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Practice Final Exam PHY 2140 – Sp/Su 2007 1. How many 100 W lightbulbs can you use in a 120 V circuit without tripping a 15 A circuit breaker. 2. Find the charge on the 4 F capacitor in the following circuit. 8 F 8 F 4 F 4V 3. A hydrogen atom initially in its ground state (n = 1) absorbs a photon and ends up in the state for which n =3. What is the wavelength of the absorbed photon? 4. What is the current through the 8.00 resistor? 2 2 8 2 4 12 V 5. A cube with an edge of length l = 0.04 m is placed in a uniform magnetic field throughout the region that has components Bx = 0, By = 4 T and Bz = 3 T. Find the flux through the top face of the cube. z x y 6. 7. The half-life of an isotope of phosphorus is 14 days. If a sample contains 3.541016 such nuclei, what is its activity? A cylindrical piece of insulating material is placed in an external electric field, as shown. The net electric flux passing through the surface of the cylinder is 8. Light with a wavelength of 4.210-7 m is used to determine the position of an electron to within one wavelength. What will be the resulting uncertainty in the electron’s velocity? 9. Determine X in the following reaction: 21 10 24 Ne ZA X 12 Mg 01n (use the table below if necessary). 10. An astronaut at rest on Earth has a heartbeat rate of 60 beats/min. When the astronaut is traveling in a spaceship at 0.80 c, what will this rate be as measured by an observer at rest on Earth? 11. Determine the amount of energy released in the fusion reaction: 1 H 1 H 2 He 1 2 3 12. A simple circuit consists of a resistor R, an inductor L, a battery and a switch that is initially open but then thrown closed. Immediately after the switch is thrown closed, the current in the circuit is R 13. An electron moves in a circular path perpendicular to a constant magnetic field. If the angular momentum of the electron about the center of the circle is 4.0010-25 J·s and the radius of its path is 10 cm, determine the magnitude of the magnetic field. ( Hint: the angular momentum of the electron is L = mvr) Please show your work in solving this problem. 14. What is the speed of a particle if its kinetic energy equals 80% of its rest energy? Please show your work in solving this problem. 15. An inductor and a resistor are connected in series. When connected to a 60 Hz, 100 V source, the voltage drop across the resistor is found to be 30 V and the power delivered to the circuit is 9 W. What is the value of the resistor? Please show your work in solving this problem. KE 1 2 p2 mv 2 2m F ma P IV P I 2R F qvB sin mv r qB I max I rms 2 Vrms V 2 R F BI sin I B 0 2r 2 F sin 0 NI NBIA sin XC VL , rms I rms X L 2 t 2f 1 2 LI 2 E v B E B E2 cB 2 P max max max max 2 0 2 0 c 2 0 tan V IZ EB v E L L X L 2fL XL XC R Pav I rms Vrms cos N I RC Q C V E c B c f t t P L LP E mc 2 p mv KE mc 2 mc 2 En nhf KEmax hf maxT 0.2898 102 m K PE h h p mv 0 a0 h (1 cos ) me c 2 mke2 2 me k e Z 2 e 4 1 2 2 2 n ln( 2) 0.693 xp E h 4 hc Ei E f E hf En r r0 A1 / 3 T1 / 2 E mc 2 2f c f B A BA cos 1 2 f C E NAB sin t I t V IR 1 1 1 Req R1 R2 B VC ,rms I rms X C v2 r Req R1 R2 VR ,rms I rms R Vmax Z R2 X L X C E N a h 4 Compton wavelength: h 0.00243 nm me c E t 1 1 RH 2 2 n ni f N R N t 1 mvr n Emax NAB L 0 N 2 A L R f 1 2 LC 1 1 v2 c2 E 2 p 2c2 m2c 4 v AB v AC vCB v v 1 AC 2 CB c min hc eV 2d sin m ( m 1, 2,3, ) En Z2 (13.6 eV) n2 N N 0 e t r n 2 a0 / Z v A x f xi a t f ti Ax Ay 2 W ( F cos ) s KE E EA cos Ax 1 2 mv 2 Ax A cos E 2 VB VA Ed F V ke q r 1 1 1 Ceq C1 C 2 A d Fx = m ax Fy = m ay Wnet = KEf - KEi KEf +PEf = KEi + PEi W PE PE k e P I 2R A I 0 1 T T0 V 2 R g = 9.8 m/s2 1 eV = 1.6 x 10-19 J 1 kWh = 3.60 x 106 J c = 3.00 x 108 m/s h = 6.63 x 10-34 J s 1 u = 931.5 MeV/c2 RH =1.097 m-1 I nqv d A r2 q1 q 2 r Q t R R0 1 T T0 ke PE qVB VA Q CV energy P IV 1 circle, cylinder: 4 0 A r 2 ,V r 2 l electron charge = 1.60 x 10-19 C For an electron: mec2=511 keV mp = 1.67 x 10-27 Kg a0 = 0.0529 9 m r0 = 1.2 15 m 1 1 1 0 H Mass (u) 1.007825 n 1.008665 2 1 3 1 3 2 H 2.014102 H 3.016049 He 3.016029 4 2 238 92 He U 1 2 C V 2 V IR Tm/A ke = 8.99 x 109 Nm2/C2 = 8.85 x 10-12 C2/Nm2 1 hour = 3600 sec me= 9.11 x 1031 kg 1.05 10 34 J s 1 u = 1.66 27 kg Power Prefix Symbol 10-12 picop 10-9 nanon -6 10 micro -3 10 millim 10-2 centic 3 10 kilok 106 megaM 109 gigaG q C eq C1 C 2 1 Q2 energy QV 2 2C R 1 2 at 2 x v0 t E ke q0 Ay A sin v v0 at F qE q1 q 2 C 0 Ay v v x 0 t 2 2 r t f ti tan 2 v 2 v0 2ax F ke v f vi 4.002602 238.050784