Physics 10: Final Exam Study Guide
Spring Term, 2008
The final exam will cover lecture material from May 7 (Lecture 13 on
Rockets and Gravity) through the last lecture (June 6, Lecture 24 on
the Frontiers of Physics). While the exam is not cumulative in the strict
sense, you will need to remember some of the basic concepts from
the first half, like force, work, energy, power. These concepts have continued
to play a role in the second half of the course.
You may also want to study the transmitter questions we saw in class.
These will be posted on the Lectures
page (look for the last entry). Note also the first-half questions after
Lecture 11 on the same page.
Below are the topics that are likely to appear in some form on
the exam. The exam will consist of multiple choice, true/false, and
short answer. I'll give you a bucket of equations on the front page
of the exam, though fewer will be needed than on the first exam, due to
the more qualitative nature of the second half of the course.
- The speed of light = 300,000,000 m/s = 3×108 m/s =
300,000 km/s (always remember this onewho knows when it'll crop up)
- Review the major concepts from the first half of the
courseconcepts that have stayed with us in the second half, such
as force, acceleration, energy, power, etc. The questions on the exam
will not focus on these concepts in the way that the first exam did,
but the fundamental concepts will be used.
- A rocket pushes against its own fuel. It requires no other
medium (air, water, land) to push against. In effect, the rocket pushes
against the inertia of the fuelin such a way as to conserve momentum.
With a given mass available in fuel, you do better flinging many small
particles fast than a few big particles slow. On a
frictionless sled on an icy lake, 25 pounds of BBs (and associated gun)
will serve better than a single 25 pound brick to get you going. In real
life, friction would render the BBs useless, but in space this would
certainly be your best bet.
- A circular orbit results when the centripetal acceleration,
a = v2/r, is provided by gravity.
Set a = g = 9.8 m/s2 to get the condition for
low-earth orbit. In effect, the curvature of the earth is such that the
earth falls away beneath the orbiting satellite as it continuously
"falls around" the earth.
- The sensation of weightlessness in orbit is not because
you are far from earth's gravitythis is far from true. Gravity is
responsible for bending the path into an orbit! The weightlessness is
because both the astronaut and the craft are falling toward the
earth at the same acceleration, so that there is no
relative acceleration between astronaut and craft.
- Newton's law of universal gravitation states that the force on a
mass, m, due to mass M a distance r away is:
F = GMm/r2, where G is the
gravitational constant (6.67×10-11 in MKSyou don't
need to remember this number). Understand qualitatively how the force
varies if we change masses and/or distances.
- Since F = ma, the acceleration of mass, m
due to M is a = GM/r2, and is independent of the mass (why a bowling ball and golf ball accelerate the same).
- You can figure any circular orbit by setting centripetal
acceleration equal to gravitational acceleration:
v2/r = GM/r2,
reducing to v2 = GM/r.
- Geosynchronous orbit results when the orbital period comes out to equal
24 hours. The satellite is still in orbit, though from our position on the
rotating earth the satellite appears to hover motionless in the sky. Think
of twirling with a ball on a string in front of you. You see the ball
always in front, but outsiders know that the ball is really making circles
- The requirement that the speed of light is measured to be the
same for all observers regardless of their state of motion
produces a variety of consequences, collectively referred to as special
- There is no well-defined notion of simultaneity in special
relativity: observers moving relative to each other will not agree on
whether two events are simultaneous. Space and time get mixed together
into what we call spacetime.
- Time appears to slow (but never reverse) for objects moving relative to
the observer. The amount of slowing goes by the ratio γ (gamma).
- Length appears to contract along the direction of travel for objects
moving relative to the observer. The "shrinkage" also goes by
the ratio γ.
- At familiar speeds, γ is 1.0. At 0.6c,
γ = 1.25. At 0.87c, γ = 2.0. As the velocity
approaches the speed of light, γ approaches infinity. No need to
remember specific numbersjust the endpoints and the general trend.
- Example: at 0.87c, γ = 2.0, so you see a meter stick
with a watch attached moving past you at this speed appear to be only 0.5
meters long (stick is oriented along direction of travel), and the second
hand only ticks once every two seconds (by your own reckoning of time).
Somewhat non-intuitively, an observer traveling with that meter stick
and clock sees your meter stick to
be only 0.5 meters long in the direction of travel, and your clock
appears to tick slowly according to their clock. The relativity of motion
(think empty space) makes it impossible to decide who is at rest and who is
in a state of motionit's relative motion that's important.
