Physics 10: Midterm Study Guide
Spring Term, 2008
The midterm will cover lecture material up through Wednesday,
04/30 on Energy in our Daily Lives. The quantitative level will be
no worse than what you've seen in the "mock quizzes" during
discussion section, and also similar to homework and
Below are the topics that are likely to appear in some form on the
midterm. The midterm will consist of 20 multiple choice, 10 true/false,
and 5 short answer questions. I'll give you a bucket of equations on the
front page of the exam, so you don't
have to spend your time memorizing them: just the concepts behind them!.
- Understand the basic properties of science, e.g., hypotheses must be
testable, about observation, experimentation, asking questions, etc. The
word "theory" means more in physics than rank speculationit
means a well-established, tested model.
- 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).
- We observe galaxies moving away from us in all directionsthe
farther the faster (Hubble's law). Though we would appear to be
at the center of expansion, any other point in an expanding
space would experience the same sensation.
- The universe (space itself) is expanding, carrying galaxies
with it like raisins in a rising loaf of bread. The galaxies
themselves don't expandthey're just carried along. (The
balloon demo fails here, as galaxy depictions on the balloon
- Space and time themselves were created in the big bangthe
universe isn't expanding into a pre-existing space.
- We can see a glowing wall in all directions 13.7 billion light
years away that represents the hot glowing plasma that existed
for the first 380,000 years of the Universe. This glowing wall
is called the Cosmic Microwave Background, or CMB.
- The CMB tells us that the universe is 13.7 billion years old.
- Careful study of the CMB (and fluctuations on it) tells us that the
geometry of the universe is flatmore like a flat rubber sheet
expanding than a closed/curved rubber balloon expanding (though in three
dimensions, not two: flat does not mean shaped like a pancake). Flat means
that parallel lines in our universe will remain parallel, and the angles
within a triangle add up to 180°.
- Observations of supernovae tell us that the expansion of the
universe is accelerating, contrary to all prior expectations.
These and other observations suggest that the universe will expand forever,
rather than reach a steady state or re-collapse. The unexpected acceleration
of the expansion plays a role in this conclusion, but since we don't know
for sure what's causing this, we have to hedge our statements about its
ultimate effect. For now, eternal expansion is the best bet.
- A concordance of information from CMB, supernovae, and galaxy
cluster measurements all point to a strange universe that is:
- only 1% stars
- only 5% (at most) ordinary matter (baryonic material: atoms)
- about 23% (gravitating) dark matter of unknown, exotic form
- about 72% (pushing/repulsive) dark energy we know next to
- Hundreds of planets have been found outside our solar system.
The wobbling of distant stars is what gives these planets away. But this
technique is so far only sensitive to very massive planets (like Jupiter)
close to the parent star. No earth-like planets have been found yet.
- Atoms are made of protons and neutrons (both in the nucleus), and electrons
forming a cloud around the nucleus. A typical atomic size is 10-10
meters across, though the nucleus is closer to 10-15 meters across,
so an atom is actually largely empty space.
- Electrons have negative electric charge, and are about 2000 times less
massive than the (comparable) protons and neutrons. The proton has a
positive charge exactly equal and opposite that of the electron. Neutrons
are electrically neutral. Electrical attraction between the positive
nucleus and negative electrons holds the atom together.
- The number of protons in the nucleus determines the type of element
the atom is. For example, hydrogen atoms have one proton, helium has two,
carbon has six, etc. Neutrons in the nucleus do not affect the elemental
type of an atom, but do effect the mass. Because the electron is so
light compared to neutrons and protons, the latter effectively determine
the mass of an atom. Different isotopes of an element have the
same number of protons, but differing numbers of neutrons (like the common
12C, or carbon-12, with 6 protons and 6 neutrons, or the rare
13C, with 6 protons and 7 neutrons).
- Electrons appear to be fundamental particles, with no constituent
ingredients. This makes them useful as probes of atomic nuclei, as we
can fling them very fast (speed of light) at protons, etc. and "see"
what's inside (and this is how we see quarks).
- Protons and neutrons are made of three quarks each (three-quark groupings
are called baryons). Up quarks have a charge of +2/3, and down quarks have
a charge of -1/3. A proton is made of two ups and one down (uud), and a
neutron is made of two downs and an up (udd). Add the charges and you'll
see that this part makes sense.
