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Objectives
1.
Observe a sequence of position vs. clock time events and present the
results in a table.
Technically:
Observe for a sequence
ot (t, x) events: {(t_i,x_i)
| 0 <=
i <= n} knowledge of
Physics I and prerequisite mathematics
·
x_i
and t_i are the observed or actual
position and clock time of an object moving along a line,
relative to a fixed point on the line and an arbitrary instant
of time.
·
n is the
number of clock-time-and-position observations.
2.
For an observed series of position vs. clock time events relate
position vs. clock time information to displacements and time
intervals between consecutive events.
Technically:
Relate
{(t_i,x_i) | 0 <=
i <= n} U {`dt_i,
`dx_i | 1 <= i
<= n} knowledge of Physics I and prerequisite
mathematics
·
`dx_i =
x_i – x_(i-1) is called the
displacement on the ith interval
·
| `dx_i | is the
distance moved by the object corresponding to the
ith interval
·
`dt_i is the time
increment, or time interval, or change in clock time,
corresponding to the ith interval
3.
For an observed series of position vs. clock time events relate
position vs. clock time information, displacements and time
intervals between consecutive events, the definition of average rate
of change, and the average rate of change of position vs. clock time
for each interval.
Technically:
Relate
{(t_i,x_i) | 0 <=
i <= n} U {`dt_i,
`dx_i | 1 <= i
<= n} U {definition of average rate} U {average rate of change of
position with respect to clock time on ith
interval, vAve_i, average velocity on
ith interval} knowledge
of Physics I and prerequisite mathematics
·
Average rate of change of A with respect to B
on an interval is defined to be the change in A on the interval
divided by the change in B on that interval.
·
The average velocity on an interval is defined
to be the average rate of change of position with respect to
clock time on that interval.
·
vAve_i
stands for the average velocity on the ith
interval.
4.
Relate
position vs. clock time information to average velocity vs. midpoint
clock time and acceleration at each clock time.
Technically:
Relate {(t_i,x_i) | 0 <=
i <= n} U {`dt_i,
`dx_i | 1 <= i
<= n} U {definition of average rate} U {average rate of change
of position with respect to clock time on
ith
interval, vAve_i, average velocity
on
ith interval} U {t_mid_i,
`dt_mid_i, approximate average rate
of change of velocity between midpoints, approximate
acceleration at
t_i, a_Ave_i
| 1 <= i <= n-1}
knowledge of Physics I and prerequisite mathematics
0.01 – 0.04 are sequenced, each being a superset of the preceding,
with quantities new to the sequence underlined at each step
5.
Relate
-
uncertainty in measured quantity
-
value of measured quantity
-
percent uncertainty in measured quantity
-
uncertainty in value of a given power of measured quantity
knowledge of Physics I and prerequisite mathematics
6.
Relate
-
uncertainties in two measured quantities
-
values of measured quantities
-
percent uncertainties in measured quantities
-
percent uncertainty in product or quotient of measured
quantities
-
uncertainty in sum or difference of measured quantities
knowledge of Physics I and prerequisite mathematics
7.
Relate
measurement using given instrument
estimated precision of instrument
estimated accuracy of measurement
justification of estimate
knowledge of Physics I and prerequisite mathematics
8.
Estimate uncertainties in measured quantities as appropriate to
means of measurement (ph1 background (see also
ch 1), intro asst, asst 0 query, asst 1
query) knowledge of Physics I and prerequisite mathematics
9.
Relate
-
domino measurements with largest and smallest ruler
-
order
of domino volumes
-
uncertainty in each measurement
-
uncertainty in volume
calculation
-
uncertainty in order of volumes
knowledge of
Physics I and prerequisite mathematics
10.
Relate
for n measurements of clock time t and position x for a
uniformly accelerating object
-
percent uncertainty in x_i
measurements
-
percent uncertainty in t_i
measurements
-
percent uncertainty in inferred v_Ave_i
-
percent uncertainty in inferred a_Ave_i
-
percent uncertainty in slope of v_Ave_i vs.
t_mid
knowledge of Physics I and prerequisite mathematics
11.
