Physics Section 2. Write it Down and Draw it Out!

Transcription

1 Physics Sectin 2 A Reminder: As yu study, d nt neglect t answer the Fur Cnceptual Questins listed belw. In particular, we wuld like t emphasize the imprtance f the secnd questin, which prmpts yu t draw ut each cncept in the frm f a picture, graph, r diagram. The MCAT authrs regularly use charts, graphs, diagrams, flwcharts, schematic drawings, and ther figures as a part f passages, questin stems, and answer chices. Graph anything and everything yu can. When yu find a figure r drawing as part f yur studies, re-draw it in the margins f yur manual, label it, and make sure yu understand all f its parts and implicatins. The habit f writing dwn and drawing ut everything is a very wise habit that will help yu nw and in the future. It will help yu t master these cncepts nw by adding visual cues that have been shwn t imprve lng-term retentin. Later, during bth practice exams and yur actual MCAT, drawing ut and writing dwn everything yu pssibly can will make it easier fr yur brain t make cnnectins, recall infrmatin, and avid errrs. Fur Questins t Test Cnceptual Understanding: 1. Can I visualize it? Write it Dwn and Draw it Out! 2. Can I draw a picture, graph r diagram f it? 3. Can I explain it t smene else in layman s terms? 4. Can I think f and describe real-life examples? Equilibrium Static vs. Dynamic Equilibrium: Objects at rest are in static equilibrium; bjects mving at a cnstant velcity are in dynamic equilibrium. In bth cases the net frce experienced by the bject must be zer. Examples f Equilibrium: Terminal velcity Cnstant velcity Objects at rest Balanced fulcrums r bards hanging frm strings Objects flating in a liquid Slving Equilibrium Prblems: Slve all equilibrium prblems by setting the frces r trques equal t each ther: F Left = F Right ; F up = F dwn ; T clckwise = T cunterclckwise. We recmmend that yu list the ppsing frces in tw clumns n yur scratch paper. In the right clumn, write dwn all f the frces (r the equatins that predict thse frces) which push the bject t the right. In the left clumn, write dwn thse frces that push it t the left. One f these frces shuld be an unknwn. Next, add up each clumn and set the sum f the tw clumns equal t each ther. Finally, slve fr the unknwn variable. Always draw a freebdy diagram and duble check yur chart fr any missing frces. IMPORTANT NOTE Watch carefully fr clues. In additin t the clues we ve already mentined, such as cnstant speed, cnstant velcity, and terminal velcity (which all clue yu in t the fact that the bdy is in equilibrium), yu nw have tw new clues yu shuld be familiar with. If an bject with a pint f rtatin is statinary, r exactly balanced, then it must be in equilibrium. If an bject is in rtatinal equilibrium, the net trque n the bject must be zer. Q1. A 15 kg ty rcket is falling tward earth with a cnstant velcity f 20 m/s. A small amunt f fuel still present in the cne creates a dwnward frce f 30 N. What is the frce due t air resistance? 383 P a g e

2 Physics 2 Altius Trque & Lever Arms Frmulas: T = Fl r T = Frsinθ r (fr gravity) T = mgl (where l = lever arm and r = distance between the frce and the pint f rtatin; rsinθ always = l, but r = l nly when θ = 90) In mst cases, yu can simply use T = Fl Q2. In what specific situatins shuld yu use T = Frsinθ? Fulcrums and Bards n Strings: These are simple equilibrium prblems as described abve. T slve, set T clckwise = T cunterclckwise. Be sure t include all trques, including the trque created by the mass f the bard (Nte: sme questins define the bard as massless, r t be f negligible mass). Fr a bard with mass, the frce due t the mass f the bard will act at the center f mass, which will always be at the exact linear center f a unifrm bard. Als, dn t frget t set trques equal t each ther, NOT frces. Yur units shuld be N*m. Finally, frces r tensins lcated exactly at the center f rtatin d nt create a trque (since r = 0) and can therefre be ignred. Fr example, fr a mass centered ver the fulcrum, gravity wuld create n trque. Q3. If 20 kg hangs exactly 3.0 meters frm the fulcrum, what mass shuld hang n the ther end, 5.0 meters frm the fulcrum, t balance the bard? Systems NOT in Equilibrium Definitin: Any prblem where the bject in questin has a nn-zer acceleratin, r net frce, is a nnequilibrium prblem (a.k.a., translatinal acceleratin prblems ). Slve these prblems in the same way yu wuld an equilibrium prblem, but add ma t the lsing side. This is preferred ver the Sum f Frces methd because it allws yu t ignre signs. Q4. Why can yu slve these prblems by adding ma t the weaker side? What are yu actually ding, r accunting fr, when yu add ma t the weaker side? Equilibrium n an Inclined Plane: In this special case, it is best t use an altered crdinate system. Write dwn all f the frces acting n the bject in tw separate clumns, as described abve. Call all frces acting dwn the plane dwn frces, and all frces acting up the plane up frces. The frce dwn the plane due t gravity is always given by F = mgsin. The frce f frictin is always parallel t the plane, but ppsite the directin f the sliding mtin. There will never be an acceleratin perpendicular t the plane, s yu can ignre these frces. After yu have accunted fr all pssible frces, set the sum f the dwn frces equal t the sum f the up frces and slve fr the unkwn. Frce Vectrs in Tw-Dimmensins: The system we have utlined abve simplifies everything int up/dwn r left/right frces. Yu may well have a frce that acts in tw-dimensins, say at an angle f 30 t the hrizntal. In such a case, simply enter int yur table the frmula that predicts the cmpnent f that frce that acts up, dwn, left r right. Fr example, suppse a rpe is attached t a bx n its right side at an angle f 60 t the hrizntal and applies a frce f 100N. On yur scratch paper, under the frces t the right clumn, yu wuld input 100cs. This is the frmula that will give the rightward frce (in the x-directin) exerted n the bx by the rpe. Q5. A 120 kg rcket is accelerating tward the grund at 8 m/s 2. The engine creates a dwnward frce f 200 N. A small parachute is attached t the rcket and slws its descent. What is the frce due t air resistance against the parachute? (Assume all air resistance is due t the parachute.) Have yur tutr drill yu n several nn-equilibrium prblems until they becme very easy fr yu. 384 P a g e