- Be able to use the velocity addition rule to add two
velocities in a manner consistent with special relativity. This
rule is V = (v1 + v2)/(1 +
v1v2/c2). Note the
ninth edition of the Hewitt book has a sign error in the denominator
on p. 703.
- Einstein wanted a reason for gravitation, and relegated
it to the status of a "fictitious" force: an artifact of not
being in a freely falling frame. In effect, while standing on the
earth's surface, the natural frame of reference falls past
us at 9.8 m/s2. Life in a falling elevator is life in a
naturally falling frame of reference. This immediately explains why
different objects experience the same acceleration in a gravitational
field. Think in terms of the accelerating box in space: it's the
box that's accelerating, not the objects "falling"
within the box. But from within the box, it looks like all objects
accelerate toward the floor at the same rate. They're just trying
to move with uniform velocity, in accordance with Newton's first law.
The floor comes up to hit them.
- Out of General Relativity came the notion of curved spacetime.
This naturally explained mass attraction as a response to curved space.
Just like bowling balls on a mattress attract each other, dimples of curved
spacetime also find each other attractive.
- The prescription of general relativity is: the presence of mass curves
spacetime, and spacetime tells mass how to move. Specifically,
falling/orbiting bodies simply follow the straightest lines they possibly
can through the curved spacetime.
- General Relativity makes definite predictions that allow it
to be rigorously tested. The three classic tests are the perihelion
precession of Mercury's orbit, the deflection of starlight (stars near sun
appear to be pushed farther from sun's edge), and the gravitational redshift
(time runs slower in presence of gravity). So far General Relativity
has passed all tests with flying colors, though its fundamental
quantum mechanics motivates further tests.
- Electrons are negatively charged, and protons are positive by the exact
same amount. Like charges repel, and unlike charges attract.
- Electric charges are transferred by rubbing, nearly always due to
one surface grabbing electrons off the other surface. Which
material donates electrons and which grabs them is not usually evident
(and almost impossible to guess). Electrons are the transferred charges
because electrons occupy the vulnerable outskirts of atoms, and are
therefore easily grabbed.
- Review the physics of sparks and lightning; the breakdown threshold
(3 million volts per meter), and how this scales to smaller lengths.
- Understand the electrostatic force law and how the force scales
with the various parameters (e.g., double one charge, half the separation,
etc.). Appreciate the similarity between this law and Newton's law of
- The electric field is a concept that not only tells you
the direction of force a charge will experience, but also
the magnitude of the force. Specifically, F
= qE, where q is the charge (in Coulombs),
F is the force vector (has magnitude, in
Newtons, and direction), and E is the electric field
vector (has magnitude, in Volts per meter, and direction).
- Electric field lines point from positive to
negative charges. An electron, being of negative charge, is attracted
to positive charge, and thus feels force against the direction of
the field lines. A positive charge feels force along the direction
indicated by the ambient field lines.
- Because the electric field mirrors the force, the electric field from a
charge diminishes as the square of the distance, just like the force does.
- Electric current is simply the motion of charges along a particular
- Review the relationship between electricity and magnetism.
Specifically, in what way can electric charges produce magnetic fields, and
in what way can magnets produce electric fields (that then move charges)?
- Be able to use the relation (frequency in Hz)*(wavelength in meters) =
(speed of light in m/s). Know also that radio antennas are optimally
one-quarter wavelength long.
- Know about the properties of electromagnetic radiation:
generated by accelerating charges (electrons); consists of oscillating
electric and magnetic fields at 90-degrees to each other; a source
can be polarized so that every wave has the same orientation (e.g.,
vertical) of the electric field vector; encompasses radio, microwave,
infrared, visible, ultraviolet, X-ray, and gamma radiation. All forms
of electromagnetic radiation travel at precisely the speed of light
(in a vacuum).
- Appreciate the pre-quantum problems in physics that motivated quantum
mechanics. Specifically, understand the argument about atoms decaying in
mere nanoseconds and also the mystery of atomic spectra.
- The energy of a single photon of light is E = hν, or E
= hf, where ν (nu) and f are two equivalent ways
of labeling the frequency. h is Planck's constant, and is
6.626×10-34 J·s. Ultraviolet photons are more damaging
because each photon packs a greater punchenough to bust up molecules
in some cases.