Precision and accuracy of measurements of various
objects using ruler copies at various levels
of reduction.
12.
Accumulation of error with successive difference quotients.
Identify and explain in terms of a simple example the
proportionalities among dQ/dt (rate of thermal energy transfer), L
(distance between points on a flow line), A_cs (cross-sectional area
of flow) and `dT/`dx (temperature gradient).
Technically:
Relate
{dQ/dt, k,
L, A_cs, dT/dx,
T_1, T_2}
13.
Identify and explain in terms of a simple example the
proportionalities among L_0 (the original length of an object), `dL
(the change in its length due to thermal expansion), A_0 (original
surface area), `dA (change in surface area), V_0 (original volume),
`dV (chagne in volume) and `dT (the change in its temperature).
Technically:
Relate
{`dL, L_0, `dT,
T_0, T_f, alpha, A_0, `dA,
V_0, `dB, beta}
14.
Relate
-
c
(specific heat of an object)
-
m
(mass of the object)
-
`dQ
(change in thermal energy of the object)
-
`dT
(change in temperature of the object)
-
T_0 (initial temperature of the object)
-
T_f (final temperature of the object)
qa_2,
class notes
15.
Relate
for an isolated collection of n objects, where the subscript i
refers to the i_th object, 1 <= i <= n
-
c_i
(specific heat of the i_th object)
-
m_i
(mass of the i_th object)
-
`dQ_i
(change in thermal energy of the i_th
object)
-
`dT_i
(change in temperature of the i_th
object)
-
T_0_i (initial temperature of the i_th object)
-
T_f (final temperature of the system
16.
For a single particle of mass m moving at speed v perpendicular to
and colliding elastically with a piston of cross-sectional area A_cs,
with time `dt between collisions, where p is the momentum, `dp the
change in momentum during a collision, F_ave the average force and
P_ave the average pressure on the piston:
-
Relate
{m, v, p, `dp, `dt,
F_ave}
-
Relate
{m, v, p, `dp, `dt,
F_ave, A_cs,
P_ave}
17.
For a single particle of mass m moving at speed v perpendicular to
and colliding elastically with the ends of a cylinder of
cross-sectional area A_cs and length L, with time `dt between
collisions, where p is the momentum, `dp the change in momentum
during a collision, F_ave the average force and P_ave the average
pressure on the piston:
-
Relate
{m, v, L, p,
dp, KE }
-
Relate
{m, v, L, `dt }
-
Relate
{m, v, L, p, `dp, `dt,
F_ave, KE, A_cs,
P_ave}
18.
For a large number N of particles each of mass m_particle moving at
speed v in a random direction in space, colliding elastically and
end of a cylinder of cross-sectional area A_cs and length L, where
F_ave is the average force and P_ave the average pressure on the
end, KE_ave the average kinetic energy and v_Ave the (rms) average
velocity of the particles, n the number of moles, U the total
rotational and translational KE of the particles, T the absolute
temperature, n the number of moles, R the gas constant, k the
Boltzmann constanct, N_A Avagodro's number and the gas monatomic or
diatomic:
-
Relate
{m_particle, N, v, L,
F_ave,
A_cs, P_ave}
-
Relate
{T,
m_particle, KE_ave,
v_rms, N, n, U,
C_p, C_v,
monatomic/diatomic, R, k, N_A}
19. Where in addition V is the volume, T_0, V_0, P_0, N_0 the initial
temperature, volume, pressure and number of particles, `dT the
change in absolute temperature, `dKE the change in KE, `dP the
change in pressure, `dN the change in the number of particles
-
Relate
{m, N, v, L,
Fave,
A_cs, P_ave,
KE_ave, V, T}
-
Relate
{direction of `dT, direction of `dKE,
direction of `dP, direction of `dV,
direction of `dN}
-
Relate
{`dT as percent of T_0, `dP
as percent of P_0, `dV as percent of
V_0, `dN as percent of N_0, `dT/T_0,
`dV/V_0, `dT/T_0,
`dN/N_0 | percent changes are small
}
20.
