Physics 107: Ideas of Modern Physics

Transcription

1 Physics 107: Ideas of Modern Physics Exam March 8, 006 Name ID # Section # On the Scantron sheet, 1) Fill in your name ) Fill in your student ID # (not your social security #) 3) Fill in your section # (under ABC of special codes) Useful constants: c= speed of light = 3x10 8 m/s sound speed in air = 340 m/s g= accel. of gravity on Earth = 10 m/s G= gravitational constant = 6.7x10-11 N-m /kg

2 1. A. A 1360 Hz tone is generated by a speaker. What is the wavelength of the sound wave? A m B..0 m C. 0.5 m D. 1.0 m E. 3.0 m Velocity = frequency x wavelength, so wavelength = velocity/frequency = 340 m/s / 1360 Hz = 0.5 m 3. A sound wave is: a. a transverse wave. b. an electromagnetic wave. c. a longitudinal wave. d. a radio wave. e. a frequency wave. 4. In your room you have two speakers in different corners. You learned about interference in Physics 107, and positioned the speakers so that at your desk you are exactly meters from each. Your roommate moved one of your speakers: you now hear a cancellation of sound at 680 Hz. How far did your roommate move your speaker toward your desk? A. 0.5 m B. 0.5 m C. 0.1 m D. 1.0 m E. 0.1 m Destructive interference occurs if your distance from the speakers is different by ½ a wavength. The wavelength is 340 m/s / 680 Hz = 0.5 meters. ½ a wavelength is 0.5 m. So moving the speaker 0.5 m closer leads to destructive interference.

3 5. Your Badger radio network broadcasts on AM This frequency is 1,310 khz (1 khz = 1000 Hz). How many football fields long is one wavelength (1 football field ~ 91 meters)? 3 a. 0.1 b. 0.5 c. 0.4 d. 1.1 e..5 Wavelength = 3x10 8 m/s / 1.31 x 10 6 Hz = 30 meters. 30 meters / 91 meters/field =.5 football fields 6. An observed source of magnetic fields is: a. magnetic monopoles b. magnetic currents c. electric charges d. voltage currents e. electric currents 7. The force between two charged particles 0.4 m apart is found to be repulsive, with magnitude x10-10 N. What is the force after the charge on each particle is doubled, with the particles still 0.4 m apart? a. 4.0x10-10 N, attractive. b. 4.0x10-10 N, repulsive c. 8.0x10-10 N, repulsive d. 0.5x10-10 N, attractive. e. 1.0x10-10 N, repulsive If each charge is doubled, then the produce increases by four. Since the force is the product of the charges, the force increases by a factor of four. 8. Suppose an eye has only two cones with spectral sensitivities shown here. Which combinations of lights will give the same color perception? A B C D E a. A&E same as C b. B&D same as C c. A&C same as D d. B&E same as D e. B&C same as D 300 nm 400 nm 500 nm 600 nm 3

4 4 9. Your microwave beams Giga-Hertz (x10 9 Hz) microwave radiation at the food inside of it. It does this because water preferentially absorbs radiation at that frequency. The oven can enhance this effect by heating the food in a resonant cavity, designed so that an integer number of wavelengths fit inside its length. What should the length of the oven be if two wavelengths fit inside? A. 0.5 m B. 6.7 m C. 1.3 m D m E m Wavelength = 3x10 8 /x10 9 Hz = 1.5x10-1 = 0.15 m. Two of these wavelengths would be 0.30 meters. 10. An electron moves continuously up and down in one corner of room. An experimenter in the opposite corner of the room measures at his location a. an electromagnetic wave. b. an unchanging electric field. c. an unchanging magnetic field. d. a charge. e. a current. 11. Apollo 15 astronauts placed a laser reflector on the moon. A laser beam from Earth reflects for this. The round trip time (to and from the moon) for the laser beam is found to be.5 seconds. How far away was the moon at this time? a. 850 m b. 7.5 x 10 8 m c x 10 8 m d x 10 6 m e. 45 m Distance = velocity x time =3x10 8 m/s x.5 sec = 7.5 x 10 8 m. The moon is half this distance = 3.75 x 10 8 m 1. Einstein s special theory of relativity is based on which one of the following postulates? a. The speed of light is constant. b. Space and time are absolutes. c. Photons have zero mass. d. Energy is always conserved. e. Space-time is curved. 4

