Spacetime diagram based question.

In summary, the conversation discusses a spaceship moving at 4/5 the speed of light and the effects of time dilation on the light travel time and clocks on the ship. Using equations and diagrams, the observer at rest is able to determine the total round trip time for the light to go from the rear to the front and back, the time for the light to go from the rear to the front, and the time for the light to go from the front to the rear. The observer also calculates the difference in synchronization between the front and rear clocks.
  • #1
ronsonol
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Homework Statement


A Spaceship is moving with speed ß=4/5.

Its length at rest is 1sec. A light is turned on at the rear of the ship, reflected back from a mirror at the front.
a.) How long does an observer at rest say it takes for the light to return to the rear of the ship (total round trip time)?
b.) How long did the light take to go from the rear to the front?
c.) How long did the light take to go from the front to rear?
d.) Use the results above to determine how far out of synchronization an observer at rest says the ship's front and rear clocks are.

∆T = 2s (proper time = 2seconds) light shining from rear to front back to rear.
y=5/3

Homework Equations



∆t=y (∆t' +ß∆x')
∆T - ∆t≈=-0.5v^2∆t

The Attempt at a Solution



For Part A I used the 1st equation:
∆t = (5/3)(2s + (4/5)(0)) = 10/3s
I'm not sure if I set it up correctly, but I got it right.

I am still trying to figure out part B and part C and have attached a diagram.

Part D I'm not sure exactly how I got the correct answer but I used the 2nd equation to estimate the difference:
2-(10/3) = -4/3s
 

Attachments

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Since this thread was moved from the Advanced to Introductory section, I thought it would be appropriate to bump, hopefully someone can offer a hint for me to continue. Thanks in advance.
 

What is a Spacetime diagram?

A Spacetime diagram is a graphical representation of the relationship between space and time. It is a 2D diagram that shows how objects move through both space and time.

How do you read a Spacetime diagram?

To read a Spacetime diagram, you must understand that the horizontal axis represents space and the vertical axis represents time. A straight line on the diagram shows an object moving at a constant speed, while a curved line indicates acceleration. The slope of the line also shows the velocity of the object.

Why are Spacetime diagrams important in physics?

Spacetime diagrams are important in physics because they allow us to visualize and understand the relationship between space and time. They are especially useful in understanding the theory of relativity and how objects move in relation to one another.

Can Spacetime diagrams be used to solve problems?

Yes, Spacetime diagrams can be used to solve problems in physics. By analyzing the diagram and using the equations of motion, we can determine the position, velocity, and acceleration of objects in both space and time.

What are some limitations of Spacetime diagrams?

One limitation of Spacetime diagrams is that they are limited to two dimensions, which may not accurately represent the movement of objects in three-dimensional space. They also do not take into account factors such as gravity or external forces, which can affect the movement of objects.

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