University of the Philippines College of Science

PHYSICS 73

2nd Long Probset

1st semester

AY 2014 - 2015

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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 CONSTANTS: Planck’s constant: h = 6.626 x 10-34 J s Electron-volt: 1eV = 1.602 x 10-19 J

Hour 18

1. Convert 251km/hr into natural units.

A. 2.32 x 10-7

B. 7.83 x 10-7

C. 4.67 x 10-7

D. 8.62 x 10-7

E. 1.04 x 10-7

2. Which one of the following is an inertial reference frame?

A. UP classrooms

B. Rocket launching into space

C. A box falling from a table

D. Hot air balloons floating in the atmosphere

E. Entire surface of the earth

3. Which of the following is invariant in among inertial reference frames?

A. the velocity of an electron

B. the speed of an electron

C. the kinetic energy of an electron

D. the distance between two electrons

E. the rest mass of an electron

4. What is the natural unit of pressure?

A. kg

B. kg/m

C. kg/m2

D. kg/m3

E. kg/m4

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Hour 19

5. Consider two events, Event A and Event B, temporally separated by a

duration of 1m as measured by the lab frame. Event A can only affect Event B

by sending light towards it. What is the spacetime interval between them?

A. 0 m

B. 1 m

C. 2 m

D. 3 m

E. 4 m

6. Consider an emitter and a detector in a lab frame spatially separated by a

distance of 2m. A particle moves with a constant velocity 0.5 from the emitter

to the detector according to the lab frame. What is the spacetime interval

between the emission and detection of the particle as measured by a rocket

frame?

A. 1.72 m

B. 5.39 m

C. 2.84 m

D. 4.58 m

E. 3.46 m

7. A particle travels from event A (1.0m, 5.0m) to event B (6.0m, 3.0m)?

What is the speed of the particle?

A. 0.40

B. 0.50

C. 1.00

D. 0.20

E. 0.30

Hour 20

8. Consider the lightcone of event A. If event B is in the future lightcone of

event A, which of the following is true?

A. Event B can affect A by using a particle with speed less than the speed of

light

B. Event B can be affected by A by using light

C. Event B can affect A by using light

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D. Event B can be affected by A by using a particle with speed less than the

speed of light

E. The two events are not causally related

9. Which of the following world lines is NOT possible for a proton?

10. What is the proper time for an observer moving along a straight world line

connecting the events shown in the figure below? (Space and time are

measured in meters)

A. 0.33 m

B. 2.83 m

C. 8.00 m

D. 1.41 m

E. 3.00 m

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11. Refer to the figure below. Which of the following events could have

caused event F?

Hour 21

12. Two firecrackers explode at locations 5 hours of light apart in an inertial

laboratory frame. If one explodes 3 hours right after the other, what should be

the speed of a rocket frame relative to the lab frame to perceive the two

firecrackers exploding simultaneously?

A. 4/5

B. 3/5

C. 5/3

D. 5/4

E. No such rocket frame

13. As recorded by the laboratory frame, an event occurs at t = 2.00 secs, x =

5.00 secs. For a rocket frame moving at a velocity + 3/5 relative to the lab

frame, what is the coordinates of the same event?

A. t = 6.25 secs, x = 7.75 secs

B. t = -1.25 secs, x = 4.75 secs

C. t = 7.91 secs, x = 9.80 secs

D. t = -1.581 secs, x = 6.00 secs

E. t = 8.33 secs, x = 1.20 secs

14. The origins of the lab frame and rocket frame space-time diagrams are

coincident. The coordinates of an event in a rocket frame are (3.0m, 4.0m).

What are the coordinates of the same event in a lab frame if the velocity of the

rocket frame relative to the lab frame is +0.5?

A. (8.1m, 8.1m)

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B. (5.0m, 5.5m)

C. (1.2m, 2.9m)

D. (5.8m, 6.4m)

E. (3.0m, 4.0m)

15. The coordinates of an event in the lab frame is (3.00m, 6.00m). In a rocket

frame, the coordinates of the same event is (3.00m, 10.0m). What is the

velocity of the rocket frame relative to the lab frame?

