the same pressure? Why?
3. Use Archimedes’ principle to explain why an empty
freighter sits higher in the water than a loaded one.
Barometers
1. Is there a buoyant force acting on you in
the air? If there is, why you are not
buoyed up with this force?
2. How does buoyancy change as heliumfilled balloon ascends?
Bernoulli’s Principle
Where the speed of a fluid increases,
internal pressure in the fluid decreases.
1. A scuba diver achieves neutral buoyancy by adjusting
the volume of air in her buoyancy compensator vest
(BCD) so that the buoyant force equals her weight. If
she then kicks her fins and swims down an additional
20 feet, will the net force now be upward, zero or
downward? Explain.
The Nature of Heat
Zeroth Law of Thermodynamics
If two systems are in thermal equilibrium with
a third system, then they are in thermal
equilibrium with each other.
First Law of Thermodynamics
The increase in internal energy of a system is
equal to the heat added plus the work done on
the system.
Third Law of Thermodynamics
Absolute zero ma be approached but
experimentally but can never be reached.
Specific Heat
The amount of heat it takes to increase the
temperature of an object by 10C is known as heat
capacity of the object.
Change of State
Latent Heat
If a material changes phase from solid to
liquid, or from liquid to gas, a certain amount
of energy is involved in its change of phase.
1. If you make the mistake of removing ice cubes from the
freezer with wet hands, the ice cubes will stick to your
hands. Why does the water on your hands freeze rather than
the ice cube melt?
2. In northern climates drivers often encounter signs that read
“BRIDGE FREEZES BEFORE ROADWAY”. Why does
this occur?