Relativity, how it affects observation.

[chewtoy929]

I'm having a bit of trouble understanding relativity, and would like some help with the following problems:
1. A spaceship passes a stationary observer at a speed that is 80% the speed of light. At rest, this ship is 65m long. What does the observer say about the length of the spaceship? How does this length compare to that
measured by an astronaut inside the spaceship?

2. A spaceship capable of flying 50% of the speed of light, travels from Earth to Proxima Centauri, the star closest to the Earth other than our own Sun at a distance of 4.3 light years. What does an astronaut inside the spaceship have to say about the length of time it takes to reach Proxima Centauri? How does this time compare to that measured by an observer stationed on Earth?

3. On Earth an astronaut has a mass of 75 kg. If they are in a spaceship that is flying at 75% of the speed of light, then what does a stationary observer have to say about the astronaut's mass? What does the astronaut have to say about their own mass?

 

[zhermes]

Why don't you start out with the concepts behind each problem; what will be the general answer to each. Then, what relevant equations do you think you might need?

 

[chewtoy929]

1= 65m from astronaut, 39 observer
2= 7.447818 astronaut, 8.6 observer
3= 75 kg astronaut, ~113 kg observer

 

[zhermes]

Looks good!

It sounded like you were having trouble with some of the concepts, however. Are they clear now?

 

[rwisz]

1. According to the theory of relativity, the observer will see the spaceship as shorter than its actual length. This is because as an object approaches the speed of light, its length appears to contract in the direction of motion. Therefore, the observer will measure the length of the spaceship to be less than 65m. On the other hand, the astronaut inside the spaceship will measure the length of the spaceship to be 65m, as they are at rest relative to the spaceship.

2. According to relativity, the astronaut inside the spaceship will experience time dilation, meaning that time will appear to pass slower for them compared to the observer on Earth. Therefore, the astronaut will measure the time it takes to reach Proxima Centauri to be shorter than 4.3 years. However, the observer on Earth will measure the time to be 4.3 years.

3. According to the theory of relativity, the observer will measure the astronaut's mass to be greater than 75 kg. This is because as an object approaches the speed of light, its mass increases. On the other hand, the astronaut will measure their own mass to be 75 kg, as they are at rest relative to themselves. This is known as the principle of equivalence, which states that all observers, regardless of their state of motion, will measure the same physical laws.