ISP209 Spring 2008
Exam #1 Study Guide:
Exam 1 will have 40 multiple choice question based on
material covered in lectures up to 1-31. A few of the questions will involve
simple calculations, so you should bring your calculator. You will NOT need
your clicker. You may bring one double-sided sheet of paper with notes for the
exam.
I Basics
- Know
scientific notation and be able to recognize that for example, 0.003 is
the same as 3.0E-3.
- Know
Gm, Mm, cm, mm, mm. For example
know 1 m = 1x106 mm and
be able to do a simple conversion.
- Know
the characteristics of science and pseudoscience
- Know
the SI units for some of the basic quantities we have been working with
- Position
– m (meters)
- Time
– s (seconds)
- Speed
– m/s
- Acceleration
– m/s^2
- Force
– N (Newtons)
- Mass
– kg (kilograms)
II Scalars, Vectors, Tensors
- A
scalar is a quantity that is just a number
- A
vector quantity has a magnitude and direction: for example you might have
a velocity of 70 mph (magnitude) East (direction)
- A
tensor is a generalization of these quantities in multiple dimensions. The
rank of a tensor gives the dimension.
- Rank
0 is a scalar
- Rank
1 is a vector
- Rank
2, or higher, describes a more complex quantity that has two directions
and two magnitudes. The metric of space-time, or the curvature of space
time are examples.
- Know
that vector quantities add. Be able to add vectors in a case such as a
boat in the river. Be able to add other vector quantities, such as displacement,
force, acceleration.
III Motion
- Know
the definition for
- Position
(Displacement)
- Velocity
- Acceleration
- What
is speed? It is the magnitude of a velocity.
- What
is distance? It is the magnitude of a displacement.
- Be
able to use a graph to determine position, velocity, acceleration
- Where
are position, speed, acceleration the largest?
- Where
are they zero?
- Be
able to do the above for the for the special cases of
- Motion
in the x-direction
- A
ball thrown up in the air and falls back down
IV Special Relativity
- Two
postulates of special relativity
- The
speed of light is a constant independent of the speed of the source
- Physical
laws are the same in all inertial reference frames (an inertial reference
frame is one that is not accelerating)
- Moving
clocks run slow. This is called time dilation.
- Know
the equation to calculate how much longer a click takes in a moving clock
given a speed in v/c.
- Moving
objects appear shorter. Know the equation for length contraction.
- Time
dilation has been proven by comparing clocks at the North Pole and
equator, by clocks flown in airplanes, and by the lifetimes of subatomic
particles.
- What
is the Twin Paradox?
V What is time?
- Time
is the thing measured by clocks
- Time
is relative and depends on the speed of the observer
- Know
that a light year is the distance light travels in one year. Be able to
calculate in what year the light left a star at the time it is observed on
Earth.
VI Force
- A
force is a push or pull
- Force
can be defined by Newton’s three laws
- If
the sum of forces is zero, the object will not accelerate
- F=ma
- To
have a force, there has to be an equal and opposite force
- Know
the implications of Newton’s laws, e.g. that the Moon pulls as hard on the
Earth as the Earth does on the Moon
- Be
able to calculate a simple F=ma problem. For a given force, if we double
the mass, what happens to the acceleration?
- Force is the rate of change of momentum. Given a graph of momentum vs time, be able to find the force.
VII History of Astronomy
- For
over 5000 years people have tried to understand the motions of the planets
and stars.
- Ptolemy
developed an accurate Earth centered system in around 100AD that was
accepted for 1400 years. This was based on deferents and epicycles.
- Tyco
Brahe made detailed measurements that allowed Johannes Kepler to develop
his three laws of planetary motion based on a Sun centered model. Until
Brahe’s data was available, there was no experimental reason to discard
Ptolemy’s model.
- Know
Kepler’s three laws and how Newton’s law of gravity explains them
- Elipitical
orbits – mathematical result of Newton’s Law
- Planets
move faster when they are closer to the Sun – force of gravity is greater
- Square
of period is equal to the cube of the semi major axis – mathematical
result of Newton’s Law, that again is related to the idea that the farther away the planet is, the weaker the force, less acceleration, and longer period of the orbit.
- Newton
unified all observations and laws in his Universal Law of Gravity
VII Gravity
- Know
Newton’s law of gravity and be able to use it to calculate the force of
gravity between two masses.
- Know
why an astronaut in orbit is weightless
- Know
that the Earth’s gravity extends to astronauts in orbit, out to the Moon,
out to the Sun, and so on. Know that the magnitude in orbit near the Earth
is about the same as it is on the surface of the Earth.
- What
happens to the force if
- one
of the masses is increased?
- the
distance between the masses is increased or decreased?
- Why
do all objects fall with the same rate of acceleration? Because inertial
mass (the mass in F=ma) is the same as gravitational mass (the mass in
Newton’s Law of Gravity). Why are they the same?
VIII Einstein and E=mc2
- Study the picture of the process of mass conversion to energy (page 19 of lecture 6).
- Know the fraction for the 5 classes of reactions (matter-antimatter, fusion, fission, chemical, mechanical)
- Be able to answer a question like: How many kg of uranium (fraction 0.001, fission) are equivalent to 10,000,000 kg of coal and oxygen (fraction 1E-10, chemical)?
IX General Relativity
- Einstein developed the theory of General Relativity
- The main postulate is that we can't distinguish gravity in one direction from acceleration in the opposite direction
- Space and time are combined into a 4-dimensional space time
- Mass warps space-time. What we experience as gravity is actually curved space
- Time slows down near a large mass. This is called gravitational time dilation.
- Time travel may be possible, but this leads to paradoxes.