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Motion Graphs Ap Physics B Homework Sheet

AP Physics

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Latest Info: 

1. NEW: 2010 Nobel Prize for Physics:

2. Log into and go to the CLASS PORTAL for assignments, handouts, pdf's, etc.

3. HRS is generating electricity! (Let me know if you are willing to help me analyze the cost/benefit)


Latest Info (latest information can be found here)
Old News (other not-so-new news)
Introduction to AP Physics
Student Resources
Ch.2 - 1-D Motion
Ch.3 - 2-D Motion  
Ch.4 - Newton's Laws 
Ch.5 - Circular Motion and Gravity
Ch.6 - Work and Energy
Ch.7 - Impulse and Momentum
Parts of Ch.8 & 9 - Rotational Motion, Torque and Equilibrium
Semester1 Exam
Ch.10 - Fluids
Ch. 11 - Vibrations and SHM
Ch. 12 - Sound
Ch. 23 - Reflection & Refraction (+ Ch. 25.2)
Ch. 24 - The Wave Nature of Light
Ch. 16 - Electric Charge and Electric Field
Ch. 17 - Electric Potential, Electric Potential Energy, Capacitance
Ch. 18 - Electric Currents
Ch.19 - DC Circuits
Ch. 20 - Magnetism
Ch. 21 - Electromagnetic Induction and Faraday's Law
Atomic and nuclear physics (coming soon)
Quantum Physics (coming soon)
Start Reviewing for the AP Exam
Student Resources
Physics that makes my head hurt!  (gravitons, virtual photons, string theory, etc...Ouch!)

Old "News":                                                
Nobel Prize in Physics 1901 - Present

Nanohigh at Lawrence Berkeley National Lab: (You Tube videos of speakers)

USGS Earthquake Page  (interactive map of recent quakes)
USGS Earthquake Preparedness Handbook (written for the San Francisco Bay Area Region)
70% chance of a big quake predicted in the Bay Area between 2000 and 2030 (
(Original 1999 report from the USGS)

Head-Royce students get some recognition:
Advanced Placement Report to the Nation 2006
(Full Report - see pg 58)


Topic Outline (from

The AP Physics exam (from the

Course Description (big pdf)
Table of information (MC & FR) and equation tables (FR, only) (pdf)
Past free response questions (2002 - 2005)

Companion website for our textbook

Ch.2: 1-D Motion


Position, displacement, average speed, average acceleration
Instantaneous velocity and acceleration
Graphing motion (x vs. t, v vs. t, a vs. t)
1-D motion Equations

Graph Paper:



Simulations & Links:

The Moving Man (JAVA simulation) Motion from the left menu bar, then select The Moving Man
.....(you may have to download the applet to your desktop)

Vector vs. scalar, vector components, vector addition, vector subtraction
Relative velocity
Projectile motion

The Physics Classroom - Vectors

Ch. 2/3 Test Review:    [Test date TBA]

Possible test questions:
- apply 1-D equations
- describe or analyze position, velocity or acceleration graphs (words, slope, area, slope of tangent to the curve)
........(see worksheets)
- freefall (dropped, thrown up, thrown down)
- determine components of a vector (mag & dir)
- add or subtract vectors (using components)
- projectiles (start and stop at same height, end at different height; find time, max ht, ht and velocity at time t)
- boat/plane problems
...... (see worksheets and ch.3 reading)

Review your worksheets, Quizzes
and class notes!
... look for the common thread(s) in all of our problems

More Ch.2 Equation Practice (with answers) (someone asked for more practice =))
"Practice Test" - sort of (coming soon)

Ch.4: Newton's Laws of Motion


Inertia, mass & weight
.... Wt. = mg
Free body diagrams (force diagrams)
Newton's 1st, 2nd & 3rd Laws
......."net external Force" = (mass)(acceleration)

...... "net Force" = the sum of all forces on acting the object
...... If A pushes B up, B pushes A down  [the forces in an action/reaction pair act on different objects!]
Tension & Normal Force
Multibody problems (the von K. way)
..... F = (coefficient of friction)(normal force)
Inclined planes
.... tilting the x & y axes
.... x-comp of wt. = mgsin(theta)
.... y-comp of wt. = mgcos(theta) most cases (i.e. where friction, wt, and N are the only forces present):
............. net force = (x-comp of wt.) - (force of friction)

