Question

The plane of clocks and measuring rods in Fig. 37-19 is like that in Fig. 37-3. The clocks along the x axis are separated (center to center) by 1light-second, as are the clocks along the y axis, and all the clocks are synchronized via the procedure described in Module 37-1. When the initial synchronizing signal of t = 0 from the origin reaches (a) clock A, (b) clock B, and (c) clock C, what initial time is then set on those clocks? An event occurs at clock A when it reads 10 s. (d) how long does the signal of that event take to travel to an observer stationed at the origin? (e) What time does that observer assign to the event?

Short answer

a) The initial time set in clock A is $t=4s$.

b) The initial time set in clock B is $t=3s$.

c) The initial time set in clock C is$t=5s$ .

d) The time taken by signal to reach origin from clock A is$t=4s$ .

e) The time assigned by the observer stationed at the origin is $t=14s$.

Step-by-step solution

 Step 1: Identification of given data

The given data can be listed below,

• The clocks are separated by the time of$1s$

Concept/Significance of time dilation

Time dilation is the difference in the amount of time that has passed since an event according to several observers. Either gravity or relativistic velocity is responsible for this time dilation.

Determination of the initial time set on clock A

The beginning time must be 4 seconds since the signal will travel 4light seconds to reach clock A, whenthe time at the origin, for the initial synchronizing signal is$t=0$ .

Thus, the initial time set at clock A is $4s$.

Determination of the initial time set on clock B

The initial time must be 3 s since the signal must travel 3 light seconds to approach clock B when the time at origin, for the initial synchronizing signal is t=0.

Thus, the initial time set at clock B is $3s$.

Determination of the initial time set on clock C

The distance between the origin and clock A is 4 light-seconds, the distance between the origin and clock B is 3 light-seconds, so, the distance between the origin and clock C is

$\sqrt{4^2+3^2}light-second=5light-second$

Thus, the initial time set at clock C is $5s$.

Determination of the initial time that a signal of that event take to travel to an observer stationed at the origin

The signal will take to reach the origin from the clock A. As the distance between the clock A and the origin is $4light-seconds$.

Determination of the time does the observer assign to the event.

As the signal starts from clock A at $t=10s$, the time assigned by the observer, stationed at the origin, to the signal will be-

$$\begin{gathered} t^{\text{'}}=10s+4s \\ =14s \end{gathered}$$

Thus, the time assigned by the observer will be $t^{\text{'}}=14s$.