72 Probset 2nd Long

Instructions: Choose the best answer

University of the PhilippinesCollege of Science

Physics 73

2nd Long Problem Set A1st Semester 2012-2013

INSTRUCTIONS: Choose the best answer and shade the corresponding circle in your answer sheet. To change your answer, cross-out and sign your original answer and then shade your new answer.

USEFUL CONSTANT: Stefan-Boltzmann constant: = 5.67 x 10-8 W/m2 K4

Hour 18

1. Which of the following quantities have the same natural units? Make an exhaustive list from the choices shown below.i. Forceii. Momentumiii. Energyiv. Mass v. Work

A. i, ii, and iii onlyB. i and ii onlyC. iii and v onlyD. ii, iii and iv onlyE. ii, iii, iv and v only

2. Which of the following is a direct consequence of Einsteins postulates for relativity?A. Invariance of distanceB. Anisotropy of the speed of lightC. Invariance of time coordinatesD. Speed of light as a constantE. Fundamental constants depend on the choice of reference frame.

3. The distance from Earth to Sun is approximately 8.0 minutes. What is this distance in meters?

A - 15

A. 2.4 x 109 mB. 4.0 x 107 mC. 1.44 x 1011 mD. 1.50 x 106 mE. 2.49 x 104 m

4. The potential difference between two plates is 1000 V. What is this voltage in natural units? (Assume that time is to be measured in meters, charge in Coulombs, and mass in kg. It may be helpful to recall that charge multiplied by voltage should have units of work or energy.)

A. 3.0 x 1011 kg/CB. 3.33 x 10-6 kg/CC. 1.11 x 10-14 kg/ CD. 9.00 x 1019 kg/CE. 1000 kg/C

Hour 19

5. Which of the following statements is true?A. The time interval between two events is the same for a moving and a stationary reference frame.B. Distance is invariant in Euclidean and Lorentz space.C. Time and space coordinates are used to describe events.D. Interval between events may be different between two different inertial reference frames.E. An event will have the same position coordinates in all inertial frames.

6. Given two sets of data for the time interval and space separation between two events, what is a possible combination of values (t, x) for the laboratory and rocket reference frames?A. Lab: (9.1 m, 8.2 m), Rocket: (4.5 m, 2.1m)B. Lab: (8.2 m, 9.1 m), Rocket: (4.5 m, 2.1 m)C. Lab: (2.1 m, 4.5 m), Rocket: (9.1 m, 8.2 m)D. Lab: (9.1 m, 4.5 m), Rocket: (4.5 m, 2.1 m)E. Lab: (4.5 m, 8.2 m), Rocket: (9.1 m, 2.1 m)

7. Consider two events C and D. Two observers, Alice and Bob, will have the following table of coordinates for the two events. Note that the entries below follow the convention (t,x).

AliceBob

Event C(0.00 m, 1.00 m)( 10.00 m, xC)

Event D(5.00 m, 7.00 m)( 50.00 m, xD)

What is |xD xC|?

A. 6.00 mB. 40.1 mC. 1611 mD. 1539 mE. 39.2 m

8. Consider the records of two inertial observers John and Marsha.

JohnMarsha

Event C(10.0 m, 0.000 m)( 50.0 m, 49.0 m)

Event O(0.000 m, 0.000 m)( 0.000 m, 0.000 m)

As discussed in our textbook, the records of John and Marsha may be obtained using a latticework of synchronized recording clocks and metersticks. To construct these records, John needs to use ______ recording clocks; while Marsha needs to use ______ recording clocks.

A. 1; 1B. 1; 2C. 2; 2D. 2; 1E. 1; 0

Hour 20

For the next two items, refer to the figure below.

9. What is the total proper time for a rocket traveling at constant velocity from point A to point D? Let the interval between grid lines be equal to 1.00 m.

A. 7.00 mB. 8.00 mC. 6.93 mD. 7.94 mE. 5.74 m

10. Which of the following is a possible relationship between events A, B, C and D?A. A massive particle from event A can affect event C.B. A massive particle can travel from event C to affect event D.C. Light from event B can affect event D.D. The only way event C can be affected by A is through particles that travel at the speed of light.E. Event A can affect what is going to happen in B.

11. Consider the following worldliness, labeled A to E, as shown in the figure below. Which of these worldliness represent a particle that starts from (2.0 m, 1.0m) and then travels to the left with the speed of light?