5 13.An Earth observer sees two spaceships approaching each other. One moves at 0.c, the other at 0.3c relative to the Earth observer. The 0.c one flashes it s headlights. The other spaceship measures the light pulse from those headlights passing at 5 A. 1.5c B. 1.c C. 1.0c D. 0.6c E. 0c Light moves at c in all reference frames, and for all observers. 14. A car is 6 meters long when it is at rest. It drives by at 0.6c relative to an observer on the street corner. The street corner observer measures the car to have a length of: a. 4.8 m b. 7.5 m c. 0.6 m d. 5.7 m e..1 m The proper length is measured in the ship frame, where ship is at rest. All other lengths are shorter by a factor 1 " = 1# ( v /c) = 1 1# ( 0.6c /c) = 1 1# 0.36 = = =1.5 The street corner observer measures 6 m / 1.5 = 4.8 m 15. An astronaut travels by the Earth at 0.6c. Someone stationary on Earth holds a meter stick. The astronaut measures the length of this meter stick to be. A. Less than one meter. B. More than one meter. C. Exactly one meter. D. Need to know Earth velocity. E. Depends on Earth reference frame. The proper length is measured by the Earthling. Any other measured lengths is shorter. 5

6 6 16.A 5 year-old astronaut travels to a nearby star and back at a speed of 0.8c, leaving behind her twin on Earth. The Earth twin measures the star to be 8 Light-Years away. When the astronaut returns, how does her biological age compare to the Earth twin? A. 0 years older B years younger C. 10 years younger D. 8 years younger E. 8 years older The proper time is in the astronaut s frame, where the events (aging process) are stationary. Any other measured time interval is longer by a factor gamma. 1 " = 1# v /c 1# 0.8c /c 1# 0.64 = = ( ) = 1 ( ) = 1 The twin time is then shorter than the Earth time by a factor of 0.6. The Earth time isx(8 LY/0.8c) = 0 yrs. The astronaut is 8 yrs younger. 17. An astronaut in a spaceship moves relative to an Earth observer. The Earth observer measures the time interval between heart beats of the astronaut. As the speed of the astronaut gets closer and closer to the speed of light (assume the astronaut does not get excited), the earth observer sees that the time between the astronaut s heart beats A. increases without bound B. decreases, getting arbitrarily close to zero. C. increases, but never exceeds c, the speed of light. D. decreases, approaching c/10. E. increases for positive speeds, decreases for negative speeds. 18. The equivalence principle of general relativity says that A. space and time are equivalent, and should be plotted together. B. energy and mass are equivalent, and can be transformed to each other. C. time dilation is equivalent to length contraction. D. gravity is equivalent to an accelerating reference frame without gravity. E. all space-time metrics are equivalent. 6

7 19. As the speed of a massive particle approaches the speed of light, the relativistic mass of the particle a. approaches the rest mass. b. does not change. c. increases without bound. d. increases slightly. e. decreases to zero The first atomic bomb exploded with an energy of 15 kilotons (15,000 tons of TNT). (1 kiloton = x 10 1 Joules). If this were accomplished by converting mass directly into energy, how much mass would have been required (1000 gram = 1 kilo-gram)? a kg b. 310,000 kg c. 700 gm d. 0.7 gm e gm 15 kilotons = 15 x 4.184x10 1 J = 6.76 x 10 1 J. So mass x (speed of light) =6.76 x 10 1 J Mass = 6.76 x 10 1 J / (3x10 8 m/s) =7x10-4 kg = 0.7 gm 1. General relativity would say a dropped ball accelerates toward the Earth because A. the speed of light is same in all reference frames. B. of the gravitational force from Earth. C. only the relative velocity of the earth and ball matters. D. the ball follows the shortest path in spacetime. E. relativistic momentum is different than Newtonian momentum. 7