A. 0.000

B. 0.500

C. 0.333

D. 0.636

E. 0.270

16. A bullet moving with a constant velocity starts from the origin of both the

lab and the rocket frame. After t = 5 secs, the lab frame recorded its position

to be at x = 3 secs. While for the rocket frame, after t' = 5 secs the bullet is at

x' = 4 secs. What is the velocity of the rocket frame as measured by the lab

frame?

A. 5/13

B. -5/13

C. 35/37

D. -35/37

E. 1/5

Hour 22

17. According to the lab frame, a box is moving at a speed of 0.70 in the

direction parallel to its length. In the lab frame, its dimensions are (L=2.0m) x

(W=1.0m) x (H=1.0m). What are the dimensions of the box in its rest frame?

A. (1.4m, 1.0m, 1.0m)

B. (2.8m, 1.4m, 1.4m)

C. (2.8m, 1.0m, 1.0m)

D. (2.0m, 1.0m, 1.0m)

E. (1.4m, 0.71m, 0.71m)

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18. Which of the following statements is true? If two events are simultaneous

in an inertial reference frame, then…

A. they are simultaneous in any inertial reference frame.

B. the spatial separation between the two events is the proper distance.

C. the two events can be connected by a light-like worldline.

D. they occur at the same place.

E. one of the events could have caused the other.

19. In a laboratory frame, Event A occurs simultaneously with the origin but

is located at the +x axis. What should be the velocity of a rocket frame

relative to the lab frame in order for Event A to occur after the origin?

A.

B.

C.

D.

E. No such rocket frame.

20. The positive muon ( is an unstable particle. How fast should it be

moving in order for its average lifetime to increase two-fold as measured in

the laboratory?

A. 0.866

B. 0.75

C. 0.5

D. 0.562

E. 0.96

Hour 23

21. A train with rest length moves with a velocity with respect to a lab

frame. As the back of the train passes the origin, its position is recorded on

the lab by marking the meterstick (Event A) at . After a time equal to

, the position of the front of the train is recorded on the lab by

marking the meterstick (Event B) at . What is the correct spacetime

diagram of events A & B along with the worldline of the front & back end of

the train as observed by the train’s rest frame?

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22. The figure below shows a two observer space time diagram. For the

laboratory frame, event L occurs at t = 9 s, x = 8 s. What is the corresponding

coordinates for the rocket frame with its axes illustrated below?

A. t‘ = 19.23 s, x’ = 18.78 s

B. t‘ = 4.91 s, x’ = 2.68 s

C. t‘ = 11.18 s, x’ 11.18 s

D. t‘ = 2.24 s, x’ = 2.24 s

E. t‘ = 5 s, x’ = 5 s

23. The spacetime diagram below shows 4 events A, B, C and D. A occurs

simultaneously with C, while B & D also occurs simultaneously after A. For

an observer that measures the same position for events A & B, what is the

correct sequence of the events (in increasing order)?

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A. A, B, C, D

B. A, B & C simultaneously, D

C. C. C, A, D, B

D. A & C simultaneously, B & D simultaneously

E. A & B simultaneously, D, C

24. Which of the following best depicts a rocket frame moving at a speed of

0.5 in the negative x-direction according to the lab frame?

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Hour 24

25. Dick drives a spacecar that moves with a velocity parameter 0.549

with respect to Earth. Jane, Dick’s avid competitor, thrusts her spaceship with

a velocity parameter 1.099 with respect to Earth. What is Dick’s velocity

as observed by Jane?

A. 0.501

B. -0.501

C. 0.929

D. -0.929

E. -0.550

26. A space ambulance located at your +x axis is moving with such speed that

light from its siren is blue shifted to yellow ( 550 nm). You know in its

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rest frame, the siren is red ( 700 nm). At what velocity is the space

ambulance moving relative to your frame?

A. 0.237

B. -0.237

C. 0.786

D. = -0.786

E. 0.120

27. Consider a rocket frame moving with a constant velocity 0.9 according to

a lab frame. If the rocket frame measures that a particle has travelled a

distance of 3m during a time 3m, what is the speed of this particle as

measured by the lab frame?

