Problems: Time Dilation

1. The animation represents two light clock travelling at 2x108ms-1relative to one another. The ball bouncing between the mirrors is in fact a photon of light travelling at 3x108ms-1 so the animation is not entirely to scale. The clock ticks every time the photon hits the bottom mirror.

If the distance between the mirrors is 3m calculate.

a. The time between ticks for the red girls clock as measured by the red girl.
b. The time between ticks for the purple girls clock as measured by the red girl

Here is what it looks like in the frame of reference of the purple girl

Now calculate
c. The time between ticks for the red girls clock as measured by the purple girl.
d. The lorentz factor γ

Note: To change the frames of reference and get the correct times in the animation I had to cheat with the velocities, Interactive physics isn't relativistic since the actual velocity of the objects is no where near fast enough.

2. The girl in the purple dress measures the frequency of a pendulum (attached to the ceiling of the rocket) to be 0.5Hz. What frequency would it have if measured by the girl in the red dress.

3. You can't see it but the girl in the red dress is holding a piece of radioactive material. She measures it's half life as 50s (rather a silly thing to do if you ask me). What will the half life be as measured by the girl in the purple dress.

4. The following animation shows a space ship travelling at a speed of 0.4c from the Earth to a star a distance of 4.4 light years away (measured from the Earth).

a. According to the red girl the time taken was 11 years, how long will the journey take according to the purple girl?

b. If the rocket is travelling at 0.4c what distance will it travel in the time measured by the girl in the rocket?

c. As the rocket passes the star a signal is sent back to the Earth how long after the rocket left the Earth will the signal get back to the Earth according to the red girl?

d. How long will this be according to the purple girl?

e. How much time will it take for the signal to get from the star to the Earth according to the purple girl?

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