Answers to "AP Ch.4 Practice" worksheet

Ch.5: Circular Motion


Uniform circular motion
... constant speed and radius
... the magnitude of the net force and acceleration are constant
... the net force and the acceleration vectors point inward to the center of the circular path
"Centripetal" means "center seeking"
We do not use the "F-word"
.... There is no such thing as centrifugal force!
"Centripetal force" = "net force" = "sum of the force vectors"

Fnet = mac
ac = v2/R

v = 2(pi)r/T
a = gtan(theta)

1. to find acceleration, apply F = ma to the whole system
2. to find tension, apply F = ma to only one object

Newton's Universal Law of Gravity

F = GMm/R2                                            so: g = F/m = GM/R2


F ~ m                                          (g is ind. of m)
F ~ M                                           g ~ M
F ~ 1/R2 (inverse square law!)       g ~ 1/R2


Fnet = Fgrav

mac = mg
   ac = g

Apparent Weightlessness (N = 0)
Force, radius, period, velocity and acceleration of orbit
Geosynchronous orbit
More ch.5 practice
........ More Circular motion practice (answers)


The Physics Classroom - Circular Motion and Planetary Motion

IUN/FYD Introductory Physics Notes

Circular Motion and the Law of Gravity

Companion website for our textbook


energy = the ability to do work

work = change in energy
W = Fd (sort of !)
W = (Fx)(x)
when work is done on a system, it gains energy
when work is done by a system, it loses energy

Mechanical Energy:
PE = mgh
KE = (1/2)mv2
EPE = (1/2)kx2           or EPE = (avg force)(dist)

Conservation of Energy:
(initial M.E.)+ (work done on the system) = (final M.E.) + (work done by the system)
If you pick a "system" big enough that their is no net external force acting on the system:
    (PE + KE + EPE)i = (PE + KE + EPE)f
   In many of our problems with friction:
   initial M.E. = final M.E. + work to overcome friction
   (PE + KE + EPE)i = (PE + KE + EPE)f + thermal energy from friction

power = rate at which work is done
P = Work/time = (change in energy)/(time)
P = Fv  (be careful!)

Units of energy and power:
Energy: Nm, J, calories, Calories (kcal or food Calories), Btu, etc.
Power: J/s, W, kW, hp, calories/sec, etc.

Efficiency = (useful output work)/(input work or energy)
ex: if an engine is 25% efficient, it must burn 400kJ worth of fuel to give the car 100kJ of KE (on level ground with no friction)

(see Student/Teacher Resources)

Work and Energy Animations

Roller coaster

Ch.7: Impulse and Momentum


p = m*v
Impulse = F*t = delta p = m*(delta v)
.... "delta" means: "change in" = "FINAL - initial"
p, v, F, delta p, delta v, Impulse are VECTORS!
.... always include a + or - or direction in your calculations!
Conservation of momentum
(even when mechanical energy is not conserved!)
.... If you pick a "system" big enough that their is no net external force acting on the system

(see Student/Teacher Resources)

Some Ch. 7 Even answers:
2) - 0.720 m/s
14) 130N; not large enough
18) a) 460 kg m/s East
......b) 460 kg m/s West
......c) 460 kg m/s East
......d) 610 kg m/s East


Chapter 6/7 Test:

Review worksheets, chapter summaries, and problems assigned from the book

Parts of Ch.8 &9: Rotational Motion, Torque and Equilibrium


Angular (or "rotational") velocity and acceleration
.... angular velocity = (change in angle)/time
.... angular acceleration = (change in angular velocity)/time
.... linear velocity = (angular velocity)(r)
.....linear acceleration = (angular acceleration)(r)
Torque = Frsin(theta)
Conditions for equilibrium:
.... net force = 0      (ie: all forces cancel)
.... net torque = 0    (ie: all torques cancel)

Torque = (moment of inertia)(angular acceleration)
rotational KE = (1/2)(momentof inertia)(angular velocity)2
The effect of shape on acceleration down an incline
.... ex: the acceleration of a disc vs. a ring
.... PE = lin KE + rot KE

See-Saw (Flash)

Semester1 Exam:   (Let me know if you have a conflict or qualify for extended time!)


Anything and everything covered so far this year :-)
Possible problems from Chs. 8 and 9 include:                 

.... equilibrium: net force = 0
.... equilibrium: net torque = 0

.... application of rotational equations for angle, velocity, acceleration and torque
............. see Ch.6-9 Practice (below) and ch.8/9 topics (above)
.... possible surprise question about conservation of energy for a rolling object :-)
See class handouts:
.......Ch.2 - 5 Review
.......Ch.6 - 9 Review
.......Ch.2 - 5 Practice  Solutions! (pdf)
Ch.6 - 9 Practice(solutions included!)                       