A. 0.4

B. 0.6

C. 0.8

D. 1.0

E. 1.2

Hour 25

28. Captain Kenway's ship fired a 1kg cannonball towards an enemy ship. If

the constant velocity of the cannonball is 0.9, what is its total energy?

A. 1.81 kg

B. 1.94 kg

C. 2.06 kg

D. 2.17 kg

E. 2.29 kg

29. What is the x-component of the momentum of a particle with mass

moving in the positive x direction in the laboratory with kinetic energy equal

to five times its rest energy?

A.

B.

C.

D.

E.

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30. What is the kinetic energy as measured in the laboratory of a particle of

mass with the worldline shown in the laboratory spacetime diagram?

A.

B.

C.

D.

E.

31. What is the momentum of a photon with frequency 1.45 x 1015 Hz?

A. 1.068 x 10-35 kg

B. 3.20 x 10-27 kg

C. 9.61 x 10-19 kg

D. 2.38 x 10-35 kg

E. 6.4 x 10-27 kg

Hour 26

32. According to a lab frame, the momentum of a particle and its energy is

measured as 7 kg and 25 kg respectively. Relative to the lab frame, a rocket

frame moves with a velocity . What are the momentum and energy of

the particle as measured by the rocket frame?

A. E = 26 kg, p = 10 kg

B. E = 26 kg, p = -10 kg

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C. E = 30 kg, p = -18 kg

D. E = 30 kg, p = 18 kg

E. E = 4.32 kg, p = 14.4 kg

33. A photon moves in an xy laboratory plane in a direction that makes an

angle with the x-axis. The photon has energy as observed by the

laboratory frame. What will be the measured of the photon for a rocket

frame moving with rapidity with respect to the lab frame? (Assume the

rocket frame is moving in the +x direction of the lab frame).

A.

B.

C.

D.

E.

34. A particle has mass . According to a lab frame, it has energy equal to

twice its mass and moves along the negative direction. For a rocket frame

moving with a velocity with respect to the lab frame, how much is

the particle’s energy?

A.

B.

C.

D.

E.

35. A particle was observed by the lab frame to have a total energy of 7MeV

and momentum of 5MeV. A rocket frame measures the total energy of this

particle to be zero. What is the velocity of this rocket frame relative to the lab

frame?

A. 7/5

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B. 2/3

C. 5/7

D. 1/4

E. No such rocket frame exists

Hour 27

36. A particle has energy equal to 25 kg and momentum 24 kg in a laboratory

frame. What is its energy as measured in its rest frame?

A. 7.00 kg

B. 1.00 kg

C. 34.7 kg

D. 0 kg

E. 25 kg

37. The following diagram shows the energy- momentum vector of a particle

moving at a constant velocity as measured in a laboratory. What is the

corresponding energy vs. momentum diagram of the same particle on a frame

that observes the particle to move at greater speed but at the opposite

direction?

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38. The energy and momentum of a particle in the lab frame is 4.0kg and -

2.0kg, respectively. In a rocket frame where the particle has energy of 9.0kg,

what is its magnitude of momentum?

A. 3.0 kg

B. 5.0 kg

C. 8.3 kg

D. 6.9 kg

E. 10.0 kg

Hour 28

39. A particle mass 2.0kg is moving to the right with a speed of 0.4. Another

particle of mass 1.0kg is moving to the left with a speed of 0.8. What is the

total momentum of these particles?

A. 0

B. -0.46kg

C. 2.2kg

D. 0.87kg

E. 1.3kg

40. Two photons, both with energy E, are moving in opposite directions. They

collide head-on and created a particle with some mass. What is the mass of

this particle?

A. 0

B. E

C. 2E

D. 3E

E. 4E

41. A particle with mass 1000MeV is moving with a constant velocity +0.4.

This collides with another particle with mass 500MeV and is moving in with a

constant velocity -0.8. If this collision is inelastic, what is the mass of the

resulting particle?

A. 1500.00 MeV

B. 1885.28 MeV

C. 1894.71 MeV

D. 1910.60 MeV

E. 1924.42 MeV

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42. A positronium (an electron and positron orbiting one another) of mass

and initial energy decays into two photons that move in opposite

directions. What is the momentum of the photon that moves in the same

direction as the initial particle?

A.

B.

C.

D.

E.