Relate,
where T_1 and T_2 are the initial temperatures of equal amounts
of gas and T_f the final temperature when mixed:
21.
Relate,
for two samples of gas in a divided container at equal pressure,
where T, V, n, m are absolute temperature,
volume, number of moles and mass,
-
{T_1, V_1, T_2, V_2, n_1, n_2, m_1,
m_2, T_f}
22.
Relate,
for two samples of the same gas in a divided container
-
{V_1, V_2, T_1, T_2, P_1, P_2,
T_f}
23.
Relate,
for a confined gas
24.
Relate,
for a confined gas
-
{P_0, T_0, V_0, N_0, P_f,
T_f, V_f,
N_f}
25.
Relate
for a capped-bottle system with an open tube, where A_cs is the
cross-sectional area of the tube, V_bottle the volume of the bottle,
`dV_tube the volume of water displaced into the tube, `dy the change
in the water level in the tube.
-
{A_cs,`dL,
V_bottle, `dV_tube,
`dV_tube/V_bottle
, `dV_tube/V_bottle
(as %), `dy }
26.
Relate
for a capped-bottle system with an open tube, where P is the
pressure inside the bottle, `dy the change in the water level in the
tube, squeeze is perceived force exerted when squeezing the bottle,
P_atm, T the absolute temperature of the gas, V the initial volume
of the bottle, `dV the change in volume ..
-
{P, `dy, squeeze}
-
{P, `dy, squeeze,
P_atm}
-
{P, `dy, squeeze,
P_atm,T, V, `dV}
27.
Relate
Atm
pressure: {rho_water, y2 – y1, L_0,
`dL, (V / V_0)_air_column,
P_atm}
28.
Relate
{P, V, T, y2 – y1, L_0, L}
29.
Relate
{P_0, V_0, T_0, n,
y_max, P_1, V_1,
T_1, T_f, P_2, V_2, T_2, `dQ,
`dPE, `dU,
eff}
30.
Relate
{P_0, V_0,
P_f, T_f, adiabatic\isothermal, `dW,
`dU, `dQ}
31.
Relate
{n, R,
mon/diam,
C_p, C_v,
`dT, `dQ}
32.
Relate
{m, v, p, `dp, `dt,
F_ave, A_cs,
P_ave}
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1.
Relate
for a traveling sine wave
- lambda (wavelength)
- f (frequency)
- omega (angular frequency)
- T (period)
- A (amplitude)
- 'time delay' between two
points
- equation of motion of point
at end
- equation of motion of
arbitrary point
- waveform at given instant t
2.
Relate
for a an oscillation driven by two independent oscillators
- f_1 (frequency of first
oscillator)
- f_2 (frequency of second
oscillator)
- f_beat (beat frequency)
- n (number of beats occurring
during time interval `dt)
- `dt (time interval)
3.
Relate
for longitudinal or transverse standing waves in a given object of
given length
- boundary conditions
- positions of nodes and
antinodes for fundamental oscillation
- lambda_1 (wavelength of
fundamental oscillation)
- positions of nodes and
antinodes for first n harmonics (n <= 4)
- pattern of positions of
nodes and antinodes for subsequent harmonics
- positions of nodes and
antinodes for nth harmonic
- lambda_n (wavelength of nth
harmonic)
- c (propagation velocity)
- f_n (frequency of nth
harmonic)
- A_max (amplitude of oscillation at antinode)
- A(x) (amplitude at position
x)
- y(x, t) (position relative
to equilibrium of point at position x along the object, at clock
time t)
- sketch of y(x) for given t
- graph of y(t) for given x
4.
Relate
for traverse standing wave in string or chain under uniform tension
- T (tension)
- c (propagation velocity)
- m (total mass)
- L (length)
5.