- There are four "fundamental" forces in nature: gravity,
electromagnetism, the weak nuclear force, and the strong nuclear force.
These are the only mechanisms we have ever seen/found that govern
interactions between particles. The latter three are described by a
coherent, quantum mechanical framework called the Standard Model.
Gravity is the odd-one-out, since we do not yet know how to describe
gravity in a quantum mechanical framework. Unification of gravity with the
other fundamental forces has been a major goal of physicists for decades.
Superstring theory is one possible answer, but the ideas are not testable
- Know what a vector means, and how it is used to specify positions,
velocities, forces, accelerations, momentum, etc.
- Understand that an acceleration is any change in
velocityspeed or direction. Know how to quantify
acceleration (if velocity changes by 3 m/s over the course of one second,
the acceleration is 3 m/s2).
- Understand what inertia is, and know Newton's three laws of motion.
Expect to apply F = ma (Newton's 2nd law) on
demand. (Furthermore, don't forget that the relation exists, in case
you need to use it as an intermediate step in a problem.)
- Acceleration due to gravity is g = 9.8 m/s2. Know
what this means, and how velocity evolves under this influence. An
object's weight is just mg, following Newton's second law. You
may in all cases use the much easier value of 10 m/s2. We're
not building bridges, just trying to understand concepts and basic
- Understand why objects of different mass or composition experience
the same acceleration due to gravity. It's because gravitational force is
proportional to mass, and F = ma. Understand this
- Velocity can be decomposed into horizontal and vertical components.
Gravity only affects the vertical component. In the absence of air resistance,
the horizontal motion of a projectile has no horizontal forces, and therefore
moves at constant horizontal velocity. This means that a
horizontally-fired bullet falls to the ground every bit as fast as a bullet
dropped beside the gun (neglecting air resistance, of course).
- Understand how forces (as vectors) can add or cancel, etc.
- The friction available on a smooth surface is never greater than the
weight (mg) of the object in question. The fraction of the weight
available to friction is called the coefficient of friction, which ranges
from zero to one. Static friction is greater than dynamic friction, which is
why skidding tires have less grip on the road than non-skidding ones.
- Terminal velocity is reached when the force of drag exactly
equals (and therefore cancels) the force of gravity. The force of drag at
sea level for most objects will be about:
Fdrag=0.65Av2. This comes out in Newtons if
A is in square meters and v is in meters per second.
- Be able to compute work: either from lifting or pushing (with
some force through some distance).
- Work is a force times distance: applied force times distance through
which object moves (in direction of applied force). For example, the
work required to lift a mass m a vertical height h
against gravity, g = 9.8 m/s2 is simply mgh
(mg is force of gravity, or weight, by F = ma, and
h is the distance through which the force of lifting acts).
- Understand that work measures energy, and that energy comes in both
kinetic and potential forms. Energy is the capacity to do work,
measured in J (Joules) = N m (Newton-meters) = (kg
- Kinetic energy of a mass in motion is 1/2 mv2.
- Understand conservation laws: energy (exchange between different forms),
momentum, angular momentum
- Energy is exchanged between potential and kinetic forms, always adding to
the same amount, given no frictional losses.
- Understand the concept of power as work per unit time, with units of
J/s = W (Watts). Guaranteed there will be power questions!
- Momentum, mv is conserved in collisions. Momentum
before equals momentum after. Don't forget that in "sticky"
collisions, the masses get added together for the mass of the final lump.
- Centripetal acceleration for circular motion
points to the center of the circle. Understand that our perceived
"centrifugal force" is fictitious, in that it is simply our
inertia trying to keep us going straight, but the environment in which we
sit (e.g., a car) is centripetally accelerated toward the center of a curve.
The amount of centripetal acceleration needed to keep something moving in a
circle of radius r with speed v is
a = v2/r.
- 93% of our world energy production ultimately comes from the sun. The
only exception is nuclear fission. Here we use the
energy stored by exploded stars (supernovae).
- Humans on average consume about 75100 W of power just sitting
still. This energy expenditure ultimately ends up as heat.