3 Physics 2 Altius Energy Definitin: THINK OF ENERGY AS: Energy = the capacity t d wrk (Nte: This is a gd wrking definitin fr the MCAT, althugh sme bks and/r prfessrs might disagree.) Frms f Energy: Be familiar with each f the fllwing frms f energy. The MCAT is especially fnd f giving yu a situatin and asking what energy transfrmatin is taking place. Lk up the crrect frmulas fr each f the fllwing types f energy. Kinetic Energy: Q6. KE =? Gravitatinal Ptential Energy: Q7. PEgravitatinal =? Elastic Ptential Energy: Q8. PEelastic =? Electrical Ptential Energy: Q9. PEelectrical =? Ptential Energy Stred by a Capacitr: Q10. PEcapacitr =? Internal Energy: The energy f the internal vibratins and randm mtins f mlecules and/r atms within a system. Nn-cnservative frces such as frictin r drag acting n a mving bject result in the transfer f kinetic energy int internal energy. Heat Energy: Energy dissipated as heat. On the MCAT, this is usually heat dissipated frm a cllisin, r frm a current-carrying wire. The terms heat energy and internal energy are used almst interchangeably. Chemical Energy: The energy cntained within chemical bnds, r the energy stred/released due t the separatin and/r flw f electrns (i.e., in a battery). Mechanical Energy (ME): ME = KE + PE In the absence f nn-cnservative frces such as frictin, drag, air resistance, etc., mechanical energy is always cnserved (a.k.a. ttal energy). Q11. Name the type f energy pssessed r created by each f the fllwing: an explsin, a chemical reactin, a cllisin, any mving bject, any bject with height, a spring, a battery, tw psitive charges, and a water in a tank. Q12. Describe the energy transfrmatins that take place as a rcket ignites, cmbusts its rcket fuel, launches int the air, rises t its maximum height, then falls back t earth and strikes the grund. 385 P a g e

4 Physics 2 Altius The Law f Cnservatin f Energy: Energy in an islated system is always cnserved. If yu add up all f the pssible frms f energy in a system (internal energy, kinetic energy, all frms f ptential energy, heat, etc.), that ttal will always remain cnstant. Energy is frequently transferred back and frth between frms, but never lst. When students think this law has been vilated it is usually because they have chsen t narrw f a system. Q13. Prvide cnceptual definitins fr the fllwing terms: pen system, clsed system, and islated system. Wrk Frmulas: Think f wrk in EXACTLY this way and in this EXACT rder: 1) W = Energy Think f wrk this way first! Be n the lkut fr any change t the ttal energy f an bject r system if energy changed, THINK WORK! Mst students tend NOT t recgnize r think abut wrk when it appears n the MCAT. Here is a list f clues that wrk has ccurred and is likely t be a necessary part f answering the questin: When yu see the fllwing, THINK WORK! 1) Change in velcity (change in KE = wrk; this is the mst cmmn example) 2) Change in height (change in gravitatinal PE = wrk) 3) Change in psitin f masses/planets/etc. in space (change in gravitatinal PE = wrk) 4) Change in psitin f a charge (change in electrical PE = wrk) 5) Cmpressin f a spring (change in elastic PE = wrk) 6) Frictin (change in internal energy = wrk) 7) Air Resistance (change in internal energy = wrk) CAVEAT: Energy change in a system culd be due t heat transfer as well. Hwever, we have never seen the MCAT intrduce this kind f heat n physics wrk and/r energy prblems. They will expect yu t knw that nn-cnservative frces such as frictin dissipate sme energy as heat, leaving less energy available t d wrk (e.g., the velcity f a ball at the bttm f an inclined plane is less with frictin than withut. This is because the energy dissipated t heat was nt available t increase the KE f the ball). Hwever, this use f the wrd heat refers t an increase in the internal energy f mlecules, nt the heat transfer (Q) included in the 1 st Law f Thermdynamics ( E = W + Q). We ll cver these tpics in mre detail in the chemistry chapters. 2) W = Fdcsθ r Favgd Think f wrk this way secnd. Any time a frce is applied acrss a distance, wrk has been dne. Students tend t think f this nly as smething like pushing a blck acrss a table. Hwever, if a ball falls frm a height h, a frce (mg) has been applied, acrss a distance (h). Similarly, if a small asterid with a velcity v strikes Earth s atmsphere and is gradually slwed dwn, a frce has clearly been exerted n the asterid by the atmsphere, cnverting its kinetic energy t heat energy. The secnd equatin can be used in such scenaris t calculate the average frce exerted n the asterid, which is equal t the change in energy (wrk) divided by the distance ver which the frce was applied (F avg = W/d). UNITS = Jules; Q14. Use the frmulas abve t determine the units that make up a Jule. Q15. When is wrk psitive? When is wrk negative? (Hint: There are tw cnventins.) Q16. Describe the wrk dne when a frce, applied at an angle f 45 degrees t the hrizntal, is used t push a bx acrss the flr. Describe the wrk dne when a bx is mved at a cnstant velcity acrss a frictinless table. Describe the wrk dne by the string when a ball n a string is swung in a circular mtin. 386 P a g e

5 Physics 2 Altius The 1 st Law f Thermdynamics: We ll discuss this again in Chemistry, but will intrduce the cncept here. Put simply, energy change is nt always cmpletely due t wrk; sme energy is ften lst t heat. Wrk and heat are the nly tw ways energy can be transferred int r ut f a system. Often, this law is simply stated as the frmula belw: E = W + Q Wrk = energy transfer via a frce Heat = energy transfer via energy flw frm ht t cld The Wrk-Energy Therem: If a net frce des wrk n a rigid bject, the wrk dne n that bject is equal t the change in the kinetic energy f the bject. W = KE final - KE initial Fcus n E: Sme students have missed questins because they were cnfused in their applicatin f the wrk-energy therem. If yu crrectly apply the principles utlined abve under the equatin W = E, there is n need t use the wrk-energy therem. Q17. Hw much wrk is dne when a 1,000kg car traveling at 40 m/s applies its brakes and cmes t a cmplete stp? Q18. What is the wrk dne n a spring cmpressed by 0.5 meters? (k = 10N/m). Simple Machines Definitin: Simple machines (a.k.a., machines) reduce the amunt f frce necessary t perfrm a given amunt f wrk. Machines never reduce r change the amunt f wrk! Withut a Machine: It is ften helpful t determine the amunt f frce necessary t lift r mve an bject withut a machine. Yu can then cmpare that t the frce necessary with the machine. These tw values will differ by an exact rati. Ntice that each f the frmulas belw includes this rati (h/d, L 1 /L 2, etc.). Fr example, a rati f 1/5 gives a 5X machine that reduces the frce necessary by a factr f 5 (a.k.a., a mechanical advantage f 5 ). Or, yu culd say that it allws a persn capable f a maximum frce, F, t create a frce f 5F when using the machine. The frce necessary t lift a mass withut a machine (at cnstant velcity) is: Fnecessary = mg Ramps: Fm = mg(h/d) ; where h is the height f the ramp and d is the distance alng its hyptenuse. F m refers t the frce necessary t d the wrk with the machine; which will be less than ding it withut the machine. Remember that the wrk with r withut the machine will always be the same! Als nte that when the MCAT states a ramp is 5 meters lng r calls it a 5 meter ramp this means the hyptenuse f the ramp is 5m. Q19. A wrker must mve a 50 kg blck nt a table that is 2.0 m ff the flr. Hw much wrk will be required withut the use f a machine? If the wrker cnstructs a ramp that is 2.0 m high and 8.0 m lng, hw much frce will be required? Hw much wrk will be required with the use f the machine? Levers: Fm = mg(l1/l2) ; where L 1 and L 2 refer t the lever arms fr the mass and the applied frce, respectively. Pulleys: Fm = mg/(# f vertical rpes directly lifting the mass) 387 P a g e