12. Based on planet Xs records, at t = 0.0 yr, an astronaut leaves planet X and travels to the left (towards the center of the galaxy) at velocity v = 0.25. At t = 3.0 yr, the astronaut decides to turn back towards planet X with velocity 0.1 to meet with a supply ship from planet X, and they meet at t = 5.0 yr. With replenished supplies, the astronaut again travels towards the center of the galaxy at velocity v = 0.3 until it reaches a colony planet Y at t = 20.0 yr. According to the astronauts clocks, how long did the total journey take?

A. 20.8 yrB. 19.2 yrC. 27.0 yrD. 20.0 yrE. 28.0 yr

Hour 21

13. The coordinates of an event according to the rocket frame is (4.1 m, 1.4 m).If the rocket frame moving is to the right with speed R = 0.200 relative to the lab frame What are the coordinates of the same event as seen in the lab frame?

A. (2.2 m, 4.3 m)B. (4.3 m, 2.2 m)C. (3.9 m, 0.59 m)D. (2.3 m, 4.5 m)E. (4.5 m, 2.3 m)

14. According to the lab observer, a flash of light was seen and it was recorded to have spacetime coordinates (t, x) = (10.1 m, 1.25 m). What coordinates will a man in a rocket moving with a speed of 0.891 to the right relative to the lab observer record upon seeing the same flash of light?


15. Consider the following records made by two observers:

LabRocket

Event L(t, x)(7.00 m, 2.00 m)

The rocket frame is moving to the right with speed 0.6. If the rocket and lab frame latticeworks of recording clocks and metersticks have the same orientation, and have the same spacetime origin, what labels will the rocket frame use for event L?

A. (7.25 m, 2.75 m)B. (10.25 m, 7.75 m)C. (7.25 m, 2.75 m)D. (8.75m, 1.6 m)E. (4.64 m, 1.76 m)

16. Consider the following records made by two observers:

LabRocket

Event L(5.00 m, 1.00 m)(t, x)

The rocket frame is moving to the left with speed 0.5. If the rocket and lab frame latticeworks of recording clocks and metersticks have the same orientation, and have the same spacetime origin, what labels will the rocket frame use for event L?


Hour 22

17. You and your friend are playing hide and seek. Your friend counts for 10.0 seconds while you hide. You decide to count along with your friend so that you know how much time you have left. However, you are running very fast so that your counting is slower and your friend has already started looking for you at the instant your clock reads 9.50 seconds. How fast did you run?

A. 0.312cB. 0.0975cC. 0.224cD. 0.0500cE. 0.0250c

18. The mast of a pirate ship, the large pole to which the sail is attached, stands (vertical) 6.33 m high. The pirate ship sails at a speed of 0.212. A man on island (stationary) will see that the mast would have a height equal to

A. 6.63 mB. 6.05 mC. 6.19 mD. 6.47 mE. 6.33 m

19. Consider two events A and B. From the records of two inertial observers Alice and Bob, we obtain the following table of values:

AliceBob

Event A(10.0 m, -3.00 m)(tA, xA)

Event B(10.0 m, 3.00 m)(tB, xB)

Bob uses a rocket frame moving to the left with speed 0.6 as measured by Alices frame. Which of the following is true?

A. Both events occur at the same place according to Alices records; Bob observes event A to occur before event B.B. Both events occur at the same time according to Alices records; Bob observes event A to occur after event B.C. Both events occur at the same time according to Alices records; Bob observes event A to occur before event B.D. Both events occur at the same time according to Alices records; Bob observes event A to occur at the same time as event B.E. Both events occur at the same place according to Alices records; Bob observes event A to occur after event B.

20. A cylindrical rocket has radius 5.00 m and length 20.0 m in its rest frame. This rocket was observed in the home frame to be moving along the direction of its length, at constant velocity 0.700 .What is the radius r and length l of this rocket according to the home frame?

A. r = 3.57 m; l = 14.3 mB. r = 7.00 m; l = 28.0 mC. r = 5.00 m; l = 14.3 mD. r = 5.00 m; l = 28.0 mE. r = 3.57 m; l = 20.0 m

Hour 23

For the next two questions, consider the two-observer spacetime diagram shown below, where the unprimed coordinate system is the laboratory reference frame and the primed coordinate system is the rocket reference frame.

21. Which of the following statements is false?A. Events C and D occur in different places according to the both reference frames.B. Events A, B and D occur in different places and times according to both reference frames. C. Events A and C occur at the same time according to the rocket frameD. Events C and D occur at the same time according to the rocket frame.E. Events B and C occur at the same place according to the lab frame.

