Things You Should Know About Physics

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1 Measuement and Mathematics HONORS Fundamental units Quantity Units Symbol Estimation: 1 kg 2.2 lbs 1 apple 1 N 1 quate 5 g kg Ode of magnitude: powe of ten (thickness of pape 10-4 m) Length mete m Mass kilogam kg Time second s Electic cuent ampee A e Fundamental Units: Thee ae only 7 (see table). All othe units ae deived units. Facto-Label Convesions: 1 goes with the pefix, exponent goes with the base. expeimental - actual %eo x 100 Mean aveage Range highest value lowest value actual Measued Uncetainties: use 1 sig fig and match decimal place of measuement eg cm ±0.1 cm (exception: exteme vaiability) Calculated Uncetainties fo multiple tials: use geatest esidual of data and match decimal place of measuement Accuacy: how close a measuement is to the accepted value (a measue of coectness) Pecision: ageement among a numbe of measuements made in the same way (a measue of exactness) Systematic Eo: all measuements off by same amount non-zeo y-intecept can be eliminated measue of accuacy Random Uncetainty: unpedictable vaiations in data the eason fo eo bas on gaph can be educed by multiple tials but neve eliminated measue of pecision Geneal Relationships: Constant y c Diect y mx Slope Δy/Δx Linea y mx + b Linea (Indiect) y mx + b Invese y c/x Invese Quadatic y c/x 2 Scalas (magnitude only) Vectos (magnitude and diection) only 9! Distance Displacement Speed Velocity Acceleation Foce (weight, nomal foce, etc.) Anything else! Momentum Impulse Fields (gavitational, electic, magnetic) Quadatic y cx 2 sin cos Squae Root y c x opp hyp adj hyp opp tan adj

2 Mechanics Vectos Equilibium: no net foce, no acceleation, constant velocity o at est, foces fom a closed figue Concuent vectos: placed tail-to-tail Component vectos: must be head-to-tail to find esultant Resultant foce F net : head-to-head and tail-to-tail with components Range of possible esultants: Maximum sum of vectos Equilibant: equal and opposite to esultant Minimum diffeence of vectos Box on a Hill in Equilibium: mgsinθ F f o F A o F T and mgcosθ F N Mass (m): inetia, amount of matte, constant fom place to place, units: kg Weight (F g ): foce of gavity, changes fom place to place, units: N Fomula: F g mg Concuent Resultant Maximum Θ 0 0 Minimum Θ Equilibant Tiangle ule sum of any 2 sides thid side fo foces to be in equilibium FA FF FT F G Inclined Plane FN F m g cosθ F m g sinθ Two names fo little g : 1) acceleation due to gavity, units: m/s 2, fomula: g GM/ 2 2) gavitational field stength, units: N/kg, fomula: g F g /m d Gaphs of Motion v Constant Velocity Two Types of Motion Constant Acceleation Slope velocity t Slope acceleation Aea displacement t Foces ae balanced Foces ae unbalanced Fnet 0, a 0 Fnet 0, a 0 In equilibium not in equilibium Newton s fist law Newton s second law Consevation Laws: electic chage, momentum, mass and enegy Distance v. Speed v. Acceleation v. Distance v. Speed v. Acceleation v. time time time time time time Fiction Static fiction (at est) applied foce until motion stats Cicula Motion F c, a c Kinetic fiction (in motion) is constant Maximum static fiction is geate than kinetic fiction Newton s Thid Law: Wheneve A exets foce on B, B exets equal/opposite foce on A. (Action/eaction pais: bat and ball, Eath and Moon, hamme and nail) Foces ae the same but the effects of the foces ae not: ma Ma v d cicumfeence 2 v t peiod T v mv ac Fc mac 2 2

Hoizontal Launch x Y d h t The same a 0 9.81 vi vi 0 vf vavg vi vi Pojectiles Hoizontal constant speed Angle Launch Vetical constant acceleation x Y d t Whole half a 0 9.

3 Hoizontal Launch x Y d h t The same a vi vi 0 vf vavg vi vi Pojectiles Hoizontal constant speed Angle Launch Vetical constant acceleation x Y d t Whole half a vi Vx Vy vf Vx 0 (top) vavg Vx Enegy Wok: foce and displacement must be paallel Mechanical Enegy: PE g + PE s + KE Total Enegy: PE g + PE s + KE + Q Intenal Enegy Q: themal enegy, heat due to fiction/ai esistance Collisions Consevation of Momentum: pbefoe pafte Isolated System: no extenal foces Elastic Collision: total KE is conseved Sticky m1v1 + m2v2 (m1 + m2)۰vf Powe: ate of change of enegy, ate of dong wok (units: Watts (W) J/s) Efficiency: useful out/total in PE g inceases if height inceases. KE inceases if speed inceases. PE s inceases if sping is stetched o compessed. Fomulas fo spings: PE s ½ kx 2 k sping constant (units: N/m) F s kx Consevation of Enegy: E T E T PE g + PE s + KE + Q PE g + PE s + KE + Q Wok-Enegy Theoem:, W ΔE T Bouncy m1v1 + m2v2 m1v1 + m2v2 Remembe Moving to the left gets a NEGATIVE sign! Explosion Equal and opposite foces, impulses, changes in momentum, and contact times Diffeent speed based on mass mama mvmv Simple Hamonic Motion 1) Pendulum 2) Mass on Sping ) Newton s Law of Univesal Gavitation F g Gm m 1 2 L 2 T 2 T 2 g M k

Electicity Conductos (metals) have fee electons, insulatos do not. Objects become chaged by losing o gaining electons (not potons). Elementay Chage: poton o electon 1 Coulomb of chage 6.