6 Physics 2 Altius CAUTION: Nt every rpe that is vertically riented shuld be cunted and entered int the abve pulley equatin. T be cunted, a vertical sectin f rpe must lift the mass directly, either by being attached t the mass, r by lifting a pulley that is attached t the mass. T test this, imagine islating a single segment f rpe and pulling upward n that segment nly. Wuld that segment lift the mass? If nt, it shuld nt be included in the calculatin. Hydraulic Lifts: Fm = mg(h1/h2) r Fm = mg(a2/a1) ; where h 1 and h 2 refer t the distances traveled by the large plunger and the small plunger, respectively; and A 1 and A 2 refer t the crss-sectinal areas f the large plunger and the small plunger, respectively. Q20. Draw schematic plans fr a ramp, lever, pulley and hydraulic lift that each prvide a fivefld mechanical advantage. Shw these t yur tutr and check that they are viable. Pwer Frmulas: Think f pwer in EXACTLY this way and in this EXACT rder: 1) P = E/t 2) P = W/t 3) P = Fdcsθ/t 4) Pi = Fvcsθ CAUTION: Equatin (4) gives nly instantaneus pwer. It shuld nly be used when yu are asked t slve fr pwer using frce and velcity. UNITS = watts (J/s) Q21. Truck engine A has twice the pwer f truck engine B. True r False? a) Truck A can accelerate the same trailer frm zer t 50m/s in half the time, b) Truck A can accelerate a trailer t a velcity v, in a time t, that is twice as massive as the trailer Truck B can accelerate t the same velcity in the same time perid, c) Truck A can accelerate the same trailer t twice the velcity in the same amunt f time. (Nte: Assume the mass f the truck is negligible cmpared t the mass f the trailer.) Sample MCAT Questin 1) If it requires 2,000 Jules f wrk t mve a 20 kg bx nt a table 10 meters high, hw much wrk will be required when using a lever that imparts a five-fld mechanical advantage? A) 0 J B) 400 J C) 1,000 J D) 2,000 J Slutin: This questin tests yur cnceptual understanding f wrk and machines. Recall that the use f a machine never changes the wrk; it nly changes the frce necessary t accmplish that wrk. The wrk required is simply the difference in energy between the state f the bject befre and after. In this case, the bx has n PE befre and has PE = mgh afterwards. That is the wrk required and it is independent f any machine used, r the path taken. Answer D is therefre crrect. 388 P a g e

7 Physics 2 Altius Electricity Charge: (-) Charge = extra electrns ; (+) Charge = relatively fewer electrns A Big Miscnceptin: We have fund many students wh while wrking electricity prblems cnceptualize psitive charges as tiny little mbile masses with an inherent charge similar t an electrn, just ppsite in charge. What they are visualizing wuld essentially be a psitrn; which is indeed analgus t an electrn, but f ppsite charge. Prtns (althugh many, many times larger) als fit that cncept f a psitively-charge mass. Hwever, the charges yu see represented in diagrams with plus signs are NOT prtns, nr are they psitrns. When we are discussing electricity and circuits, psitive charge is always a lack f electrns! Similarly, negative charge is always a surplus f electrns. In a battery, fr instance, the psitive ple is deficient in electrns, and wuld need t gain mre electrns t becme neutral. The negative ple has excess electrns, and wuld need t lse electrns t becme neutral. Either the atms f the material itself lack electrns (i.e., they are catins, with fewer electrns than prtns), r yu are cmparing a place f high electrn density t a place f lw electrn density. There are NEVER actual psitrns r prtns mving arund. It may be helpful t remember that utside f radiactive decay r atmic bmbs, prtns stay in the nucleus! Illustratins t crrect this miscnceptin: Psitive charge in a battery: We say that ne terminal f a battery is psitive and the ther is negative. Is the psitive terminal psitive because it has a large number f psitrns? N. It is labeled psitive because it is deficient in electrns relative t the ther terminal. Psitively charged ins: Catins are psitively charged. Is this because they have excess psitrns? Is it because they have extra prtns? N n bth accunts. It is because they are deficient in electrns. They have fewer electrns than they d prtns. Psitive charge as part f a diple: We discussed diples and diple mment in a previus chemistry lessn. Is the psitive side f a plar bnd psitive because it has mre psitrns r mre prtns? N. It is psitive because the electrns are being pulled tward the side f the mre electrnegative atm. The negative side thus has extra electrn density and the psitive side is slightly deficient in electrns cmpared t nrmal. Mving psitive charges: Yu have prbably seen drawings f psitive charges lined up n the surface f an bject. This is ften seen when discussing inductin r static electricity. These are NOT islated prtns mving arund, and they certainly are NOT islated psitrns. They wuld have t be sme atm r mlecule that is deficient in electrns and therefre bears a psitive charge. Charge is quantized accrding t: e- = 1.6 x C Cnservatin f Charge: The universe always has zer net charge. Charge is created by separatin. If yu separate ne electrn frm a neutral atm yu have created ne independent unit f negative charge (the electrn), but yu have simultaneusly created ne independent unit f psitive charge (the catin). Cnductance: Q22. What is a cnductr? What is a resistr? D cnductrs resist? D resistrs cnduct? What is an insulatr? What is a semicnductr? What is a supercnductr? 389 P a g e