- Light is both a particle and a wave. But it can
behave like both, or more generally like one at a time. The bottom
line is that there's a wave-particle dualitylight comes with both
properties simultaneously. Moreover, all particles have a
wave-like nature, characterized by the de Broglie wavelength: λ =
h/p, where h is Planck's constant, and p = mv is
the particle's momentum.
- The Heisenberg Uncertainty Principle states, in one form, that
it is impossible to simultaneously achieve arbitrary precision in knowing
both the position and momentum (velocity) of a particle. It's
not a matter of poor measurement techniques, but stems from the fact that
the act of localizing the particle precisely ends up imparting some unknown
momentum to the particle in questioneffectively adding uncertainty to
the particle's momentum.
- Diffraction is an example of the uncertainty principle in action.
Light that goes through a tiny opening is localized very well, so
that its momentum in the direction/dimension of localization is poorly
known. Thus it spreads. The tighter the aperture, the greater the spread
- The quantum view of electrons in atoms (e.g., hydrogen) is not
one of electrons whizzing about in orbits, but rather of static
(stationary) probability distributions describing where one might find the
electron if one tried to localize it. A variety of possible configurations
exist, each having a distinct energy value. The steps in energy explain
the atomic spectra, and why each element's spectrum is different (different
sets of levels in each element). The stationary aspect of the electron
distribution solves the problem of atom decay: the electrons are not
accelerating around the nucleus in orbits, which would require that they
lose energy by electromagnetic radiation and spiral into the nucleus.
- Know the wavelength range associated with visible light.
- Understand why the sky is blue and by association, why sunsets are
- Understand color combination: if R, G, B represent red, green, and
blue, C, M, Y represent cyan, magenta, yellow, and W means white, then:
- R + G + B = W;
- R + G = W − B = Y;
- R + B = W − G = M;
- G + B = W − R = C.
- The additive laws cover color addition, as one gets by adding light
sources (TV, computer screen, LEDs, light bulbs). The subtractive laws
deal with absorption by paints and dyes. So mixing yellow and magenta
paints is basically combining blue and green absorbers, so red should result.
- Understand the geometry of rainbows: specifically where in relation to
the sun one must look to find a rainbow.
- Despite their mutual electric repulsion, the positive charges in a
nucleus are bound together by a more powerful attractive force: the
(short-range) strong nuclear force.
- A given isotope of an element (X)
has in its nucleus A nucleons consisting of Z
protons and N neutrons, such that A represents the total
number: A = Z + N. We denote this element as AX. For
example, uranium-238 (238U) has 92 protons and 146 neutrons for
a total of 238 nucleons.
- Uranium and plutonium are special, in that these are the only two
elements with isotopes that can undergo fission via the introduction of an
extra wandering neutron.
- Before and after nuclear reactions, the total number of nucleons hasn't
changed, but their rearrangement releases energy pent up in the binding
energy of the nucleus. The end product is always less massive than the
initial fuel, and this mass difference has produced E =
mc2 of energy. For fission, the products are about 0.1%
less massive than the starting mass.
- Iron is at the peak of the nuclear binding energy curve. This
means on the light side of iron, fusion pays off, and on the heavier side,
it's fission. We'll never build plants for fission of light elements: this
would result in a loss of energy. Likewise we (and also stars
during normal operation) will not fuse beyond iron.
- Fusion would be a fantastic source of energy: nearly unlimited
supply of raw material, almost no radioactive by-products, and far more
efficient than fission, even. But it's challenging to make a 50 million
degree contained plasma. And it always seems to be 50 years in the future.
- Basic research often has unanticipated payoffs. Shockley
wasn't trying to build a computer when he invented the transistor.
The world-wide-web sprung out of scientists trying to distribute
information over DARPA-funded communications lines.
- There are four fundamental forces in nature that we know about:
gravity, electromagnetism, and the strong and weak nuclear forces. We have
united the latter three under the banner of quantum mechanics, but gravity
remains the odd-man-out. It is still unclear what further unifications may
- Many of our advances in physics have come from new appreciations about
the nature of space and time. This trend is likely to continue into the
- Science is driven by questions and exploration. Never content to
blindly accept the current theories, scientists are always challenging
assumptionspushing at the edges and exposing the weaknesses of the
current state of affairs. The final arbiter of scientific dispute is
experiment. Science is forced to "follow the data"even if
it leads in new and strange (and unwanted) directions.