Unit 9 Test

Question 1

Einstein’s theory of relativity is applicable only in inertial reference frames.

Answer 1

true

Question 2

Two spaceships A and B are moving relative to an observer O. The spaceships’ gamma values satisfy the relationship gA < gB. Which of the following accurately represents their speeds?

Answer 2

vA < vB

Question 3

The gamma factor that appears in the special theory of relativity is a function of velocity. Which of the following is the range of values for g?

Answer 3

γ >= 1

Question 4

An inertial observer O notes that O’ is moving with speed v relative to O. Suppose O measure a time interval delta t. Which of the following should be the corresponding time interval delta t’, based on O’’s clock as calculated by O?

Answer 4

delta t’ = γdelta t

Question 5

A rod is moving with respect to an observer O, in a direction perpendicular tot he rod’s length. Suppose L0 is the proper length of the rod. Which of the following is the length L of the object measured by O?

Answer 5

L=L0

Question 6

Suppose the two rods A and B are moving at two speeds (1/4)c and (3/4)c, respectively, relative to an observer O at rest. Both A and B have the same proper length in a given reference frame. Which of the following accurately compares the lengths of A and B as measured by O ?

Answer 6

lA > lB

Question 7

Suppose two inertial observers are each moving with the speed of light in the opposite directions. What is their relative speed?

Answer 7

c

Question 8

Two inertial observers are moving with relative speed v. An observer, O, measures the speed of an object in her reference frame to be u and notes O’s speed to be v. What is the speed of the object in the prime inertial frame according to O ?

Answer 8

u’ = u-v/1-uv/c2

Question 9

An observer in an inertial frame O ′ sees another inertial frame O moving to the right at a speed of (1/3)c. In O, the speed of an object moving to the right is (1/3)c. According to the galilean transformation, O will measure the object’s speed to be (2/3)c. According to the special theory of relativity, what is the speed of the object measured by the observer in O ?

Answer 9

Less than (2/3)c

Question 10

O observes O ′ move to the right with velocity v. O ′ measures the coordinates, (x ′, t ′ ), of an event. What are the Lorentz transformations that will enable the observer in O ′ to calculate the coordinates of the same event in the O reference frame?

Answer 10

x = γ(x' + vt')
y = γ(t' + vx'/c^2)

Question 11

Suppose two rockets, A and B, are moving to the right as observed in an inertial frame. The velocity of both the rockets is (1/4)c. What is the relative speed of the two rocket ships?

Answer 11

0

Question 12

Suppose S’ is moving to the right with velocity v = 0.866c as measured by an observer in S. The observer in S’ measures the coordinates of an event: x’ = 2*10^8m and t’ = 0.5s. What is the position and time coordinates of the events as measured by S?

Answer 12

x = 9.2 x 10^8 and t = 2.2s

Question 13

The coordinates of two events in S are such that delta x > 0. Which of the following condition will guarantee that the corresponding interval delta x’ in S’ is always positive?

Answer 13

delta x > c delta t

Question 14

Evaluate the following as true or false. According to the special theory of relativity, because v < c, the momentum p = γm0v can never increase without bounds.

Answer 14

false

Question 15

An object has a rest mass of 2 g. Based on the special theory of relativity, which of the following is the energy equivalent of the object’s mass?

Answer 15

1.8*10^14 J

Question 16

An observer O notes a particle moving to the right with velocity v. Another observer O ′ is moving with speed v relative to O along the direction of the motion of the particle. Which of the following is the value of the particle’s mass as measured by O and O ′?

Answer 16

O measures m and O’ measures m0

Question 17

A light particle, or photon, has zero rest mass. Which of the following is incorrect?

Answer 17

The total energy of a photon is zero.

Question 18

A particle with rest mass m0 = 1.6*10^-16kg is moving at a velocity equal to half the speed of light. Which of the following is the momentum of the particle?

Answer 18

17.3 kg*m^2/s^2

Question 19

In the relativistic case, which of the following is equal to the kinetic energy when an object is at rest?

Answer 19

0

Question 20

In Newtonian physics, kinetic energy equals ½ mv 2. Which of the following is the relativistic definition of kinetic energy?

Answer 20

γm0c2 - m0c2

Question 21

In an isolated system, momentum is conserved. Which of the following is not equivalent to the momentum conservation law?

Answer 21

p = 0

Question 22

The reference frames A and A′ describe events with unprimed coordinates (x, y) and primed coordinates (x′, y′ ), respectively. Relative to A, A′ moves at a constant speed v in the direction of negative y. If the origins of the two frames coincide at the instant t = 0, which of the following equations correctly relates the coordinates y and y′ ?

Answer 22

y′ = y + vt

Question 23

P and Q are traveling in the boxcars of two trains that are moving parallel and opposite to each other with relative speed v. Both observers are standing in the middle of their boxcars. As the observers pass each other, as shown in the figure, each turns on a light bulb and the light signal strikes the respective walls on each boxcar. Which of the following statements is not correct?

Answer 23

P notes that the light signal strikes the two ends simultaneously in Q’s car.

Question 24

Consider the light clock in the figure; the two mirrors are separated by a distance d. A clock tick consists of a roundtrip travel of a light beam from A to B and back to A. Which of the following is the value of d (in miles or meters) for which a tick equals one second

Answer 24

93,000 miles

Question 25

The proper length and width of a rod are l0 and w0, respectively. To an observer O, the rod is moving to the right with velocity v, as shown in the figure. Which of the following is the length l and width w of the rod measured by O?

Answer 25

l = l0
w = w0/γ