8 Physics 2 Altius Sample MCAT Questin 2) A very small parallel plate capacitr cnnected t a battery is charged until it bears a maximum charge f 8.0 x C. A change in the dielectric causes the charge n the plates t decrease slightly. Which f the fllwing culd be the new charge? A) 1.9 x C B) 4.8 x C C) 4.0 x C D) 7.9 x C Slutin: In the case f this nan capacitr, the charge n the capacitr is due t exactly five electrns. Recall that charge is quantized and that the charge n ne electrn is 1.6 x C. The charge can never decrease r increase by a number that is nt a multiple f 1.6 x Answer B is the nly answer that fits this criterin. It reflects the lss f tw electrns. Usually capacitrs in appliances perate with ver electrns and cannt be individually measured. Electric Fields Definitin f an Electric Field: THINK OF A FIELD AS: Field = An invisible influence that can exert a frce n a mass r charge. Field Lines: Always drawn with their tails at the psitive charge pinting away r pinting tward the negative charge. Clser lines represent a strnger field; Lines further apart represent a weaker field. Q23. D field lines best apprximate electrn flw r current flw? Equiptential Lines: These lines are drawn perpendicular t field lines and represent areas f equal vltage (i.e., electrical ptential). Q24. Draw field lines and equiptential lines fr a) a single pint charge, and b) tw pint charges near ne anther. Are equiptential lines always cncentric circles? Electric Diples: A diple is a separatin f psitive and negative charges f equal magnitude. When the MCAT discusses diples they will either be tw ppsite charges f equal magnitude very near ne anther in space, r any bject/mlecule with a charge separatin wherein ne side bears a full r partial psitive charge and anther side bears a full r partial negative charge (i.e., a plar bnd). When a diple is expsed t an electric field it will tend t align itself with that field. A diple that is NOT aligned with the electric field has ptential energy because alignment with the field is a lwer energy state than alignment against the field. 390 P a g e

9 Physics 2 Altius Tw Types f Electric Fields: Pint Charge Fields (equate t real gravity r gravity in space) Cnstant Electric Fields (equate t assumed gravity r gravity near earth) Q25. Prvide cnceptual definitins fr bth pint charge and cnstant electric fields. Cmparing Electric Field Equatins t Gravity: T learn all f the electric field equatins (and there are quite a few), review yur gravity equatins and nly memrize hw they relate t each ther: g (strength f gravitatinal field) = E (strength f electric field) G (cnstant) = K (cnstant) h (distance) = r r d (bth variables are used fr distance in electric field equatins) m (mass) = q (charge) F = F (used straight acrss) gh (gravitatinal ptential) = V (vltage, electrical ptential) Deriving Electric Field Equatins: T derive the crrect electric field equatin, simply apply the cnversins abve t the equatins yu already knw fr gravity. Be sure t differentiate between cnstant electric fields and pint-charge fields. Cnstant electric field equatins are derived by cmparisn t gravity near earth; pint-charge field equatins are derived by cmparisn t actual gravity (i.e., what gravity really des near earth, r gravity in space). Frce Fr gravity near earth: F = mg Fr cnstant E-field: F = qe Fr real gravity: F = Gmm/r 2 Strength f the Field Fr pint charge E-field: F = Kqq/r 2 (Culmb s Law) Fr gravity near earth: g = F/m (frm F = mg) Fr cnstant E-field: E = F/q (r E = V/d) Fr real gravity: g = Gm/r 2 Fr pint charge E-field: E = Kq/r 2 Electrical Ptential Energy Fr gravity near earth: PE = mgh Fr cnstant E-field: PE = qed Fr real gravity: PE = -Gmm/r Vltage Fr pint charge E-field: PE = Kqq/r (attractive if it invlves ppsite charges, and repulsive if it invlves like charges) Fr gravity near earth: V = gh Fr cnstant E-field: V = Ed (d measured against E) Fr real gravity: V = -Gm/r Fr pint charge E-field: V = Kq/r 391 P a g e

10 Physics 2 Altius Tw additinal ways t think f vltage: 1) Vltage = ptential energy/charge r mass (V = PE/q) 2) Vltage =an entity yu can multiply by mass r charge t get PE (gh*m = mgh = PE gravitatinal ; Ed*q = PEelectrical = V*q) Q26. Which f the tw scenaris represents the greater vltage (r vltage equivalent, gh)? [Nte: Assume gravity near Earth is a cnstant field] a) A 1 kg rck held 10 m abve the Earth s surface vs. the same 1 kg rck held 10 m abve the surface f Venus? (g n Venus = 8.8m/s 2 ); b) A 1 kg blck held 10 m abve Earth s surface vs. A 1 kg blck held 20 m abve Earth s surface; c) A 1 kg blck held 10m abve Earth s surface vs. a 20 kg blck held 10 m abve Earth s surface; d) An electrn 2 cm frm the psitive plate f a parallel plate capacitr vs. an electrn 4 cm frm the psitive plate; e) A charge f -2 C held 2 cm frm the psitive plate f a parallel plate capacitr vs. a charge f -4 C held 2 cm frm the psitive plate f the same capacitr. Sample MCAT Questin 3) A cmparisn can be made between the gravitatinal field near the earth and a cnstant electric field. It can be said that a rck near the earth has a gravitatinal ptential similar t the vltage (electrical ptential) that exists acrss a cnstant electric field. In this analgy, the vltage f the rck will: A) increase if the rck is raised t a greater height abve the grund B) decrease if the rck is raised t a greater height abve the grund C) remain cnstant if the rck is raised t a greater height abve the grund D) increase if the rck is lwered t a lesser height abve the grund Slutin: The strength f the electric field in a pint-charge field changes with distance. Hwever, in a cnstant electric field the field strength is cnstant. The frmula fr vltage in a cnstant field is V = Ed, where d is the distance change ging against the field. In terms f gravity, we culd translate this t V = gh where the height h ges against g. As the rck mves upward, g des nt change, but h des, increasing the vltage f the rck. Answer A is therefre crrect. Nte that answers B and D say essentially the same thing. If the prblem was a psitive charge instead f a mass, and there were a cnstant E field pinting dwnward, the vltage wuld increase as we raised the charge. 392 P a g e

11 Physics 2 Altius Magnetism THINK OF MAGNETISM AS: Magnetism = Analgus t electricity, with these changes: 1) Replace psitive charges with nrth ples 2) Replace negative charges with suth ples 3) Magnetic field lines prceed frm nrth t suth, instead f frm psitive t negative Magnetic fields are created by changing electric fields Changing electric fields create magnetic fields, and changing magnetic fields create electric fields. Magnetic fields are als created by currents (mving charges) Any mvement, velcity, rtatin, etc., f a charged particle causes a change in the electric field created by that charge, and thus creates a magnetic field. All f the fllwing invlve mving charges and thus create a magnetic field: Nuclei with an dd atmic r mass number (because they exhibit nuclear spin) Electrns (because they rbit and spin) Current (because it is mving electrns) Bar Magnets Bar magnets are usually made f nickel, irn, r an assciated ally. Nrmally, the electrns in a metal are apprximately split between spin states, and thus the tiny magnetic fields they create cancel each ther ut. In a bar magnet they are partially aligned, creating a net magnetic field. Frmula: The frce exerted n a charged particle mving in a magnetic field is given by: F = qvbsin ; where is the angle between v and B. UNITS f B = N*s/C*m r Kg/A*s 2 = tesla (T) Q27. Will the nrth ple f a magnet attract r repel psitively charged particles? Q28. What will be the effect f each f the fllwing n the frce experienced by a charged particle in a magnetic field? a) velcity slws t zer, b) the particle mves at an angle f 90 degrees with respect t the magnetic field vectr, c) the particle mves at an angle f 180 degrees with respect t the magnetic field vectr, and d) the particle mves in the same directin as the magnetic field vectr. RIGHT HAND RULE: Be sure yu can use this tl, the MCAT likes this ne! Q29. Becme familiar with the right hand rule and use it t determine the directin f the vectr fr: a) the magnetic field prduced by a current-carrying wire with electrns flwing frm right t left acrss this page, b) the frce n a charged particle mving at a velcity v straight ut f this page, thrugh a magnetic field riented frm left t right acrss this page. Circuits Current: Current flws ppsite t the directin f electrn flw. I = q/ t ; It is mre intuitive t think f current as the amunt f charge (i.e., electrns) that flws past a fixed pint per unit time. Current flws frm psitive (+) t negative (-) Electrns flw frm negative (-) t psitive (+) Q30. a) Draw a battery attached t a circuit. Which way des current flw? Which way d the electrns flw? b) Explain hw yu cnceptualize current. What is current made up f? 393 P a g e