Relate
- waveform y_1(x), given
mathematically or graphically
- waveform y_2(x), given
mathematically or graphically
- superposed waveform y_1(x) +
y_2(x), constructed graphically
- superposed waveform y_1(x) +
y_2(x), represented mathematically
- equation y_1(t, x) of
traveling or harmonic wave
- equation y_2(t, x) of
traveling or harmonic wave
- equation of superposed wave
6.
Relate
- traveling sine wave y_1(t,
x) traveling in positive direction, traveling sine wave y_2(t,
x) traveling in opposite direction, both with common propagation
speed c, frequency f and amplitude A
- evolution of waveform of
superposed wave between two specified points
- boundary conditions
- number of harmonic
- matching selection of points
- evolution of cycle of given
harmonic
7.
Relate
- traveling wave incident on
fixed or free boundary
- reflected wave
8.
Relate
for a wave traveling through a medium
- amplitude
- frequency
- mass per unit length
- energy per unit length
- propagation velocity
- power
9.
Relate
(Doppler effect)
for a wave created by a source moving with velocity v_s and
observed by an observer moving with velocity v_o through a
medium in which propagation velocity of the wave is c
10.
Relate
for a sound wave
- pressure amplitude
- intensity
- area
- power of source
- threshold intensity
- decibel level
11.
Relate
for an aluminum rod which is supported at its middle and free at
both ends
- length
- frequency of fundamental
harmonic of longitudinal wave
- wavelength
- propagation velocity of
sound in aluminum
- small change in position of
support
- change in beat frequency as
proportion of original beat frequency
12. Relate
for two broken-line paths, each defined by three points in the
coordinate plane
- coordinates of the three
defining points for each path
- x and y intercepts of the
paths
- point(s) of intersection of
the paths
- triangles formed by paths
with one another and with the coordinate axes
- sets of similar triangles
and relative dimensions
and apply to image formation by thin lenses.
13.
Relate
for a thin converging or diverging lens
- image distance
- object distance
- focal distance
- magnification
- nature of image
- diagrams of principle rays
14.
Relate
for a given point (x_0, 0) on the x axis of the coordinate plane,
two points (0, y_1) and (0, y_2) on the y axis and a wavelength
- length of path 1 from (x_0,
0) to (0, y_1)
- length of path 2 from (x_0,
0) to (0, y_2)
- difference in path lengths
- difference in path lengths
as a multiple of wavelength
15. For points (0, -a/2) and (0, a/2)
on the coordinate plane and a wavelength lambda < a
- using a sketch depict the
path difference corresponding to a distance observer, along
paths making angle theta with the x axis
- calculate the path
difference
- calculate the path
difference as a multiple of lambda
- determine angles for which
the path difference is an integer multiple of lambda
- determine angles for which
the path difference is an integer multiple of lambda plus a
half-wavelength
- apply to situations
involving the two-slit phenomenon
16.
Relate
for two lenses
- focal lengths
- position of object with
respect to first lens
- position of image formed by
first lens
- position of second lens
- position of image formed by
second lens
- characteristics of each
image
17.
Relate
for a plane wave incident from one medium at a plane interface with
a second:
- indices of refraction
- angle of incidence
- angle of refraction
- speed of light in each
medium
18. Sketch and analyze the path of
light incident on an reflected or refracted by a thin lens, a mirror
or a prism.
19. Sketch and analyze the path of
light incident on a thick cylindrical interface. 20. Analyze image formation by a
combination of thin lenses.
21. Analyze interference patterns for thin films, single
slits, double slits and diffraction gratings. 22. Explain how radio waves could be
polarized when passing through a series of vertical or horizontal
metal posts, and whether the resulting waves would be polarized
vertically or horizontally.
23. Calculate Brewster's angle for light incident from a
medium with index of refraction n_1 on a smooth flat surface with
index of refraction n_2.
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1.
