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Physics 2020 Spring 2009 Stephan LeBohec DATA SHEET - FINAL SEAT # Constants & mathematics: N A =6.02×1023 Boltzmann's constant k =1.38×10−23 J⋅K −1 k= R=8.31 J⋅mol−1⋅K −1 1 =9.0×10 9 N⋅m2⋅C−2 4 0 −7 −1 0=4 ×10 T⋅m⋅A e=1.602×10−19 C Q Proton=e & Q Electron=−e c= 1 =299,792,458 m⋅s−1≈3×10 8 m⋅s−1 0 0 1 2 Kinetic energy E K = m⋅v 2 cos 2 f t ≈−2 f sin 2 f t t sin 2 f t ≈2 f cos 2 f t t Thermodynamics: T K =T C 273 P⋅V =N⋅k⋅T =n⋅R⋅T n= N m = & R=N A⋅k NA M e Actual = 3 Ideal monoatomic gas: U = n⋅R⋅ T 2 Isobaric: W =P V f −V i Isochoric: W =0 Isothermal W =n⋅R⋅T ln First law of thermodynamics: U =Q−W Vf Vi W Cycle Q =1− C QH QH 3 Adiabatic: W =− n⋅RT f −T i & 2 P⋅V =Constant 5 with = for monoatomic gases 3 e Carnot =1− TC TH Waves: =c⋅T = c 1 as f = f T In a gas c Sound = Isotropic sound intensity: I = c String = 5 P with = for a monoatomic ideal gas 3 P 2 4 ⋅r Comparing intensities =10 log10 Doppler effect: f o= f s Standing wave frequency (string or open pipe) c f n=n with n=1,2,3,⋯ 2L Electric force, field and potential: Force on a point charge in an electric field: =q E F Force between two point charges: q q ∣=k 1 2 2 ∣F r Electric potential from a point charge: V r =k Capacitance: C= q r q V R= I1 in dB I2 c±v o c∓v s Standing wave frequency in pipe open at one end c f n=n with n=1,3,5,⋯ 4L Electric field generated by a point charge: ∣=k q ∣E r2 Work by operator moving a charge in an electric potential: W =q⋅V f −V i Electric circuits: Power in an electric circuit: P=V⋅I Resistivity: m F with = L L A Power from harmonic voltage and current: I V P=I RMS⋅V RMS with I RMS = 0 and V RMS= 0 2 2 Equivalent resistance for resistors in parallel: 1 1 −1 R Parallel = R1 R2 Equivalent capacitance for capacitors in series: 1 1 −1 C Series = C1 C 2 Electric field in a parallel plate capacitor: ∣= V = ∣E d 0 Energy stored in a capacitor: 1 1 1 q2 U = q⋅ V = C⋅ V 2= 2 2 2C Ohm's law: V =R⋅I Temperature dependence of resistivity: =0 1T −T 0 Equivalent resistance for resistors in series: R Series= R1R 2 Kirchhoff's junction rule: ∑ I IN =∑ I OUT and loop rule: ∑ V UP =∑ V DOWN Equivalent capacitance for capacitors in parallel C Parallel =C 1C 2 Magnetic force and field: ∣=∣q∣⋅∣v∣⋅∣ Magnetic force on a charge: ∣F B∣sin Magnetic field produced by an infinitely long wire: r ∣= 0 I ∣B 2 r Electromagnetic induction: Magnetic flux: = A⋅∣ B∣cos Self inductance: L= Transformers: Magnetic field inside a solenoid: N ∣ B∣=0 I =0 n I L Faraday's law: V =−N Induction in a moving wire V =L⋅∣v∣⋅∣ B∣ Mutual inductance: M = ∣=I⋅L∣ Magnetic force on a current: ∣F B∣sin t Induction in a rotating set of coils V =2 f N⋅A⋅∣ B∣sin 2 f t S IP Mutual induction: V =−M I Self induction: V =−L VS NS IP = = V P NP IS I t I t Work, force & displacement relation ∣⋅ x⋅cos W =∣F Electromagnetic waves: =c⋅T =c / f Doppler effect: f o= f s 1±v o /c ≈ f s 1±v rel /c 1∓v s /c Reflection of light: Law of reflection: R = I Mirrors equation: Spherical mirror: f = 1 1 1 = f dI dO Magnification: M = Snell's refraction law n1 sin 1 =n2 sin 2 Triangle geometry: a Malus law: I T =I I cos 2 µ E b c 2=a 2b2 cos =b/c sin =a /c tan =a/b hI d =− I hO dO Brewster angle: tan B=n 2 /n1 (ABD) and (ECD), similar triangles AB DB AD = = EC DC ED c R 2 A D C B Physics 2020 Spring 2009 Stephan LeBohec 1 FINAL Name:_____________________________________ TA (circle one): Adam Isaac Michael Student ID #:___________________________ Sarah A) [36 points, 3 points per question] For each statement, circle all the options you find appropriate. You do not need to show your work. 1) When the temperature of an ideal gas doubles, the root mean square velocity of the molecules is multiplied by 1/2 2) 1 1/ 2 2 2 Two different gases are in thermal equilibrium. Their molar masses are in a ratio square velocities of the two species of molecules are in a ratio v1RMS /v 2RMS = 1/2 1 1/ 2 4 m1 /m2 = 2. The root mean 2 2 4 3) When two different gases are mixed in a container they are always both at the same pressure. TRUE FALSE 4) When the distance from a spherical wave source is multiplied by 10, the intensity is multiplied by 0.01 5) 0.1 0.1 1 10 100 When the distance from a spherical wave source is multiplied by 10, the intensity level is changed by 0dB 1dB 2dB 10 dB 10dB 20dB 100dB 6) An acoustic wave is perceived by an observer at a higher frequency than the emitted frequency. With time, the observer and the source are getting FURTHER APART CLOSER TOGETHER 7) Two waves are interfering. A given point is reached by wave crests from one wave at the same time as by wave troughs from the other wave. The interference at that point is then said to be: DESTRUCTIVE CONSTRUCTIVE 8) A standing wave arises when two waves with different frequencies are propagating in opposite directions. TRUE FALSE 9) The electric force acting on an electron points in the opposite direction of the electric field. TRUE FALSE 10) In order to bring two electric charges of opposite signs closer together, an operator needs to provide a positive amount of work. TRUE FALSE 11) The electric field points in the direction of increasing electric potential. TRUE FALSE 12) Two 12V batteries connected in series can be made equivalent to a 24V battery. TRUE FALSE Physics 2020 Spring 2009 Stephan LeBohec 2 FINAL Name:_____________________________________ TA (circle one): Michael Sarah Student ID #:___________________________ Adam Isaac B) Four moles of a monatomic ideal gas go though a temperature change from T i =600K to T f =400K while 2972J of heat flow out of the system. 1) [5 points] What is the change in internal energy? 3 3 U = n R T = ×4×8.31×400−600=−9972 J 2 2 2) [6 points] How much work is done by the gas? W =Q− U =−2972 J −−9972 J =7000 J 3) [5 points] Assuming the process is isobaric at W =P⋅ V so V = P=105 Pa , what is the change in volume? W 7000 J = 5 =0.07 m 3 P 10 Pa P=3.96×10 26 W . The Earth is at a distance C) The total power radiated by the Sun, is from the Sun. 1) [4 points] What is the intensity of the solar radiation at this distance? I= 2) P 3.96×10 26 W = =1400 W.m−2 2 9 2 4 R 4 ×150×10 m [6 points] A solar panel of area A=0.5m 2 is used during 1 hour to charge up a 12V battery with no initial charge. What is the total amount of electric charge available in the battery? (We assume an ideal solar panel with a 100% efficiency at converting all of the solar radiation to electric energy) W = AI t=Q V so Q= 3) R=150×10 9 m AI t 0.5 m2×1400 W.m−2×3600 s = =2.1×10 5 C V 12V [6 points] After it has been charged, how long can the battery be used to power a Q⋅ V 2.1×105 C×12 V Q P=V⋅I =V⋅ = =9×10 4 s=25 hours so t= −1 t P 28 J.s 28W light bulb? Physics 2020 Spring 2009 Stephan LeBohec FINAL Name:_____________________________________ TA (circle one): Michael D) Sarah Adam 3 Student ID #:___________________________ Isaac A loud speaker at A and a loudspeaker at B ( AB=3.2m ) are in phase and producing harmonic waves of frequency f =214Hz . The speed of sound is c=343 m⋅s −1 . 