12 Physics 2 Altius Resistance: Resistance can be cnceptualized as the equivalent f drag in fluids, r frictin between slids. The equatin belw describes resistance in circuits, but the same parameters are rughly applicable t heat flw and fluid flw as well. Frmula fr Resistance: R = ρl/a ; where ρ = resistivity, L = length, A = crss-sectinal area Temperature Dependence: Fr gd cnductrs (i.e., metals), it is generally true that resistivity increases linearly with temperature. Hwever, this is nly true f cnductrs, and nly if ne is starting arund rm temperature. The resistivity f semicnductrs actually decreases with temperature. Q31. In cnstructing a hme t maximize safety and energy efficiency, shuld ne use lnger wires between utlets r shrter wires? Shuld ne use larger r smaller diameter wiring? Q32. Explain n the mlecular level why increased temperature increases resistance. The wires between any tw elements in a circuit are assumed t be perfect cnductrs (i.e., resistance here = zer; all resistance ccurs at the resistrs) Vltage: THINK OF VOLTAGE AS: Vltage = the amunt f ptential energy a system is capable f string per unit charge (V = PE/q). T prve this t yurself, divide the frmula fr the ptential energy f a pint charge by the variable fr charge. What d yu end up with? Anther intuitive way t think f vltage: Vltage = the amunt f wrk necessary t mve a charge against an electric field. Mving the charge a lnger distance against the field wuld require mre wrk per unit charge, s that means mre vltage. This aligns with the general bservatin that vltage increases with distance. If the electric field were strnger, mving a charge the same distance against the field wuld require mre wrk per unit charge, s that wuld als mean mre vltage. Bth f these cncepts are demnstrated in the tw equatins we ve presented thus far fr vltage: V = Ed and V = Kq/r Ohm s Law: V = IR A cmmn prblem with manipulating equatins using Ohm s Law: It CANNOT be said that if vltage increases, and current remains cnstant, resistance will increase. That is nt true. Resistance is a permanent quality f the resistr itself. Saying that increasing vltage will increase resistance if current remains cnstant, is rather like saying that increasing frce while acceleratin is held cnstant will increase mass. Lk again at the frmula fr resistance given earlier in this lessn. Ntice that neither vltage nr current are in this equatin. The nly way t change the resistance is t either 1) physically remve ne r mre resistrs frm the circuit and replace them with ther resistrs that have different Ohms ratings, r 2) change the temperature f the resistr. If yu were very careful, yu culd say it this way: If vltage increases, in rder fr current t remain cnstant, I wuld need t increase the resistance in the circuit. Which is smething I culd d by adding mre resistrs. What will happen autmatically if yu increase vltage (withut altering circuit cmpnents r temperature)? Current will simply increase. 394 P a g e

13 Physics 2 Altius Capacitrs: Capacitrs stre energy and charge by hlding electrns n plates separated by a very small distance. Symbl: Tw vertical lines f equal length Frmulas: Capacitance: C = Q/V PE stred by a capacitr: U = ½QV; U = ½CV 2 ; U = Q 2 /(2C) Only memrize ne f the abve equatins. Then slve C = Q/V fr the missing variable and plug it int the ne yu ve memrized. This will allw yu t get bth f the ther tw. We recmmend yu memrize U = ½CV 2 because it is s similar t the frmula fr KE. Q33. Demnstrate that yu can derive all three f the abve equatins frm U = ½CV 2. The Dielectric: The dielectric is the substance between the tw plates. All capacitrs have a dielectric, even if it is just air. Other dielectrics are ften inserted between the plates, such as gels r cmpsites. Once inserted, sme energy stred in the capacitr is used t align the plar mlecules in the dielectric (i.e., diples) with the field between the plates. Increasing the strength f the dielectric increases the capacitance allwing mre charge and energy t be stred. Increasing dielectric strength, increases capacitance. Q34. The dielectric must always be an insulatr/cnductr (chse ne). Variables that Affect Capacitance: Q35. Hw des increasing r decreasing each f the fllwing affect capacitance: plate area, plate thickness, distance between plates, strength f the dielectric and vltage. Charge vs. Time Graphs: Q36. Draw a charge vs. time graph fr the charging and discharging f a capacitr. Use the cnceptual skills yu ve been wrking n t predict its shape. Think n a mlecular level abut the species invlved and hw their interactins will change as the capacitr fills r discharges. Batteries: Symbl: tw vertical lines f unequal length. The lnger line represents the psitive terminal and the shrter line represents the negative terminal. This cnventin is very imprtant. Often it will be the nly clue as t which directin current/electrns are flwing in a circuit. THINK OF BATTERIES AS: Electrn pumps that push electrns nt the negative terminal f the battery. This creates a separatin f charge and therefre a ptential difference between terminals that will drive electrn flw arund the circuit t the psitive terminal. Anything that separates charge creates a vltage and can therefre be thught f as a type f battery (and treated accrdingly). A few frmer MCAT questins have invlved very nntraditinal batteries nt easily recgnized as such. The key t recgnizing them as batteries is t bserve that they are causing a separatin f charge. Resistrs: SYMBOL: zig-zag line There is always a vltage drp acrss any resistr when current flws thrugh it. Internal Resistance: Batteries experience internal resistance due t the resistivity f their internal cmpnents. This results in a vltage drp per the rule stated abve and therefre decreases (slightly) the actual terminal vltage f the battery. Current flw thrugh parallel resistrs is always apprtined inversely based upn resistance. Fr example, if ne resistr has twice the resistance, it will receive nly half the current. 395 P a g e