Have a great Winter Break!

Ho Ho Ho

Ch. 10 - Fluids


Density does not = weight!
         D = m/V = mass per unit of volume
         [density units = kg/cubic meter]
Specific Gravity of a substance = (density of the substance)/(density of water)
         spec. grav. = (D of the substance) / (D of water)
    so: alcohol has a sp. grav = (0.80 g/cc)/ (1 g/cc) = 0.80
Pressure does not equal force!
         P = F/A = force per unit area
         [pressure units = N/square meter = Pascals]
Fluid Pressure
         P = mg/A
    so: P = Dgh  where h = the depth of the fluid
How a monometer measures pressure
Air Pressure
         1 atm = 101,000 Pascals
= 14.7 lb/square inch = 760 mm of Hg
so:that's a force of 101,000 N per square meter!!
Absolute Pressure vs. Guage Pressure
         Guage Pressure = (Absolute pressure - 1 atm)
so: a flat tire has a guage pressure of zero, but an absolute pressure of 1 atm :-)
Pascal's Principle (and hydraulics)
          Pout = Pin
          Fout/Aout = Fin / Ain
          Hydraulics applications
Archimedes Principle
         Bouyant force = wt. of the displaced liquid
         If floating:
          (Vol. submerged)/(total V) = (D of object) / (D of liquid)
Equation of continuity
         (A)(v) = const.
         (A1)(v1) = (A2)(v2)
Bernoulli's Principle
         (see equation 10-5 on page 290)
         Applications of Bernoulli's Principle
short bernoulli ppt

Ch. 11 Vibrations and waves


Mass on a Spring
...F = kx                    or F = -kx
...EPE = (1/2)kx2           or EPE = (avg force)(dist)
...T = 2(pi)(m/k)^0.5
.....max v = A(k/m)^0.5
.....max a = (max F)/m = (kx)/m
.....Energy conservation

Simple Harmonic Motion
...F ~ (-x)
...graphs x, v & a vs. time
...x = Acos(2(pi)t/ T)    if x = A at t = 0
.....comparison of SHM with Uniform Circular Motion (motion and equations)
............max v = (2(pi)A)/ T

...T = 2(pi)(L/g)^0.5
....Energy conservation: max PE = max KE to find max v

...frequency of a wave = frequency of the source (for stationary sources)
...the wave Equation:  v = (freq)(wavelength)
....reflection at fixed and free end
....reflection and transmission as a wave moves from slow to fast, or fast to slow
.........(note changes in wavelength andwhen the waves flip upside down)
....constructive and destructive wave interference

Standing waves
...Standing wave shapes
...the nth harmonic = (n)(fundamental frequency)
...v = (freq)(wavelength)
........where the wave speed is the same for each harmonic
..............(speed is NOT effected by amplitude or frequency!)



Sound waves are longitudinal waves (compressions and rarefactions)
Speed of sound in solids, liquids, gases (fast, medium, slow)
Speed of sound in air = 343 m/s  (approx)
... v = (331 + 0.6T) m/s
Transverse standing waves on strings
...f = v / (w.l.)
...v = (T/(m/l))^0.5
Longitudinal standing waves in columns of air
...O - C column of air produces odd harmonics
Doppler Effect
...moving listener changes the relative velocity of sound waves: f = v'/(w.l.)
...moving source changes the wavelength of the sound waves: f = v/(w.l.)'
...see textbook for equations!

...(more later!)

Ch.11/12 Test Review/Tips:

Ch.11/12 Test - Equations and Tips (pdf)
Ch.11/12 Test- Equations ansd Tips (Word doc)


Ch. 23 Reflection & Refraction

Locate images in a plane mirror by ray tracing
Locate images formed by curved mirrors and lenses by ray tracing
Apply the magnification equation and the mirror equation to curved mirrors
.....M = hi/ho = -di/do           .....1/f = 1/di + 1/do
..........Convex (-f), Concave (+f),
.........(-di) for virtual images, (+di) for real images, (-M) for inverted images
.....Index of refraction
......... n = c/v
..........(n)(wl) = (n')(wl')
.....Snell's Law
..........n1sinA1 = n2 sinA2
.....Lateral displacement
.....Multiple layer shortcut
Total internal Reflection
....critical angle (only when slow to fast!)
....sinA = (n2/n1)
....Converging (+f) are thicker in the middle, Diverging (-f) are thinner in the middle
....M = hi/ho = -di/do           .....1/f = 1/di + 1/do

....(more later!)

