Physics 73 PS 2

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University of the Philippines

College of Science

Physics 73

Second Long Problem Set

Second Semester, AY 2015–2016

Name: Instructor:

Section/Class Schedule: Student Number:

Course: College:

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Second Long Problem Set Second Semester, AY 2015–2016 Physics 73

Instructions: Choose the letter of the best answer to each of the following questions. To

change your answer, cross (X) out the shaded letter and supply your new answer with your

signature beside the item. Any form of cheating in examinations or any act of dishonesty in

relation to studies, such as plagiarism, shall be subject to disciplinary action.

USEFUL CONSTANTS

Speed of light in vacuum: c = 3 × 108 m/sPlanck’s constant: h = 6.626 × 10−34 J · s

USEFUL CONVERSION FACTOR

1 eV = 1.602 × 10−19 J

Hour 17

1. Frame Master. Which of the following is an inertial reference frame?

A. Freely falling debris

B. Powered spacecraft

C. Space station near a massive planet

D. Plane on earth’s atmosphere

2. Natural Momentum. What is 5.00 ×

10−21 kg-m/s of momentum in natural units?

A. 7.81 × 10−39 kgB. 4.39 × 10−3 eVC. 1.67 × 10−29 kgD. 3.12 × 10−2 eV

3. Survive. Which of the following ideas from Newtonian dynamics survived after Einstein’s

postulates?

A. simulteneityB. causality

C. absolute time

D. velocity transformation

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Hour 18

4. Spam. In a lab frame, events A and B occur at the same time at locations xA = 2 m andxB = 11 m, respectively. If the same events occur at times t

A

= 1 m and tB

= 8 m in arocket frame, what is the space separation of the two events in the rocket frame?

A. 5.60 m

B. 32.0 m

C. 11.4 m

D. 130 m

5. Relative speed. An observer in a lab frame observes two events that occur at the same

location but separated in time by 6.00 s. If the same events are separated in time by 9.00 s

in a rocket frame, what is the speed of the rocket frame relative to the lab frame?

A. 0.67

B. 0.41

C. 0.35

D. 0.75

6. Traveller. Consider a space traveller leaving Earth bound for Alpha Centauri, on a space-

ship that is moving with velocity 0.6. Alpha Centauri is 4.2 light-years away from Earth.What is the proper time between the event that the space traveller has left Earth and the

event that the space traveller has reached Alpha Centauri?

A. 2.52 y

B. 4.20 yC. 5.60 y

D. 11.67 y

7. Extreme. An event occurs at (t, x) = (5 m, 3 m) in some lab frame. At what speed of the

rocket frame will this event have the largest time separation with respect to the common

origin of the inertial frames?

A. 3/4

B. 4/5

C. 3/5

D. 1

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Hour 19

8. Affected. Consider events A–D and O in the spacetime

diagram. Which of the following statement(s) is (are)TRUE?

I. Event O can affect event A by particle emission.

II. Event C could have been affected by event D by

light-ray emission.

III. Event D can affect event O by particle emission.

A. I and II only

B. II only

C. I and III only

D. III only

9. e-World Line. Which of the following represents a world line of an electron through space-time?

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10. Longest. Which of the following particle worldlines have the greatest proper time?

Hour 20

11. Velocity. Disintegration of a particle occurs at (4.0 m, –3.0 m) in the lab frame. If this

event is observed at (7.0 m, 2.0 m) in the rocket frame, what is the velocity of the rocket

frame relative to the lab frame?

A. +0.59

B. −0.59C. +0.85

D. −0.8512. Missing Link. In frame S , event O occurs at (0.00 m, 2.50 m). This same event is also

observed in frame S (which moves at a constant velocity of β > 0 relative to frame S )and frame S (which moves at a constant velocity of β = +0.68 relative to frame S )upon coincidence of the origins of the three frames. If event O occurs at time t = 4.00 min frame S , what are the coordinates of event O in frame S ?

A. (9.81 m, 10.12 m)

B. (9.81 m, 1.07 m)

C. (10.12 m, 9.81 m)

D. (1.07 m, 9.81 m)

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13. Nyan Cat and Doge. Nyan Cat moves with speed 0.800 relative to Doge. Doge observesan event occurring at coordinates (1.50 m, 0.900 m). What are the coordinates accordingto Nyan Cat?