14 Physics 2 Altius Switches: SYMBOL: a diagnal break in the line between circuit cmpnents Clsed = electrns flw; Open = n electrn flw Slving Circuits Using Ohm s Law: FIRST: Yu must have a simplified circuit. Simplified means n mre than ne f each cmpnent is present (ne resistr, ne battery, ne capacitr). T arrive at a simplified circuit, cmbine the circuit cmpnents accrding t the fllwing rules: Resistrs in series: add the resistance f each resistr directly Rttal = R1 + R2 + R3 Resistrs in parallel: add the inverses f the resistance fr each resistr, then take the inverse f that sum 1/Rttal = 1/R1 + 1/R2 + 1/R3 Capacitrs in series: add the inverses f the capacitance fr each capacitr, then take the inverse f that sum 1/Cttal = 1/C1 + 1/C2 + 1/C3 Capacitrs in parallel: add the capacitance f each capacitr directly Cttal = C1 + C2 + C3 Batteries in series: add the vltage f each battery directly; hwever, current (Amps) and capacity [amp-hurs, (Ah)] will remain the same Vttal = V1 + V2 + V3 Batteries in parallel: add the current (Amps) r capacity (Ah) ratings fr each battery directly, but vltage will remain the same. Fr example, if yu wire tw 12 V batteries with a 50 Ah capacity tgether in SERIES, yu will get the equivalent f ne 24V battery with a 50 Ah capacity. If yu wire the same tw 12 V batteries tgether in PARALLEL, yu will get the equivalent f ne 12 V batter with twice the capacity: 100 Ah. SECOND: If the abve steps d nt yield a simple circuit, try Kirchff s rules. Kirchff s 1 st Rule: ttal current int a nde = ttal current ut f a nde Kirchff s 2 nd Rule: in any clsed lp circuit, the sum f the vltages equals zer (i.e., the sum f the vltage drps acrss each resistr equals the ttal vltage f the battery) Kirchff s rules will ften prvide yu with the missing piece f infrmatin. Then yu may need t return t the rules abve t finish simplifying yur circuit. THIRD: Yu can use Ohm s Law acrss a single resistr. Ding s may be necessary t get a piece f infrmatin needed t simplify the circuit. Be sure yu are using nly infrmatin fr that resistr and NOT fr the main battery, current thrugh the circuit as a whle, etc. Ohm s Law acrss a resistr states that: Vltage drp acrss that resistr = current thrugh that resistr multiplied by the resistance f that resistr. FOURTH: When yu have a simplified circuit yu can use Ohm s Law (V = IR) t slve fr any f the three variables. 396 P a g e

15 Physics 2 Altius Electrical Pwer Frmulas: P = IV; P = I 2 R; P = V 2 /R Much like capacitance, nly memrize P = IV; Slve V = IR fr the missing variable and plug it in t get the ther tw. Q37. Demnstrate hw t derive the secnd and third equatin starting with P=IV. Husehld Electrical Pwer: Alternating Current (AC) vs. Direct Current (DC) Q38. What are the primary differences between AC current and DC current? Which type is utilized by husehld electric wiring, autmbile electrnics, and yur cell phne, respectively? Which ne can be represented by a sine wave? Q39. Explain the terms rt mean square current and rt-mean-square vltage as they apply t husehld AC current. Sample MCAT Questin 4) An electrmagnet uses electrn flw t generate a magnetic field. Such a magnet is placed near a pile f metal shavings. The shavings accelerate tward the magnet until they cllide with and attach t its surface. The magnitude f the acceleratin f the shavings tward the magnet will be decreased by: A) impeding electrn flw within the magnet. B) lwering the temperature f the magnet. C) decreasing the distance between the magnet and the shavings. D) decreasing the mass f individual metal shavings. Slutin: Currents (mving charges) always create magnetic fields. The greater the current, the greater the magnitude f the magnetic field created. Thus, impeding the flw f electrns (Answer A), which wuld reduce the current, wuld indeed decrease the magnetic frce created by the magnet. This reduced frce wuld decrease the acceleratin f the shavings tward the magnet. Answer A is therefre crrect. Lwering the temperature f the magnet wuld increase current (and therefre the magnetic field strength), because fr cnductrs, such as these electrmagnet wires, temperature and resistance are directly related. This makes Answer B false. Decreasing the distance between the magnet and the shavings wuld increase the strength f the frce, and therefre the acceleratin, making Answer C false. If the mass f each shaving were decreased, the acceleratin wuld increase accrding t a = F/m, making D false. 397 P a g e

16 Physics 2 Altius Waves Wave Characteristics: Q40. Prvide cnceptual definitins fr each f the fllwing variables used t describe waves: wavelength, perid, velcity, amplitude, frequency, intensity, and phase. Q41. Which f the abve variables must be shared by tw waves in rder fr thse waves t have the same phase? Intensity: Intensity is defined as pwer per unit area. Waves have pwer (ften called sund pwer ) because they transfer energy frm ne lcatin t anther within a specified time (a.k.a., energy flux). The intensity f any sund r mechanical wave is directly prprtinal t the amplitude squared and the frequency squared: I A 2 f 2. Fr light waves, the intensity is als prprtinal t the amplitude squared, but nt t the frequency squared. Units: W/m 2 Many waves, such as sund, travel utward frm their rigin in all directins simultaneusly creating a wave frnt in the shape f a grwing sphere. Because intensity is measured per square meter, its magnitude decreases accrding t the area f the grwing sphere (i.e., the m 2 term increases, decreasing the intensity): A = 4r 2. Attenuatin: The gradual lss f intensity as a wave passes thrugh a medium. In nndispersive mediums this is due t scattering (i.e., reflectin) f sme waves and absrptin f wave energy. Q42. If persn A is psitined three times as far frm the surce f a sund as persn B, what will be the rati f the intensity f the sund experienced by persn A t that experienced by persn B? The Decibel System: The decibel system is a rating system fr the intensity f sund within the range f human hearing. It is similar t the Richter scale used t rate earthquakes in that bth systems use lg scales. The difference is that 10-fld increases in earthquake intensity are represented by 1.0 unit increases n the Richter scale, but 10-fld increases in sund intensity are represented by 10.0 unit increases n the decibel scale. Fr example, a sund 10 times mre intense is rated as 10 decibels higher, a sund 100 times mre intense is rated as 20 decibels higher, and a sund 1,000 times mre intense is rated as 30 decibels higher. Intensity in Decibels = 10*lg(I/I0); where I is the intensity f the sund wave in W/m 2 and I 0 is the threshld f human hearing (I 0 = 1 x W/m 2 ; which is usually given). Q43. At a sccer match, the sund level suddenly rises frm 20 decibels t 60 decibels. Hw much luder (mre intense) is the sund at the end f this increase? Types f Waves: Transverse vs. Lngitudinal: Transverse waves cause disturbances perpendicular t their directin f travel (e.g., electrmagnetic waves, a wave n a string); Lngitudinal waves cause disturbances parallel t their directin f travel (e.g., sund waves, p-wave earthquakes) Electrmagnetic Waves: N medium required; capable f prpagating in a vacuum; transfer energy and mmentum thrugh space (e.g., visible light, micrwaves, radi waves, etc.) Transverse nly Mechanical Waves: Require a medium t prpagate; cannt prpagate in a vacuum; transfer energy in the directin f prpagatin, but d nt transfer matter. Whether r nt mechanical waves transfer mmentum is smething physicists like t debate, s the MCAT wn t test that questin directly. (e.g., sund waves, a wave n a string, cean waves, etc.) Transverse (e.g., strings n a musical instrument); Transverse mechanical waves require a fairly stiff medium t prpagate and therefre cannt prpagate in liquids r gases. Lngitudinal (e.g., sund waves) 398 P a g e