Relate
for a sphere with a single point charge at its center, where phi is
the electrostatic flux through the sphere, Q the charge, a the
radius of the sphere, E the magnitude of the electric field at a
point on the surface of the sphere, q a charge at distance r from
the center, PE(r) the electrostatic potential energy of the system,
V(r) the electrostatic potential at the position of q due to the
charge Q.
{Q, phi, A, E, q, r, PE(r), V(r)}
2.
Relate
{F,
E, `ds, q, `dW_on,
`dPE_elec, `dV}
where F is
the force exerted on charge q at a certain position, E the
field at that position, `ds a displacement of q small enough
that the field E does not change significantly, `dPE_elec the
change in the electostatic potential energy due to the displacement
of q, `dW_on the done on q by the field during the displacement, `dV
the change in electrostatic potential between the initial and final
positions of q
3.
Relate
for current I in a short segment of length `dL in a charge
carrier in the presence of magnetic field B, where `dF
is the force exerted by the field on the segment:
{I, B, `dL, `dF}
4.
Relate
for a circuit element with resistance R, where I is the current
through the element and V the potential difference across the
element:
{I, R, V}
5.
Relate
{P, I, V, R}
for a circuit element with resistance R, where I is the current
through the element and V the potential difference across the
element, and P is the power required to maintain the current.
6.
Relate
for long cylinder carrying an axially symmetric charge distribution
of density lambda, where phi_E is the electrostatic flux of the
distribution, a its radius and E the magnitude of the electric field
at distance r from the cylinder (where the distance from the point
to the nearest end of the cylinder is much greater than r):
{Q_enclosed,
lambda, L, phi_E, a,
E, r}
7.
Relate
for
a plane distribution of constant charge density, at a point much closer to plane
than to any of its edges:
{`dA,
sigma, `dQ, phi_E,
N, E}
where sigma is
the charge density, N a vector normal to the surface,
`dA is the area of a cross section in a plane perpendicular to N
of an appropriately positioned rectangular 'box' all of whose
points are much closer to the plane than to any of its edges, `dQ
the charge enclosed in the box, phi_E the electrostatic flux through
an end of the box and E the electric field at the point.
8.
Relate
for
a parallel-plate capacitor in air, where A is the area of each
plate, d the separation, E the electric field between the plates, V
the potential difference between the plates, C the capacitance and Q
the magnitude of the
charge on each
plate:
9.
Relate
for two
conducting elements of the same material, each of constant
cross-section both subject to the same potential difference V
between its ends:
{A_cs_1, A_cs_2, I_1, I_2, L_1, L_2}
where A_cs
indicates cross-sectional area, I current, L length of the
conductor in the direction normal to the cross-section.
10.
Relate
{C, Q, I, R, V_s, V_c, `dt, `dQ,
`dV_c},
for a series circuit consisting of a
source, a capacitor and a resistance element, with V_s is the
voltage of the source, C the capacitance, Q the charge on the
capacitor, V_c the voltage of the capacitor, I the current, R the
resistance, `dt a short time interval, `dQ the change in the charge
on the capacitor, `dV_c the change in the voltage across the
capacitor.
11.
Relate
{V, R_1, R_2, `dV_1, `dV_2, I_1,
I_2}
for a series or a parallel circuit with
two resistance elements, where V is the voltage of the course, R_1
and R_2 the two resistances, `dV_1 and `dV_2 the respective voltage
drops, I_1 and I_2 the currents through the respective resistors.
12.
Relate
for short current segment `dL, position r relative to
`dL, the magnetic field contribution `dB at that
position; theta is the angle of `dL with respect to r
{`dL, `dB, I, r,
theta}
13.
Relate
{I, orientation, a, B} for a circular current
loop of radius a in which a current I flows with a given
orientation, B the magnetic field at the center of the loop.
14.
Relate
for a plane region of area A, electric field of magnitude E whose
angle with respect to the specified normal of the plane is theta,
phi_E the flux of the electric field through the region
{E, theta, A, phi_E}
15. Solve problems related to voltage
induced by changing magnetic flux.
16. Explain self-induction.
17.