67 x 10-27 kg If two o moe identical chaged sphees touch, the final chage on each is the aveage chage (total chage # of sphees). The total chage is conseved.

4 Electicity Conductos (metals) have fee electons, insulatos do not. Objects become chaged by losing o gaining electons (not potons). Elementay Chage: poton o electon 1 Coulomb of chage 6.25 x elementay chages Chage of Electon: q -1e OR q x C Mass of Electon: m 9.11 x kg Chage of Poton: q +1e OR q x C Mass of Poton: m 1.67 x kg If two o moe identical chaged sphees touch, the final chage on each is the aveage chage (total chage # of sphees). The total chage is conseved. A neutal object will be attacted (neve epelled) by any chaged object. If two objects attact, they could have opposite chages o one could be neutal. If two objects epel, they must have the same type of chage. Chaging by conduction: diect contact - electoscope gets same chage as od Chaging by induction: no diect contact - electoscope gets chage opposite of od Electic potential diffeence (voltage): wok done pe unit chage (V W/q) Coulomb s Law (electic foce, electostatic foce) Electic Field (units: N/C o V/m) F e E kq q F e Lines go fom + to -. Lines neve coss. Lines show diection of foce on small positive test chage. Field is most intense whee field lines ae most dense. q Resistance of a wie: R ρl/a whee A π 2 Least esistance (best conducto): shot, fat, cold Most esistance (wost conducto): long, hot, skinny Voltmete: connect in paallel, infinite intenal esistance Ammete: connect in seies, zeo intenal esistance Seies Cicuit Contol: cuent Paallel Cicuit R1 V1 P1 R1 I2 P2 R2 V2 P 2 R I P Contol: voltage Two Paallel Plates (Capacito) Unifom electic field between plates same E eveywhee and same F eveywhee Used to stoe electic chage e E V d Resistance adds up (geate than geatest) Adding exta esisto inceases total esistance and deceases total cuent. Resistance adds down (less than least) Adding exta esisto deceases total esistance and inceases total cuent.

Resistance: R V/I Ohmic Device: follows Ohm s law (Vα I at constant T) constant

Diection of lines diection of compass needle Potential diffeence V Volt V J/C Cuent

Joules J N m Mechanical Powe: P W/t Fd/t Fv Electical Powe: P VI I 2 R V 2 /R 1

6 x 10 6 J Thee units of enegy: joules, electonvolts, kilowatt hous Two Pinciples of

5 Resistance: R V/I Ohmic Device: follows Ohm s law (Vα I at constant T) constant esistance Slope 1/R Slope R Magnetic Fields Fom N to S, density stength (intensity) Diection of lines diection of compass needle Potential diffeence V Volt V J/C Cuent I Amps A C/s Resistance R Ohms Ω V/A Powe P Watts W J/s Chage q Coulombs C Enegy W Joules J N m Mechanical Powe: P W/t Fd/t Fv Electical Powe: P VI I 2 R V 2 /R 1 electonvolt (ev) 1.60 x J 1 kilowatt hou (1000 W)(1 h) 3.6 x 10 6 J Thee units of enegy: joules, electonvolts, kilowatt hous Two Pinciples of Electomagnetism: 1) An electic cuent (o moving chaged paticle) geneates a magnetic field. 2) A changing/moving magnetic field induces an electic cuent (electomagnetic induction). Tansfome: All tansfomes V P / V S N P / N S Electomagnetic induction: emf V BLv (move wie pependicula to field lines fo maximum induced potential diffeence) Ideal tansfomes P P P S V P I P V S I S Step-up: N s > N P, V s > V P, I s < I P Step-down: N s < N P, V s < V P, I s > I P