22. What is the speed of the rocket frame relative to the lab frame?

A. 1/3B. 3C. 1/3D. 3E. 1

For the next two questions:A rocket frame is moving to the left with respect to the lab frame with velocity v = 1/3. The two-observer spacetime diagram containing events 1 to 5 is in shown in the figure below. The diagram is drawn from the perspective of the lab frame. The worldlines are labeled from A to E.

23. The set of all events occurring at the spatial origin of the rocket frame trace out a worldline. What worldline is it?

24. On this spacetime diagram, what worldline represents all events that occur at the same time, t = 0.0 m according to the rocket frame?

Hour 24

25. What is the velocity of a bullet relative to a rocket moving at a rate of 0.89c relative to the Earth if the bullet moves with a speed of 0.56c relative to the Earth?

A. 0.22B. 0.66C. 0.97D. 0.66E. 0.22

26. The velocity of the runner was measured in two reference frames, the lab and the rocket frame. In the lab frame, the velocity is 0.341, while it is 0.553 in the rocket frame. What is velocity of the rocket frame relative to the lab frame?

A. 0.261 to the left of the lab frameB. 0.261 to the right of the lab frameC. 0.752 to the right of the lab frameD. 0.752 to the right of the lab frameE. 0.212 to the right of the lab frame

27. In the rocket frame, the velocity of an object is 0.63 along the positive x-direction. The rocket frame moves with speed 0.20 along the negative x direction according to the lab frame. According to the lab frame records, the velocity of the object must be:

A. 0.492B. 0.737C. 0.492D. 0.737E. 0.830

28. In the rocket frame, the velocity of a proton is 0.700. According to the lab frame, the velocity of the same proton is 0.350. What is the velocity of the rocket frame according to the lab frame?

A. 0.464B. 0.464C. 0.843D. 0.843E. 0.350

For the next two questions, consider that the costume of The Flash emits in its rest frame a wavelength of 620 nm (red).

29. The Flash thought of a way of making himself invisible by running very fast away from a super villain. What would be the minimum speed The Flash needs to run in order to appear invisible, or for his costume to emit outside the visible spectrum (701 nm) as seen by the villain.

A. 0.122B. 0.122C. 1D. 0.0613E. 0.0613

30. The Flash wants to deceive his enemy by trying to look like Superman while he is running at relativistic speeds. Assuming Supermans costume (without the cape) emits a blue wavelength of around 455 nm, what should The Flash so he can deceive his arch nemesis?A. Run towards his nemesis at a speed of 0.30B. Run away from his nemesis at a speed of 0.30C. Run towards his nemesis at a speed of 0.15D. Run away from his nemesis at a speed of 0.15E. Run at the speed light in any direction

31. A detector is stationed at the spatial origin, while a light source is somewhere along the positive x-axis. If the detector measures the wavelength of the light source, the velocity of the light source is v, and the measured wavelength of the light source in its own frame is 0 , then _______________.A. ( / 0 ) = [(1v)/(1+v)]1/2B. ( / 0 ) = [(1+v)/(1v)]1/2C. ( / 0 ) = [(1v2)/(1+v2)] 1/2D. ( / 0 ) = [(1+v2)/(1v2)] 1/2E. ( / 0 ) = [1/(1+v)]1/2

32. A troubled student, upon seeing his transcript with red marks, decides to accelerate until he reaches a speed v while carrying his transcript towards his parents. For his parents to see blue marks, he must be______________________.(Wavelengths of red and blue light: Red= 690 nm; Blue= 490 nm)A. moving away from them at speed 0.33B. moving toward them at speed 0.33C. moving toward them at speed 0.17D. moving away from them at speed 0.17E. moving toward them at speed 0.71

Hour 25

For the next two questions, consider a particle of mass m = 2.1 kg moving at a speed of 0.91c.