17 Physics 2 Altius Wave Speed: Frmula V = λf The 3 Cardinal Wave Rules: 1) Wave speed (velcity) is determined by the medium 2) Frequency never changes when a wave mves frm medium t medium 3) Wavelength des change when a wave mves frm medium t medium Q44. Wave A has twice the amplitude, ne-half the wavelength, and three times the frequency f wave B. Which wave will travel with the greater velcity thrugh an identical dispersive medium? Wave Velcity in Varius Mediums: Wave speed is typically equal t the square rt f an elastic prperty f the medium divided by an inertial prperty: v = sqrt(elastic/inertial). The elastic prperty is ften called a mdulus. The inertial prperty is a type f density. Velcity f a wave n a string: The elastic prperty that prvides the restring frce in a string is its tensin. The inertial prperty is mass per unit length, the linear mass density : v = sqrt(t/). Increased tensin always increases velcity. A thicker string (increased mass per length) always decreases velcity, prvided the tensin stays the same. Velcity f sund waves in a gas: The elastic prperty is called the bulk mdulus, B. The inertial prperty is the density f the gas, : v = sqrt(b/). The bulk mdulus turns ut t be directly prprtinal t bth density and temperature, hwever, s fr gases, the velcity ends up having this temperature dependence: v ~ sqrt(t). Velcity f sund waves in a slid: Althugh the densities f slids are typically thusands f times higher than the densities f gases, the elastic mduli are increased by an even larger factr. This prperty causes slids t spring back extremely quickly fllwing defrmatin. Sund (cmpressin) waves in slids are therefre much faster than sund waves in gases. Superpsitin f Waves: Cnstructive Interference: Regins where the amplitudes f superimpsed waves add t each ther, increasing amplitude. Destructive Interference: Regins where the amplitudes f superimpsed waves subtract frm each ther, decreasing amplitude. Q45. Using pictures r diagrams, demnstrate bth cnstructive and destructive interference. Q46. What will be the result f adding tw therwise identical waves that are: a) 180 degrees ut f phase, b) 360 degrees ut f phase, c) 270 degrees ut f phase? Standing Waves: This is a special case f simultaneus cnstructive and destructive interference between tw waves with identical frequencies, mving thrugh the same medium, but in ppsite directins. At pints f maximum destructive interference, the waves cancel entirely, frming a nde. At pints f maximum cnstructive interference, the waves add cmpletely t frm an antinde. The result is a wavefrm in which the areas between the ndes appear t scillate up and dwn frm a crest t a trugh. A standing wave exhibits n net transprt f energy and des nt itself prpagate. In ther wrds, there is n translatinal mvement f ndes r antindes. 399 P a g e

18 Physics 2 Altius The Beat Frequency: Occurs when tw waves with clse t the same frequency interfere. fbeat = f1 f2 Q47. Demnstrate a beat and the beat frequency by drawing a lng series f evenly-spaced vertical lines representing a lngitudinal sund wave. Return t the first line in yur series. Beginning directly n tp f that first line, draw a secnd series f evenly-spaced vertical lines, this time decreasing the space between lines by apprximately 1/3. What happens peridically? The Dppler Effect: Frmulas: (Simplified versins) f/fs = v/c /s = v/c The Dppler shift perceived by the bserver is dependent upn the relative velcity between the surce and the bserver. The greater the relative velcity the greater the shift in frequency r wavelength. The equatins abve may nt lk quite like what yu learned in physics class. They nly hld true when the relative velcity, v, is much smaller than the speed f the wave, c. Hwever, these equatins shw all the crrect relatinships that are ften tested n the MCAT such as the fact that a greater relative velcity will result in a greater Dppler shift, and light (being a much faster wave than sund) will prduce a much smaller fractinal change in frequency fr the same relative velcity. Q48. What will be the change in frequency due t The Dppler effect when the surce and bserver are traveling the same speed? Q49. What is the relative velcity in each f the fllwing cases? a) bserver has zer velcity, surce is traveling tward the bserver at 5m/s, b) bserver and surce are traveling in ppsite directins, bth at 5m/s, c) bserver is traveling east at 5m/s, surce is traveling east at 2m/s, d) bserver and surce are traveling tward ne anther, ne at 5m/s and the ther at 2m/s. Q50. Car A is traveling at 20m/s tward car B, and car B is traveling tward car A at 15m/s. Car B hnks its hrn, and car A perceives the frequency f that sund as f. After they pass ne anther, car B slws dwn t 5m/s and hnks its hrn again. What must the mtin f car A be at that exact mment, in rder fr the perceived frequency f the secnd hrn t equal f? Clr Shifts: IMPORTANT NOTE Remember three key pints with respect t the Dppler frmula: a) the variable v is relative velcity, nt the velcity f either bject, b) the variable c is the speed f the wave, either 3 x 10 8 m/s fr light r 340 m/s fr sund, and c) the answer is the change in the frequency r wavelength (ften NOT what is asked fr). This value must be added r subtracted frm the initial value t get the actual value due t the Dppler effect. Add t the frequency (subtract frm the wavelength) if the relative mtin is twards each ther; d the ppsite if the relative mtin is away frm each ther. White light will shift blue if the Dppler effect causes a perceived increase in frequency (perceived decrease in wavelength). White light will shift red if the Dppler effect causes a perceived decrease in frequency (perceived increase in wavelength). 400 P a g e