A. (−0.500 m, 1.30 m)B. (1.30 m,−0.500 m)C. (3.70 m, 3.50 m)

D. (3.50 m, 3.70 m)

14. Relative. Two astronauts, one at a lab frame and another on a rocket frame moving at some

velocity with respect to the lab frame, both possessing identical metersticks. The astronaut

in the lab frame observes that the meterstick on the rocket frame is a bit shorter than the

one in lab frame. What will the astronaut in the rocket frame observe about the length of

the lab frame meterstick compared to the rocket frame meterstick?A. Shorter

B. Longer

C. Shorter if approaching, longer if receding

D. Shorter if receding, longer if approaching

Hour 21

15. Javelin Throw. You threw a meterstick such that it moves at a constant speed of 0.500

with respect to you. How long is the stick as measured in your reference frame?

A. 1.00 m

B. 1.15 m

C. 0.866m

D. 0.750m

16. TGIF. Hobbes, while at rest, is holding a 10- m long tree branch. Calvin, who is mov-ing, measures the branch’s length to be 4 m only. What is Calvin’s speed with respect toHobbes?

A. 0.9

B. 2.7

C. 1.1

D. 0.8

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17. Bad blood. Taylor heared two consecutive explosions at a time interval of 3.0 m. If Tayloris moving at 0.75 relative to Selena, what would be the time interval between the two

explosions according to Selena?

A. 4.5m

B. 2.0mC. 1.5m

D. 3.0m

18. Marvin the relativistic metal man. Marvin running at 0.62 moves across the length of

a big rectangular metal sheet with length 100 m and width 70 m. What is the area of the

rectangular metal sheet according to Marvin?

A. 7000m2

B. 5492m2

C. 4309m2

D. 8922m2

Hour 22

19. Same position or same time? Consider the t-x axes of an inertial observer O, and the

events plotted on the diagram shown. Which of the following is correct regarding the

marked events?

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A. There exists an inertial observer moving to the right such that E and G are

simultaneous.

B. There exists an inertial observer moving to the left such that F and G occur at

the same position.

C. There exists an inertial observer moving to the left such that E and F occur atthe same position.

D. There exists an inertial observer moving to the right such that G and H are

simultaneous.

20. Spacetime diagram. Two spaceships, each of proper length L, pass near each other head-ing in opposite directions. Events P, Q, R, and S are defined as follow.

Which of the following correctly depicts the two-observer spacetime diagram of the prob-

lem?

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21. Esme’s Pets. Consider the given two observer spacetime diagram, where (t, x) denote rocketframe coordinates and (t, x) denote lab frame coordinates. The rocket frame is moving withrespect to the lab frame. Which of the following events does the rocket frame observe to happen

at the same place as event P?

A. ELK

B. CAT

C. DOG

D. FOX

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22. Ti-prime, Ex-prime. Which of the following shows the correct time and space axes of a

rocket moving at β = 1/3 to the left relative to the lab frame, assuming that their originscoincide?

Hour 23

23. At Last I See It. Rapunzel is at rest in a rocket which is moving with a constant velocity

0.50 according to a lab frame. If Rapunzel measures a particle which has travelled a dis-

tance of 25.m during a time 25.m, what is the speed of the particle as measured by the labframe?

A. 0.40

B. 0.60

C. 0.80

D. 1.0

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24. θ-θ,. Shown in the table below are the rapidity measurements by the lab and rocket framesfor a particle moving at constant velocity. What is the velocity of the rocket frame as

measured by the lab frame?

Reference Frame Rapidity

Lab 6.52

Rocket 5.15

A. −0.879B. 0.879

C. −0.999D. 0.999

25. Doge chase cate. Two dogs, Pluto and Scooby are chasing a cat, Hello Kitty. If Pluto sees

Hello Kitty running away from him at 0.50 and Scooby running towards him at 0.25, how

fast is Hello Kitty according to Scooby? (Assume all motion are in one line.)