33. What is the particles momentum?

A. 1.9 kgB. 4.6 kgC. 5.1 kgD. 2.1 kgE. 0.79 kg

34. What is the particles total energy?


35. A particle has mass 1.673 x 10-27 kg. If it is moving to the left with speed 0.300, then the energy and momentum px of the particle must be:A. E = 1.75 x 10-27 kg, px = 5.26 x 10-28 kgB. E = 1.75 x 10-27 kg, px = 5.26 x 10-28 kgC. E = 7.523 x 10-29 kg, px = 5.02 x 10-28 kgD. E = 7.523 x 10-29 kg, px = 5.02 x 10-28 kgE. E = 7.523 x 10-29 kg, px = 5.26 x 10-28 kg

36. Two photons of the same energy E = 8.36 x 10-28 kg have an equal and opposite momentum along the x-direction, of magnitudes p = 8.36 x 10-28 kg. The two photons disappear after the collision and a new particle of total energy ETOT and pTOTx. What are ETOT and pTOTx?

A. ETOT = 8.36 x 10-28 kg, pTOT = 8.36 x 10-28 kgB. ETOT = 8.36 x 10-28 kg, pTOT = 0.00 kgC. ETOT = 1.67 x 10-27 kg, pTOT = 1.67 x 10-27kgD. ETOT = 1.67 x 10-27 kg, pTOT = 0.00 x 10-27kgE. ETOT = 1.67 x 10-27 kg, pTOT = 1.67 x 10-27kg

Hour 26

37. A particle is at rest relative to a rocket frame and has mass m = 8.25 kg. Relative to a stationary observer in a laboratory frame, this rocket frame is moving with speed 0.225 along the +x axis. What is the particle's energy and momentum relative to the laboratory frame?

A. E = 8.25 kg, p = 0 kg B. E = 8.03 kg, p = 1.81 kg C. E = 1.81 kg, p = 8.03 kg D. E = 1.91 kg, p = 8.47 kg E. E =8.47 kg, p = 1.91 kg

38. What is the momentum of a particle of mass m = 0.55 kg that is at rest in the lab frame as seen in a rocket that is moving with speed 0.77?

A. 0.42 kgB. 0.35 kgC. 0.66 kgD. 0.86 kgE. 0 kg

39. Consider a particle traveling along the x axis with momentum px = 19.0 eV and total energy E = 30.0 eV, as measured by a stationary observer in a laboratory. If another inertial frame is moving at constant speed vframe = 0.900 in the positive x direction, what would be the particle's momentum and total energy relative to the moving reference frame?

A. E' = 29.6 eV , px' = 18.3 eVB. E' = 108 eV, px' = 105 eV C. E' = 18.3 eV, px' = 29.5 eVD. E' = 105 eV, px' = 108 eVE. E' = 68.8 eV, px' = 8.28 eV

40. A photon has an energy E = 9.109 x 10-31kg and momentum in the negative x direction px= 9.109 x 10-31 kg as measured by observer Alice. Bob, another observer, is moving in the +x direction with velocity vBob = 1/2. According to Bob the photon must have an energy E =____ and momentum px = _____________.A. 7.88 x 10-31kg; 10.5 x 10-31kg in the positive x directionB. 15.8 x 10-31kg; 15.8 x 10-31kg in the negative x directionC. 15.8 x 10-31kg; 15.8 x 10-31kg in the positive x directionD. 5.26 x 10-31kg; 5.26 x 10-31kg in the positive x directionE. 5.26 x 10-31kg; 5.26 x 10-31kg in the negative x direction

Hour 27

41. A particle has rest mass of 3.5 kg relative to the lab frame. The particle is moving relative to the lab frame with a speed of 0.32. What is the rest mass of the particle relative to a rocket frame that is moving with a speed of 0.78 relative to the lab frame?


42. Which of the following statements is true?A. The speed of a massless particle can vary depending on its direction of motion.B. The momentum of a massless particle is equal to its energy.C. The momentum of a massless particle is zero.D. The total momentum of a non-isolated system is conserved. E. The total mass of a system consisting of zero mass particles is zero.

43. A particle has a momentum of 4.0 eV and a total energy of 5.0 eV. What is the mass of the particle?

A. 1.0 eVB. 9.0 eVC. 3.0 eVD. 6.4 eVE. 41 eV

44. A particle has energy 5.0 x 10-9 kg and momentum 2.0 x 10-9 kg in Alice's frame. In Bob's reference frame, the particle has energy 10.0 x 10-9 kg. What is the magnitude of the momentum in the Bob's frame?

A. 8.9 x 10-9 kgB. 8.5 x 10-9 kgC. 3.2 x 10-9 kg D. 4.6 x 10-9 kgE. 10.0 x 10-9 kg

Extra:

45. Consider the events labeled A to E. Which of these events can affect or cause event W but never be affected by event W?

End of Long Problem Set