1) [5 points] How are the two waves interfering at location C? ( BC =2.4m )? c 343 m.s−1 = = =1.6 m f 214 Hz ∣AC −BC∣= 3.222.42−2.4=1.6m= so the interference is constructive at point C. 2) [13 points] What is the closest location D can be from A so that there is destructive interference at location D? Start with D = A, there ∣BD− AD∣=3.2 m−0 m=2 and the interference is constructive. The closest point D where there is destructive interference is such that ∣BD− AD∣=1.5=2.4 m so we write AB2 AD 2− AD=2.4m or AB2 AD 2=2.4 m AD 2 =2.4m2 AD 24.8 m× AD and finally AD= E) AB2−2.4 m 2 3.2m2−2.4 m 2 = =0.9333 m 4.8 m 4.8 m A particle with vi =4m⋅s −1 1) m=0.04kg and electric charge q=3×10−6 C is released with an initial velocity at a distance d i=3m from a charge Q=20×10−6 C which can not move. [7 points] What is the closest possible distance charge q can get from the fixed charge Q ? qQ qQ 1 =k m v 2I and d F =k qQ . Numerically, dF dI 2 E 6 6 3×10 ×20×10 1 3×106×20×106 E=9×10 9 ×0.04×42=0.5 J and d F =9×10 9× =1.08 m 3 2 0.5 E=U F =U I K I so 2) E=k [7 points] What is the speed of the particle once it is a very great distance from the fixed charge Q ? E=K F =U I K I so 1 2 E= m⋅v F and 2 vF= 2E 2×0.5 = =5 m.s−1 m 0.04 Physics 2020 Spring 2009 Stephan LeBohec 4 FINAL Name:_____________________________________ TA (circle one): Michael Sarah Adam Student ID #:___________________________ Isaac F) [36 points, 3 points per question] For each statement, circle all the options you find appropriate. You do not need to show your work. 1) Two 12V batteries connected in parallel can be made equivalent to a 24V battery. TRUE FALSE 2) A resistor is connected to a generator. Increasing the resistance value by a factor four results in multiplying the power delivered by the generator by: 1/ 4 1/2 1 2 4 3) A freely moving charged particle in a region with a uniform magnetic field always has uniform circular motion. TRUE FALSE 4) A straight wire transporting an electric current is under the effect of a magnetic force. The magnetic field must be perpendicular to the wire. TRUE FALSE 5) A circuit with a resistor is placed in a uniform magnetic field that varies harmonically with time. Doubling the frequency of the magnetic field variation results in multiplying the power dissipated in the resistor by: 1 2 6) 1 2 1 2 2 4 A transformer steps the voltage down from 110V to 11V. The current in the secondary is like the current in the primary multiplied by 0.01 0.1 1 10 100 7) coil A circular coil is exposed to an electromagnetic wave polarized horizontally. Electromagnetic induction in the is maximal when the coil is HORIZONTAL VERTICAL,WITH NORMAL VERTICAL , WITH NORMAL TOWARD THE SOURCE 90o FROM THE SOURCE 8) The exact value of the speed of light c=299,792,458m / s was set to define the meter. TRUE FALSE 9) A polarizing filter is rotating at a rate of 10 rotations every second. A constant intensity of non polarized light is sent through the rotating filter. The transmitted intensity varies with a frequency of: 0Hz 10) 10Hz 20Hz A polarizing filter is rotating at a rate of 15 rotations every second. A constant intensity of