# Motion Graphs Ap Physics B Homework Sheet

**AP Physics**[ovonkugelgen@headroyce.org]

What do you want to learn about this year?

Do you know of a good applet or website?

Send me email!

**Latest Info: **

1. NEW: 2010 Nobel Prize for Physics: http://www.nobelprize.org/nobel_prizes/physics/laureates/2010/

2. Log into http://www.headroyce.org 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)

**Contents****:**

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 - SoundCh. 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 ExamStudent 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: http://www.lbl.gov/nanohigh/

http://www.lbl.gov/msd/highlights/youtube-msd.html?p=954C311769FAF77E (You Tube videos of speakers)

Earthquakes:

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 (sfgate.com)

(Original 1999 report from the USGS)

Head-Royce students get some recognition:

Advanced Placement Report to the Nation 2006

(Full Report - see pg 58)

**Introduction**

Topic Outline(from CollegeBoard.com)

The AP Physics exam(from the CollegeBoard.com)Note:

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__

**Topics:**

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

Freefall

**Graph Paper:**

graph_paper.pdf

**Tutorials:**

**Simulations & Links:**

The Moving Man(JAVA simulation)

......select 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)and class notes!

Review your worksheets, Quizzes

... 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__

**Topics: **

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)

Friction

.....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)

.....inmostcases (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" worksheetanswers**

__Ch.5: Circular Motion__

**Topics:**

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"

Equations:

F_{net}= ma_{c}

a_{c}= v^{2}/R

v = 2(pi)r/T

a = gtan(theta)Tricks:

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/R^{2 }^{ }so: g = F/m = GM/R^{2}

proportions:F ~ m (g is ind. of m)

F ~ M g ~ M

F ~ 1/R^{2}(inverse square law!) g ~ 1/R^{2}Orbits:

F

_{net}= F_{grav}ma

_{c}= mg

a_{c}= gApparent Weightlessness (N = 0)

Force, radius, period, velocity and acceleration of orbit

Geosynchronous orbitMore ch.5 practice

........ More Circular motion practice (answers)

**Tutorials:**

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

**Simulations:**

Energy:

energy = the ability to do work

Work:work = change in energyW = Fd (sort of !)

W = (F_{x})(x)when work is doneona system, it gains energy

when work is donebya system, it loses energy

Mechanical Energy:

PE = mgh

KE = (1/2)mv^{2}

EPE = (1/2)kx^{2 }or EPE = (avg force)(dist)

Conservation of Energy:(initial M.E.)+ (work doneExample1:onthe system) = (final M.E.) + (work donebythe 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}

Example2:

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:P = Work/time = (change in energy)/(time)

power = rate at which work is done

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: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__**Topics:**

p = m*v.... "delta" means: "change in" = "FINAL - initial

Impulse = F*t = delta p = m*(delta v)".... always include a + or - or direction in your calculations!

p, v, F, delta p, delta v, Impulse are VECTORS!(even when mechanical energy is not conserved!)

Conservation of momentum

.... 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 __

**Topics:**

Angular(or "rotational") velocity and acceleration

....angularvelocity = (change inangle)/time

....angularacceleration = (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

Torque

See-Saw (Flash)

See-Saw2

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

__Semester1 Exam__:

TBA

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__**Topics:**

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) = 0.80Pressure 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 fluidHow amonometermeasures pressureAir Pressure= 14.7 lb/square inch

1 atm = 101,000 Pascals= 760 mm of Hgso: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'sPrinciple (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 Principleshort bernoulli ppt

**Ch. 11 Vibrations and waves**

**Topics:**

Mass on a Spring...F = kxor F = -kx...EPE = (1/2)kx^{2}^{ }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 conservationSimple 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)/ TPendulum...T = 2(pi)(L/g)^0.5

....Energy conservation: max PE = max KE to find max vWaves...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...v = (freq)(wavelength)

Standing waves

...Standing wave shapes

...the nth harmonic = (n)(fundamental frequency)........where the wave speed is the same for each harmonic

..............(speed is NOT effected by amplitude or frequency!)

Etc.