Ch. 24 The Wave Nature of Light

Huygen's Principle
... (wl') = (n/n')(wl)
... for waves "in phase":
........ if the path difference =  0 wl, 1 wl, 2 wl, ...(m) wl, we get constructive interference
........ if the path difference = 0.5 wl, 1.5 wl, (m + 0.5) wl, we get destructive interference
..............where m = 0,1,2,3,....
Interference pattern for circular water waves
... "nodal lines"
... "changes in the interference pattern when the source separation and/or wavelength changes
Double Slit Interference (Young's Experiment)
.... thin slits produce circular waves
... these circular waves interfere to produce bright and dark "interference fringes"
... constructive interference if path difference = (m) wl (see above)
....... dsinA = (m)(wl)             MAXIMA
... destructive interference if path difference = (m + 0.5) wl
........dsinA = (m + 0.5) wl      MINIMA
....Given slit separation "d", distance to screen "L", distance between maxima "x"
........tanA = x/L
.............using tanA = sinA (small angle approximation)
.............(m)(wl) = dsinA = dtanA = dx/L
........wavelength of the light = (dx)/L
Single slit
........To find the distance "x" from centerline mth order minima:
........ bsinA = (m)(wl)
Multiple slit diffraction gratings
........Same as double slit, but the maxima are more discrete
The visible spectrum (ROYGBV)
... Red to Blue:  (long wl, low freq)  to (short wl, high freq)
....Colors separate due to refraction and different speeds (indexes of refraction)
....Due to dispersion and total internal reflection
Spectrometer and spectroscopy
....prisms and/or diffraction gratings spread light
....emission spectra (bright line spectra) vs. absorption spectra
....elements have "fingerprints" shift and blue shift
Thin film interference
....caused by constructive and/or destructive interference of waves reflected at boundaries
....(careful, sometimes the waves flip upside down when reflection, other times they reflect rightside up)
....see book for equations
Colors on Bubbles and CD's
....colors are due toconstructive and/or destructive interference
....parallel axes => 50% transmission
....perpendicular axes => 0% transmission
....glare from windows and water is usually polarized
.........glare from horizontal surface is polarized horizontally  <------->

Huygen's principle

Ch.23/24 Test:

Ch 23/24 review sheet (pdf)

Ch23/24 test - question types (2006/2007)
1. Ray diagrams and location and characteristics of images
a. Plane Mirror
b. Curved Mirrors
c. Lenses

2. Apply the mirror and lens equations to mirrors and lenses
.....1/f = 1/di + 1/do......M = hi/ho = -di/do          

3. Refraction: sketch the path of light and apply Snell's Law
..... n1sinA1 = n2 sinA2

4. Critical angle angle and total internal reflection
..... n1sinA1 = n2 sin90

5. Interference of two or more sources
.....double slit and diffraction gratings

6. Single slit interference pattern

7. Conceptual question(s) about
......visible spectrum
......dispersion (prism)

Ch. 16: Electric charge and Electric field


Positive and Negative Charge
Charge is "conserved"
Like charges repel; opposite charges attract
Methods of charging an object
...."friction" (two objects are rubbed together)
...."conduction" (also called "contact")
...."induction" (and grounding)
Coulomb's Law
.     F = kqQ/R2                      (for point charges)
.          where k = 9 x 109 Nm2/C2
.          F is a vector
.          F ~ 1/R2 (inverse square law!)
Electric Field
.     E = F/q                             (anytime!)
.     E = kQ/R2                        (for point charges)
.          E is a vector     
.          by convention, E points toward a negative charge and away from a positive charge
Problems involving 2 or more point charges (see Ch.16 HW)
.     Find F on a particle (by adding vectors)
.     Find E near charged particles (by adding vectors)
Electric field inside a conductor
.      Charge in or on the conductor will move until E = 0

Charged rod and pith ball
Charging an Electroscope
Electric field and equipotentials
Electric field around two charges
Charging by friction
Charge theft - why a VDG loses charge