19 Physics 2 Altius Sund General Characteristics: Sund Prductin: Sund is always created by a vibrating medium. These vibratins prpagate thrugh liquids r slids, and generate pressure waves that prpagate thrugh gases such as air. As a mechanical wave, sund CANNOT prpagate in a vacuum. Pitch: Pitch is clsely related t frequency, but nt identical. Pitch is a musical term nt a scientific term. It is ften defined as the perceptin f frequency by the human ear. The MCAT will NOT require yu t differentiate these tw terms; just fcus n the fact that higher pitch sunds have higher frequencies, and lwer pitch sunds have lwer frequencies. Q51. Differentiate between infrasund and ultrasund. Sund Resnance: All bjects have ne r mre natural frequencies at which they will vibrate when disturbed. Sme bjects prduce a randm array f different vibratinal frequencies. Other bjects (e.g., musical instruments) vibrate at nn-randm natural frequencies which are integer multiples f a number (e.g., 200Hz, 400Hz, 600Hz, 800Hz). These rderly frequencies are called harmnics. When ne bject is vibrating near anther bject it can cause the neighbring bject t begin vibrating at that same frequency. If the exact frequency at which the secnd bject is caused t vibrate happens t be ne f its natural frequencies (e.g., harmnics), the tw bjects are said t be in resnance. Via cnstructive interference, tw such instruments can prduce a much luder sund. If the first bject causes a vibratin in the secnd bject that is NOT a match t ne f its natural frequencies, resnance des nt ccur. Sample MCAT Questin 5) Sund-prfing materials are used t islate audivisual prductin rms and prevent the passage f sund int r ut f the designated rm. Rms that are NOT cnstructed t such standards ften allw the passage f sund thrugh a wall because sund waves: A) can pass thrugh micrscpic pres in natural building materials. B) can pass thrugh slid bjects withut lsing amplitude r velcity. C) pass thrugh slid bjects, lsing sme amplitude, but maintaining cnstant velcity D) pass thrugh slid bjects, exiting the slid with the same velcity as they had prir t entering the slid. Slutin: Sund waves can indeed pass thrugh slids. In fact, they require a slid, liquid, r gas t act as the medium. Sund cannt travel in a vacuum. Answer A is false because sund waves pass thrugh slids by vibrating thrugh the slid itself, nt by wrming their way thrugh tiny pres. Answer B is false because sund waves always lse sme amplitude when passing thrugh a slid, due t reflectin at the surface. Answer C is false because sund waves will increase speed when traveling thrugh a slid cmpared t a gas (because f the higher bulk mdulus f the slid). Answer D is crrect. Recall that the medium determines the velcity. Assuming the air n either side f the bject is equivalent, the speed f the wave will als be the same n bth sides. 401 P a g e

20 Physics 2 Altius Harmnics: L = n/2 (string r pipe with matching ends bth ndes, r bth antindes) Gives all harmnics n = 1, 2, 3... This equatin may be mre useful rearranged t give: = 2L/n L = n/4 (ne nde and ne antinde; e.g., pipe pen at ne end nly) Gives nly the dd harmnics; n = 1, 3, 5... This equatin may be mre useful rearranged t give: = 4L/n Q52. Explain why a pipe pen at bth ends gives all harmnics, but a pipe pen at ne end and clsed at the ther, gives nly the dd harmnics. Use a diagram t illustrate yur pint. Imprtant Characteristics: The frequency f the first harmnic is called the fundamental frequency. Each additinal harmnic has its wn unique frequency and wavelength. The frequency f any harmnic is equal t n*fundamental frequency (e.g., if the first harmnic is exactly 200 Hz, the 2 nd is 400 Hz, the 3 rd is 600 Hz, etc.) Each harmnic has ne mre nde, and ne mre antinde, than the previus harmnic. Overtnes: The terms 1 st vertne, 2 nd vertne, 3 rd vertne, etc., are used ccasinally. The 1 st vertne is NOT the same as the 1 st harmnic! The first harmnic is called the fundamental frequency, the secnd harmnic is the 1 st vertne, the third harmnic is the 2 nd vertne, and s frth. Fr scillatrs with matching ends, the wavelength f the secnd harmnic equals the length f the string r pipe ( = L). Drawing Harmnics: The harmnics shwn belw are all fr a single vibrating guitar string f the same length. Ntice that the 1 st harmnic is nly ne-half f a wavelength, the secnd harmnic is exactly ne wavelength, and the third harmnic is ne and ne-half wavelengths. Q53. Draw three diagrams, similar t thse shwn belw, fr the first three harmnics f a) a pipe pen at ne end (antinde) and clsed at the ther end (nde); and als fr b) a pipe pen at bth ends. 402 P a g e

21 Physics 2 Altius Sample MCAT Questin 6) A student blws int a pipe pen at bth ends and creates a fundamental frequency. He then increases his pitch gradually until he reaches the 2 nd and 3 rd harmnics. While the 3 rd harmnic is resnating, the student puts his hand ver ne end f the pipe. T attain the 3 rd harmnic fr the new system, the student must: A) increase the frequency f the sund. B) decrease the frequency f the sund. C) maintain a cnstant frequency. D) decrease the wavelength f the sund. Slutin: A pipe pen at bth ends will always resnate at a shrter wavelength (fr the same harmnic) than a pipe f the same length pen at ne end and clsed at the ther. Cnsider the fundamental frequency t prve this pint: Fr the 1 st Harmnic, the wavelength f an pen-clsed pipe system is 4 times the length f the pipe. In ther wrds, nly ¼ f a wavelength fits within the pipe. Hwever, ½ f a wavelength will fit within the same exact pipe if it is pen at ne end and clsed at the ther. In ther wrds, the wavelength is nly 2 times the length f the pipe. Fr the same length f pipe, the wavelength f the pen-clsed arrangement is greater. In this case, the student cnverts the same pipe frm an pen-pen arrangement t an pen-clsed arrangement. The third harmnic fr the new pen-clsed system will have a lnger wavelength and a smaller frequency. Therefre, t reach the 3 rd harmnic fr the new system, the student will need t decrease the frequency; making Answer A the best chice. Light Dual Nature: Q54. Prvide a cnceptual definitin fr the particle and wave mdels f light. Q55. What is the phtelectric effect and hw des it relate t the particle mdel f light? Energy f a Phtn: E = hf ; h = Planck s cnstant, which is always given. Q56. Many questins require yu t cmbine the frmula fr the energy f a phtn with the wave speed frmula. Can yu d this? What des it allw yu t d? Yung s Duble Slit Experiment: Set-Up: Yung shne a mnchrmatic light thrugh a screen with a single slit in it. The purpse f this slit was t create cherent wavefrnts (since lasers weren t arund in Yung s day). Behind the first screen he placed a secnd screen with tw narrw, parallel slits. These created the diffractin pattern. Finally, behind the secnd screen he placed a third screen. Light traveled thrugh the first tw screens and frmed alternating pattern f light and dark bands n the third screen. Fr this experiment t wrk, the light traveling thrugh each f the tw slits in the middle screen must be cherent and have the same frequency and plarizatin. 403 P a g e