6 Waves Mechanical: needs medium Electomagnetic: no medium Tansvese: pependicula Longitudinal: paallel Radio Wave: electomagnetic wave speed 3.00 x 10 8 m/s Peiod (T): seconds/cycle Fequency (f): cycles/second Wave equation: v fλ Sound Longitudinal, mechanical Speed 331 m/s (STP) 340 m/s (oom temp) Amplitude loudness (volume) Fequency pitch Enegy α amplitude Speeds up when going fom ai to wate Can t be polaized Light Tansvese, electomagnetic Speed c 3.00 x 10 8 m/s (vacuum) Amplitude α bightness (intensity) Fequency α enegy (E hf) Slows down when going fom ai to wate Can be polaized Red: long wavelength, low fequency Blue: shot wavelength, high fequency In Phase: A, E, I Out of Phase by o λ/2: A, C In one medium : f α 1/λ Contol: speed - you can only change the speed of the wave by changing the popeties of the medium) Law of Reflection: θ i θ Cossing a bounday: v α λ Contol: fequency stays the same, so does peiod and phase Had eflection: out of phase Soft eflection: in phase Constuctive intefeence: in phase θi θ Refaction: changing diection when changing speed when cossing a bounday FAST: into fast, bend away fom nomal (high n to low n) into slow, bend towads nomal (low n to high n) Diffaction: bending aound obstacle o speading though opening Noticeable diffaction: when size of opening appox. equal to size of wavelength as opening gets smalle, moe diffaction effects Destuctive intefeence: out of phase Dopple Effect: appaent change in fequency due to elative motion Constant low fequency, Deceasing amplitude Dopple Shift fo Light: blue shift object moving towads ed shift object moving away Constant high fequency, Inceasing amplitude Standing Wave: Two identical waves taveling in opposite diections in the same medium intefee Light slows down, bends towads the nomal, and has a shote wavelength when it entes a medium with a highe index. The fequency stays the same. Resonance: enegy is tansfeed to a system by making it vibate at its natual fequency esulting in lage amplitude standing waves Examples: guita stings, bidges, swings, wine glasses Fundamental Wave: lowest fequency (f 1 ), λ m Thid Hamonic: f 3 3f 1 λ 3 1/3 λ 1 Visible Light: 400 nm (violet) 700 nm (ed)

Total Intenal Reflection Citical Angle (θ C ): incident angle fo which the efacted angle

suface, none is efacted only occus when light tavels fom high to low index and incident

components due to efaction each colo has slightly diffeent index and speed sin C n n 1 1

Polaization Only tansvese waves can be polaized light yes, sound no.

polaized when it eflects off a suface 50% of unpolaized light tansmits though a single

7 Total Intenal Reflection Citical Angle (θ C ): incident angle fo which the efacted angle is 90 0 Fomula: sin θ C n 2 /n 1 Total Intenal Reflection: all light is eflected at suface, none is efacted only occus when light tavels fom high to low index and incident angle is geate than θ C Majo use: fibe optic cables Dispesion: speading out of light into components due to efaction each colo has slightly diffeent index and speed sin C n n p q f hi q m h o p L Blue Bends Best - slowest Red Resists Refaction - fastest Polaization Only tansvese waves can be polaized light yes, sound no. Polaized Light: vibates in only one diection Natual Polaization: light is patially polaized when it eflects off a suface 50% of unpolaized light tansmits though a single polaize. Focal length ½ adius of cuvatue Paallel polaizes: 50% passes though both Pependicula polaizes: 0% passes though second

T Phase Changes Photoelectic Effect Incoming photon (if high enough enegy fequency above theshold fequency) ejects electon some enegy needed to elease electon (wok function) emaining enegy is kinetic

8 T Phase Changes Photoelectic Effect Incoming photon (if high enough enegy fequency above theshold fequency) ejects electon some enegy needed to elease electon (wok function) emaining enegy is kinetic enegy E photon hf + KE o h p h mv max Inceasing fequency of light inceasi g KE of electons Inceasing intensity of light inceasing numbe of electons Photoelectic effect gaphs: Slope Planck s constant Y- intecept -wok function X-intecept theshold fequency Moden Physics Light (Enegy) Matte Wave-Paticle Duality Wave Natue - Diffaction - Intefeence - Dopple Effect - Electon Diffaction - Matte Waves Compton Scatteing (Photon Collisions) Afte collision, photon s enegy deceases, momentum deceases, fequency deceases, wavelength inceases photon + Matte Waves (de Boglie wavelength): not noticed since too small fo eveyday objects o max Paticle Natue Photo-electic Effect Collisions (e.g. Alpha paticle scatteing) Atomic Specta Gound state: lowest enegy level Excited state: highe enegy level Ionization: zeo enegy level E photon ΔE n Photon quantum (paticle) of light Highe fequency highe enegy (E hf) Highe intensity moe photons photon o + Mass defect: m + Δm m (nuclei weigh less than sum of thei pats) E mc 2 (only use if E is in Joules and m is in kg) 1 u 9.31 x 10 2 MeV Antimatte same mass, opposite chage Alpha paticle helium nucleus (2 potons and 2 neutons) Positon positive electon Poton uud Neuton udd m

Things You Should Know About Regents Physics

Things You Should Know About Regents Physics Measuement and Mathematics Estimation: 1 kg 2.2 lbs 1 apple 1 N 1 quate 5 g 0.005 kg Ode of magnitude: powe of ten (thickness of pape 10-4 m) Fundamental units Quantity Units Symbol Length mete m Mass