9.2.2 Solving Problems Using the Lorentz Transformations

Question 1

Solving Problems Using the Lorentz Transformations

Answer 1

• The relativity of simultaneity and the phenomena of time dilation and length contraction are all contained within the Lorentz transformation equations.
• The Lorentz transformation equations are very useful in problem solving. Once you have picked the relevant equation(s)you can just plug in what you know. But be careful with the details—it is easy to confuse events or reference frames or make sign mistakes.

Question 2

Two boxcars are moving relative to each other. In Boxcar S, an observer turns on a light bulb at t = 0 as Boxcar S’ passes by as shown in the figure. The light signal strikes the left and right walls of Boxcar S, whose total length is L.
Which of the following are the position coordinates xL and xR of the two events and delta x as measured by Boxcar S?

Answer 2

xL = -L/2
xR = L/2
delta x = L

Question 3

Suppose reference frame S’ is moving to the right with a velocity of 0.866c as measured by an observer in reference frame S. The observer in S’ measures the coordinates of the event:
x’ = 1.5*10^8m and t’ = 1s.
Which of the following lists the position and time coordinates of the events as measured by S? Note that for v = 0.866c, g = 2.

Answer 3

x = 8.2*10^8 m
t = 2.8 s

Question 4

Two boxcars are moving relative to each other. In Boxcar S, an observer turns on a light bulb at t = 0 as Boxcar S′ passes by as shown in the figure. The light signal strikes the left and right walls of Boxcar S, whose total length is L.

Answer 4

tL’ = g(L/2c + v/x^2 * L/2)
tR’ = g(L/2c - v/x^2 * L/2)
delta t’ = -gv/c^2L

Question 5

Suppose two events occur and the coordinates of the events in S are such that delta x > 0. Which of the following conditions ensures that in S’ the interval delta x’ for the same two events is always positive?

Answer 5

delta x > c delta t

Question 6

Consider a reference frame S’ moving to the right of a reference frame S with velocity v, and suppose two events occur and the coordinates of the events in S are such that delta t > 0. Which of the following conditions ensures that in S’, the interval delta t’ for the same two events is always positive?

Answer 6

delta t > delta x / c

Question 7

Two boxcars are moving relative to each other. In Boxcar S, an observer turns on a light bulb at t = 0 as Boxcar S’ passes by as shown in the figure. The light signal strikes the left and right walls of Boxcar S, whose total length is L.
Which of the following lists the time coordinate of tL and tR of the tow events and delta t as measured by Boxcar S?

Answer 7

tL = L/2c
tR = L/2c
delta t = 0

Question 8

An observer in a reference frame S sees a reference frame S ′ move to the right with velocity v. An observer in S ′ measures the coordinates (x ′, t ′ ) of an event. Which of the following Lorentz transformations enables the observer in S ′ to calculate the coordinates of the same event in the S reference frame?

Answer 8

x = g(x' + vt')
y = g(t' + vx'/c^2)

Question 9

Two boxcars are moving relative to each other. In Boxcar S, an observer turns on a light bulb at t = 0 as Boxcar S’ passes by as shown in the figure. The light signal strikes the left and right walls of Boxcar S, whose total length is L.
Which of the following lists the position coordinates xL’ and xR’ of the two events and delta x’ as measured by Boxcar S’?

Answer 9

xL’ = g(-L/2 - vL/2c)
xR’ = g(L/2 - vL/2c)
delta x’ = gL

Question 10

Suppose two rockets, Rocket A and Rocket B, are moving to the right as observed in an inertial frame. The velocity of both the rockets is (3/4) c. Which of the following is the relative speed of the two rockets?

Answer 10

0