A. 0.67

B. 0.29

C. 0.86

D. 0.75

Hour 24

26. E! A 3.1 × 10−27 kg-particle is travelling at 0.5. What is its energy?A. 1.2 × 10−27 kgB. 5.7 × 10−27 kgC. 3.6 × 10−27 kgD. 9.8

× 10−27 kg

27. Super bird. A super bird flying at relativistic speed is measured to have a total energy of

30 MeV and a momentum of 13 MeV. What is the speed of the bird?

A. 0.48

B. 0.43

C. 0.39

D. 0.52

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28. Photon momentum. What is the momentum of a photon with frequency 3.41 × 1016 Hzmoving to the right?

A. 2.51 × 10−34 kgB. 2.26

× 10−17 kg

C. 7.53 × 10−26 kgD. 1.75 × 10−33 kg

Hour 25

29. Doppler Frequency. A photon with frequency 2.00 MHz is emitted at an angle of 60.0◦

with respect to the x-axis of a lab frame. What is the measured frequency of this photon in

a rocket frame moving at a velocity 0.50 with respect to the lab frame?

A. 2.89 MHzB. 1.73 MHz

C. 1.34MHzD. 2.00MHz

30. Run to you. Your friend holding a monochromatic light of wavelength 670 nm is runningtowards you at a speed of 0.45. What will be your perceived wavelength of the light?

A. 1088 nm

B. 972nm

C. 369nmD. 413nm

31. What Rocket? A particle was observed by the lab frame to have a total energy of 7 kg andmomentum of 5 kg. 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. 2/3

B. 5/7

C. 1/4

D. No such rocket frame exists

32. Energy. Consider a particle moving with velocity β = 0.8 along the +x-direction relativeto an inertial observer O. The measured energy of the particle is 15.00MeV, relative to O.Another inertial observer O’ is moving with some unknown velocity β relative to O. If theenergy of the particle as measured by O’ is 41.00MeV, what is β ?

A. -0.2

B. 0.4

C. 0.6

D. -0.8

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33. Momenergy. According to a lab frame, the momentum and energy of a particle is mea-

sured as 7.0 kg and 25kg respectively. Relative to the lab frame, a rocket frame moveswith a velocity 0.60. What are the momentum and energy of the particle as measured by

the rocket frame?

A. E = 26 kg, p = 10. kgB. E = 26 kg, p = −10. kgC. E = 30 kg, p = −18kgD. E = 30 kg, p = 18 kg

Hour 26

34. April 29. The energy and momentum of a particle in the lab frame is 4.0 kg and −2.0 kg,respectively. In a rocket frame where the particle has energy of 9.0 kg, what is its magnitudeof momentum?

A. 3.0 kg

B. 5.0 kg

C. 8.3 kg

D. 6.9 kg

35. When photons collide. Two photons with energies E and 2E in the lab frame are on ahead-on collision. What is the total mass associated with this system?

A. 2√

2E

B. 3E

C. zero

D. E √

2

36. Don’t rest yet! A particle with kinetic energy K moves with speed 0.600. What is theparticle’s rest mass?

A. 4K

B. 32K

C. 35K

D. 45K

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37. System Mass. Consider a particle of mass 2m and totalenergy 4m non-interacting with a photon with energy 6mshown in the figure. What is the mass of this system?

A. 2√ 23mB. 52m

C. 2√

13m

D. 2m

Hour 27

38. Bang Bang. A particle with rest mass m and kinetic energy 3m collides with a stationaryparticle with the same rest mass, forming a single moving particle. What is the rest mass

of the resulting particle?

A.√

5m

B.√

10m

C.√

15m

D.√

20m

39. Positronium Gaming. A positronium of mass m and initial energy E = 2m decays into

two photons that move in opposite directions. What is the momentum of the photon thatmoves in the same direction as the initial particle?

A. m

B. (1 +√ 3

2 )m

C. (1 −√ 3

2 )m

D.√ 3

2 m

40. To p or not to p. A particle of mass M decays from rest into two particles that move in

opposite directions. One particle has mass m and the other particle is massless. What isthe velocity of particle m?

A. 1

B. m2

M 2 + m2

C. M − mM + m

D. M 2 − m2

M 2

+ m2

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