vertically polarized light is sent through the rotating filter. The transmitted intensity varies with a frequency of: 0Hz 15Hz 30Hz 11) In water, nothing can go faster than light. TRUE FALSE 12) One can start a fire by placing a piece of paper at the location of the image of the Sun formed by a diverging lens. TRUE FALSE Physics 2020 Spring 2009 Stephan LeBohec 5 FINAL Name:_____________________________________ TA (circle one): Michael Sarah Student ID #:___________________________ Adam Isaac G In the circuit in the figure, V =3V , R1 =30 , R 2=60 , R 3=40 and R 4=20 . With an ammeter, it is verified that the current flowing through R 4 is I 4=0 Amps . 1) [8 points] What is the value of RX ? Since there is not current through R 4 , the two points it is connected to are at the V⋅R2 V⋅R 3 = or R1 R2 R X R 3 R 1 R 3 30 ×40 RX= = =20 R2 60 same electrical potential and so 2) [8 points] What is the power dissipated in P 2=R 2 I 22=R 2 H R X= R 3 R 1R 2 −R 3 R2 R2 ? 2 2 V 3V =60 × =0.0666 W R1R 2 30 60 [16 points] A compass is placed inside a solenoid with 100 coils per ° meter. The solenoid is positioned with its axis at 90 from the direction of the terrestrial magnetic north pole. When the solenoid is powered with a V =9V battery through a R=50 resistor in ° series, the needle of the compass is observed to point =30 from the direction of the terrestrial magnetic north pole. What is the magnitude of the terrestrial magnetic field? BSolenoid BEarth B Solenoid B Solenoid 0 n I 0 n V so B Earth= = = . B Earth tan tan R tan 4 ×10−7×100×9 Numerically, B Earth= =39.2×10−6 T 50 tan 30° tan = (A top view of the problem) Physics 2020 Spring 2009 Stephan LeBohec FINAL Name:_____________________________________ TA (circle one): Michael Sarah Adam 6 Student ID #:___________________________ Isaac [16 points] A circular coil A=1.0m 2 with N =4000 loops is r =10.0m from a f =60Hz power line transporting a current I t= I 0 sin 2 f t with I 0=400A . What is the amplitude V 0 of the induced electromotive force in the coil? (As an approximation, you can consider the magnetic field to be uniform over the entire area of the coil as if the entire coil was 10.0 m from the power line) I 0 I t NA 0 I t and the flux is =NAB= so the absolute value of the induced 4r 4 r NA0 I NA 0 NA 0 f I 0 = =V 0 cos 2 f t with V 0= 2 f I 0= electromotive force is ∣V∣= . t 4 r t 4 r 2r 4000×1×4 ×10−7×60×400 Numerically we obtain V 0= =12.06 V 10 The magnetic field is B t= 0.5mm in diameter. J The dot at the end of this sentence is 1) [5 points] When you hold the page 30cm from your eyes, what is the angle under which you see the dot? ≈tan−1 0.5mm /300mm=0.0955° or 1.666×10−3 rad 2) [6 points] You use a f =30mm converging lens to better examine the dot. You place the lens 20cm from you eye and just 30mm from the paper. What is the angle under which you see the dot through the lens? Lens ≈tan−1 0.5mm /30mm=0.955° or 16.66×10−3 rad 3) [5 points] Does your answer to question 2) depend on the distance from your eye to the lens? In a short sentence, explain why it does or does not. The paper is in the focal plane of the lens so the virtual image of the dot is at an infinite distance. Changing the distance from the eye to the lens does not change the distance from the eye to the virtual image. For the reason the answer to question 2) does not depend on the distance from the eye to the lens.