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 transmitter questions.

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 speculation—it 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 one—who knows when it'll crop up).
• We observe galaxies moving away from us in all directions—the 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 expand—they're just carried along. (The balloon demo fails here, as galaxy depictions on the balloon did expand.)
• Space and time themselves were created in the big bang—the 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 flat—more 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 nothing about
• 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 yet.
• 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 velocity—speed 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 computations.
• 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 connection.
• 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: F_drag=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 m²)/s²
• 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 75–100 W of power just sitting still. This energy expenditure ultimately ends up as heat.