**Links/Simulations:**

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!

Interference

Beats

Etc.

...(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 = h_{i}/h_{o }= -d_{i}/d_{o}.....1/f = 1/d_{i}+ 1/d_{o}..........Convex (-f), Concave (+f),

.........(-d_{i}) for virtual images, (+d_{i}) for real images, (-M) for inverted images

Refraction

.....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)

Lenses

....Converging (+f) are thicker in the middle, Diverging (-f) are thinner in the middle

....M = h_{i}/h_{o }= -d_{i}/d_{o}.....1/f = 1/d_{i}+ 1/d_{o}_{}....(more later!)

**Ch. 24 The Wave Nature of Light**

Huygen's Principle

Diffraction

Refraction

... (wl') = (n/n')(wl)

Interference

... 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 changesDouble SlitInterference (Young's Experiment)

.... thin slits produce circular waves

... these circular waves interfere to produce bright and dark "interference fringes"

...constructive interferenceif path difference = (m) wl (see above)

.......dsinA = (m)(wl) MAXIMA

... destructive interference if path difference = (m + 0.5) wl

........dsinA = (m + 0.5) wlMINIMA

....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)/LSingle slit

........To find the distance "x" from centerline mth order minima:

........ bsinA = (m)(wl)Multiple slitdiffraction 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)

Dispersion

....Colors separate due to refraction and different speeds (indexes of refraction)

Rainbows

....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"

....red 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

Polarization

....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/d

_{i}+ 1/d

_{o}......M = h

_{i}/h

_{o }= -d

_{i}/d

_{o}

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)

......polarization

**Ch. 16: Electric charge and Electric field**

**Topics:**

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/R^{2}^{ }(for point charges)

. where k = 9 x 10^{9}Nm^{2}/C^{2}

.F is a vector

. F ~ 1/R^{2}(inverse square law!)

Electric Field

.E = F/q(anytime!)

.E = kQ/R^{2}(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

Etc.

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**

**Topics:**

Work = Fd (sort of)

Work = change in energyElectric Potential = "voltage" = (Electric Potential Energy)/(q)

. = Joules per Coulumb = volts

Work, energy and electric potential arescalars(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

. soE = 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)CV^{2}

For point charges (if we set EPE = 0 when R = infinity):

.EPE = kQq/R.V = kQ/RBreakdown of air occurs when E = 3 x 10^{6 }V/m

Note the units of Electric Field: N/C = V/mEtc.

Factors affecting capacitance

Lightning

Electric field and voltage

Current:= charge passing each second = coulombs per second = amperes

I = q/t

Voltage:= electrical energy per coulomb = Joules per coulomb = volts

V = EPE/q

Ohm's Law:............ I ~ V

I = V/R

............ I ~ 1/R

Resistance:............R ~ L

R = (resistivity)L/A

............R ~ 1/A..................note: A = 2(pi)r^{2}so R ~ r^{2}

Power:= J/s

P = E/t = IV=watt

Energy:E = (J/s)(s) =

E = (P)(t)J

E = (kW)(hrs)= kWh

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

Joules or kWh

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 outParallel 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 litCompound Circuit

Circuit Analysis:

... determine the current and voltage drop for each component in a circuitCircuit overload:

... fuses and circuit breakers+.....

Capacitors revisited:

Series:

...1/Ctotal = 1/C1 + 1/C2+ 1/C3... Q1 = Q2 = Q3 = ...

... V = Q/C...Ctotal = C1+ C2 + C3 +...

Parallel:

...Qtotal = Q1+Q2 + Q3 +...

...V = Q/C

Capacitor RC time constant

**Links/Simulations:**

**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

.....EMF~speed

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)....EMF = -N(change in flux/time)

4. Apply Faraday's Law....EMF = BLv

5. Motional EMF....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))....(P)in = (P)out

6. Transformers

....(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 examsPast 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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- McCallum, P.
- Sohn, M.
- Martinez, A.
- Dass, S.
- AP Biology
- AP Chemistry
- AP Physics
- Cockburn, B.
- Fiore, C. - Principal
- test teacher

- Resources
- Calendar