Relate
for a plane region of area A, magnetic field of magnitude B whose
angle with respect to the specified normal of the plane is theta,
phi_B the flux of the magnetic field through the region
{B, theta, A, phi_B}
18.
Relate
for a plane region of area A, magnetic field of magnitude B whose
angle with respect to the specified normal of the plane changes from
theta_1 to theta_2 it time interval `dt, phi_B_1 the flux of
the magnetic field through the region at the beginning of the
interval and phi_B_2 the same quantity at the end, `dPhi_B the
change in flux, ave_Rate the average rate of change of flux with
respect to clock time, V_ave the approximate average induced
voltage:
{B, theta, A, phi_B_1, phi_B_2, `dPhi_B, ave_Rate, V_ave}
19.
Relate
for charge q moving with velocity v in electric field E
and magnetic field B, where F_E and F_B are the
forces exerted by the respective fields
{q, E, B, v,
F_E, F_B}
20.
Relate
for segment `dL carrying current I, in the presence of
magnetic field B, where `dF is the force exerted on
the segment,
{`dL, B, I, `dF
}
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1.
Relate
for an electron in a classical circular orbit about a proton, where
m_e is the mass of electron, v its oribtal velocity, r its distance
from the proton, F_coul the Coulomb attraction between the
particles, F_centrip the classically-predicted centripetal force, KE
and PE the kinetic and potential energies of the orbit (PE relative
to infinite separation)
{m_e, v, KE, r, F_coul,
F_centrip}
2.
Relate
for the preceding situation with the additional quantization
condition on angular momentum, where lambda and circumf are the
deBroglie wavelength of the electron and circumf the circumference
of the classical orbit
{m_e, v, KE, PE, r, F_coul,
F_centrip, n, angular momentum, lambda, circumf}
3.
Relate
where n_1 and n_2 are angular momentum quantum numbers, `dKE and `dPE
the kinetic and potential energy changes for the Bohr model of the
hydrogen atom, f the frequency of the photon associated with the
change in orbit
{n_1, n_2, `dKE, `dPE, f}
4.
Relate
where E is the energy equivalent of mass m and c the speed of light
{E, m, c}
5. Analyze masses of two given isotopes of a
given element to determine if a given transition is possible.
6. Given the information in a periodic table of elements and
their isotopes, identify possible decay chains involving alpha, beta
and gamma decays.
7.
Relate
where E is the energy equivalent of mass m and c the speed of light,
lambda the wavelength of a photon with equivalent energy
{E, m, c, lambda}
8.
Relate
where N_p is the number of protons and N_n the number of neutrons in
a nucleus, m_p and m_n the masses of proton and neutron (masses in
SI units, AMU or equivalents), m_nucleus the mass of the nucleus, '
indicates properties of the resulting nucleus after a nuclear
transition, m_defect the mass defect associated with the transition
and E the energy released by the transition:
{N_p, N_n, m_p, m_n, m_nucleus,
N_p', N_n', m_p, m_n, m_nucleus', E}
9.
Relate
where N_p is the number of protons and N_n the number of neutrons in
a nucleus, ' indicates properties of the resulting nucleus after a
nuclear transition, and transitionType indicates the type of
transition (alpha, beta, gamma)
{N_p, N_n, N_p', N_n',
atomicNumber, atomicNumber', transitionType}
10.
Relate
where all quantities have been defined in preceding objectives
{N_p, N_n, N_p', N_n', m_p, m_n,
m_particle, atomicNumber, atomicNumber', transitionType}
11.
Relate
where E_bind is total binding energy, E_per is binding energy
per nucleon, other quantities as previously defined:
{E_bind, E_per, m_p, m_n,
m_nucleus}
12.
Relate
where v is the relative velocity of two reference frames, L and L '
the lengths of a given object as measured in the two frames, `dt and
`dt' the time interval between two events as measured in the two
frames, m and m ' the masses of a given object as measured in the
two frames:
{v, c, L, L', `dt, `dt', m, m'}
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