Ch. 17 Electric Potential, Electric Potential Energy, Capacitors


Work = Fd (sort of)
Work = change in energy
Electric Potential = "voltage" = (Electric Potential Energy)/(q)
.                                           = Joules per Coulumb = volts
Work, energy and electric potential are scalars (easy math)
For Uniform electric field (like between parallel charged plates):
.       W = change in EPE
.       W = Fd = (qE)d
For Parallel Plate capacitors
.       W/q = Ed      
.               so E = V/d          
.       C = Q/V       
.               where C = capacitance, not coulombs
.       C = (epsilon-sub-zero)(A)/d
.               where epsilon-sub-zero = 8.85 x 10-12 F/m
.        Stored Energy = (1/2)QV = (1/2)CV2
For point charges (if we set EPE = 0 when R = infinity): 
.        EPE = kQq/R
.        V = kQ/R
Breakdown of air occurs when E = 3 x 106 V/m   
Note the units of Electric Field:     N/C = V/m

Factors affecting capacitance
Electric field and voltage

I = q/t
= charge passing each second = coulombs per second = amperes

V = EPE/q
= electrical energy per coulomb = Joules per coulomb = volts

Ohm's Law:     
I = V/R
............ I ~ V
............ I ~ 1/R

R = (resistivity)L/A
............R ~ L
............R ~ 1/A
..................note: A = 2(pi)r2     so R ~ r2

P = E/t = IV
= J/s = watt

E = (P)(t)
E = (J/s)(s) = J
E = (kW)(hrs) = kWh

Energy Units:
Joules or kWh   
1 kWh = 3,600,000 J


The Ohm Zone (quite good, but the applet does make occasional errors)

Ch. 19 DC Circuits

Series vs. Parallel Circuits
Series circuit:

...all electrons follow the same path
...Total resistance increases as more resistors are added in series.
......Total R = R1 + R2 + ...
...the current is the same for each component (ie: battery, bulbs or resistors)
...the battery's voltage is divided among the components (ie: bulbs or resistors)
......voltage drop is proportional to the resistance (bulbs with higher resistance have higher voltage drop)
...remove one bulb and they all go out
Parallel circuit:
...electrons have a choice of paths
...Total resistance decreases as more resistors are added in parallel
......1/Rtotal = 1/R1 + 1/R2 + ...
...the voltage is the same for each component
...the battery's current is divided among the components
......current is inversely proportional to the resistance (bulbs with higher resistance have less current)
...remove one bulb and the others stay lit
Compound Circuit
Circuit Analysis:

... determine the current and voltage drop for each component in a circuit
Circuit overload:
... fuses and circuit breakers
Capacitors revisited:
   ...1/Ctotal = 1/C1 + 1/C2+ 1/C3
... Q1 = Q2 = Q3 = ...
   ... V = Q/C
   ...Ctotal = C1+ C2 + C3 +...
   ...Qtotal = Q1+Q2 + Q3 +...
   ...V = Q/C
   Capacitor RC time constant


The Ohm Zone (quite good, but the applet does make occasional errors)

Ch18/19 practice (sorry, the best I could do with the little time I had)

ch.18/19 practice  (no solutions yet)

Ch. 21 Electromagnetic Induction and Faraday's Law

Most important Magnetic Induction topics for the AP Physics B exam:

1. A changing magnetic field near a coil induces a voltage in the coil (Farady's Law).
.....EMF~number of turns
2. A voltage will be established (and current will flow) in a coil that opposes the change in flux (Lenz's Law).
3. What is magnetic flux? (Calculate magnetic flux)

....Magnetic flux = BAsin(theta)
4. Apply Faraday's Law
....EMF = -N(change in flux/time)
5. Motional EMF
....EMF = BLv
....which end of a rod moving in an external magnetic field has higher voltage? (RHR: F=qvB)
....calculate emf and force for a rod moving in an external magnetic field has higher voltage (RHR: F=ILBsin(theta))
6. Transformers
....(P)in = (P)out
....(IV)in = (IV)out
....(N2/N1) = (V2/V1) = (I1/I2)
7. Why is power sent at high voltage in transmission lines?
8. How does a generator work? (compare and contrast to a motor)

(ppt from lecture on request)

1. Physics Facts
List of 100+ basic physics concepts you are expected to know for the AP Exam in May.

2. Start reviewing the equations listed in the equation tables!
....College Board website for AP PhysicsB
....2007 Equation tables for the B and C exams
....Past free response questions AND solutions

....Review for the AP Exam (suggestions and links)

3. Click here: AP exam review

Student/Teacher Resources

Recognizing Forces (EXCELLENT PRACTICE)  Test your ability to identify ALL forces acting on an object

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