Modern Physics Qs - Time Dilation & Relativity

[omer10000]

Q1. Time Dilation Question

Homework Statement


Three identical triplets leave Earth when they reach the age of 21, in the year 2121. Each triplet goes on a spaceship journey that takes T years, as measured by a clock in each spaceship. During the journey they travel at a constant speed v, as measured on earth, except during the relatively short acceleration phases of their journey. (Triplets occur when three babies are born together.)

Part A)
The triplets return to Earth in different years according to people who stay on Earth. Rank the triplets on the basis of the year on Earth when they return from their journey. That is, work out the year when each triplet returns, and then rank the triplets according to the largest return year to the smallest return year.

A- T= 20 years, v=0.4
B- T= 10 years, v=0.8
C- T= 10 years, v=0.4

Part B)
Calculate the age of each triplet when they return from their journey. Rank the triplets on the basis of their return age.

A- T= 10 years, v=0.4
B- T= 20 years, v=0.4
C- T= 10 years, v=0.8

Homework Equations

Δt' = x*b where b = √(1-(v/c)^2) → x = (Δt')/√(1-(v/c)^2) => PART A

The Attempt at a Solution

Part A - Solving for x: A = 22 yrs...B = 17 yrs...C = 11

Is this correct? I don't think so; answer might be: B A C. How is this possible?

Part B

Shouldn't the answer be same as Part A? Apparently it may be: C A B. Why?

Q2. Relativity

1. Homework Statement

A spaceship passes Earth moving at 0.80c. The spaceship then passes the Moon. How much time, according to the ship's clock, elapses between the time a person looking out the ship's window sees Earth pass by and when the Moon passes by. The Earth-Moon distance is approximately 3.84*10^8m

Homework Equations

Δt = Δx/v

Δt'=Δt*√(1-(v/c)^2)

The Attempt at a Solution

Δt = Δx/v = (3.84*10^8m)/((3.0*10^8)*0.80c) = 1.6s
Δt'=Δt*√(1-(v/c)^2)=1.6*√(1-0.8^2)=0.96s

|^| Is this in reference to person in spaceship?

Thanks

 

[Doc Al]

The Attempt at a Solution

Part A - Solving for x: A = 22 yrs...B = 17 yrs...C = 11

Is this correct? I don't think so; answer might be: B A C. How is this possible?

Why do you think your answer is not correct?

Part B

Shouldn't the answer be same as Part A? Apparently it may be: C A B. Why?

You are basically told the answer to this one. (You are told their clock readings during the trip.)

Δt = Δx/v = (3.84*10^8m)/((3.0*10^8)*0.80c) = 1.6s
Δt'=Δt*√(1-(v/c)^2)=1.6*√(1-0.8^2)=0.96s

Δt is the time as measured by Earth clocks; Δt' is the time measured on the ship, which is what you want.

 

[omer10000]

Why do you think your answer is not correct?You are basically told the answer to this one. (You are told their clock readings during the trip.)

It is odd that the answer is uniformly fitting the given options; ie. A B C options are answered CORRECTLY as A B C

Δt is the time as measured by Earth clocks; Δt' is the time measured on the ship, which is what you want.

I knew the answer to this but just wanted to double check for certainty.

Thanks

 

[Doc Al]

Part A)
The triplets return to Earth in different years according to people who stay on Earth. Rank the triplets on the basis of the year on Earth when they return from their journey. That is, work out the year when each triplet returns, and then rank the triplets according to the largest return year to the smallest return year.

A- T= 20 years, v=0.4
B- T= 10 years, v=0.8
C- T= 10 years, v=0.4

Part B)
Calculate the age of each triplet when they return from their journey. Rank the triplets on the basis of their return age.

A- T= 10 years, v=0.4
B- T= 20 years, v=0.4
C- T= 10 years, v=0.8

Why do parts A and B have different data?

 

[omer10000]

Why do parts A and B have different data?

They are just arranged in a different manner. Since I answered with their abbreviations (ie. A, B, C), it makes sense that I organize it in such a manner.

Therefore:

A- T= 20 years, v=0.4
B- T= 10 years, v=0.8
C- T= 10 years, v=0.4

Part A = A B C but answer maybe B A C
Part B = A B C but answer may be B C A. If that's the case (silly me) then B and C are same then it is A but that still doesn't explain HOW Part A is B A C.

Thanks

Ps. Sorry for late reply.

 

[Doc Al]

They are just arranged in a different manner. Since I answered with their abbreviations (ie. A, B, C), it makes sense that I organize it in such a manner.

Your notation is confusing. I thought A, B, and C referred to the different triplets. So the data should be consistent.

Therefore:

A- T= 20 years, v=0.4
B- T= 10 years, v=0.8
C- T= 10 years, v=0.4

I will accept this as the given data.

Part A = A B C but answer maybe B A C

Again, why do you think your answer A B C is wrong? (Obviously, both answers cannot be correct.)

Part B = A B C but answer may be B C A.

Those answers are not compatible, so which is it?

If that's the case (silly me) then B and C are same then it is A but that still doesn't explain HOW Part A is B A C.

Tell me WHY you think part A could be B A C.

 

[omer10000]

Your notation is confusing. I thought A, B, and C referred to the different triplets. So the data should be consistent.

You are right; A B C refer to the triplets.

Again, why do you think your answer A B C is wrong? (Obviously, both answers cannot be correct.)

Those answers are not compatible, so which is it?

Tell me WHY you think part A could be B A C.

I have calculated the answers using Δt' equation and have found the answer to be such but this question has already been asked (http://au.answers.yahoo.com/question/index?qid=20100914220049AAG5sHf) and propose different answers. For ease, I copy and pasted the question from the aforementioned website and that's why I had triplet information arranged in a different manner.

How I see the question is that Part A = A B C and Part B (as you have already mentioned/hinted) is pre-given in the question information = (CB), (A). Part B is calculated using the number of years they traveled as their ages is increasing relatively to the spaceships.

Thanks

 

[Doc Al]

I have calculated the answers using Δt' equation and have found the answer to be such but this question has already been asked (http://au.answers.yahoo.com/question/index?qid=20100914220049AAG5sHf) and propose different answers.

Note that no explanation is given for the answers. They make no sense to me.

How I see the question is that Part A = A B C and Part B (as you have already mentioned/hinted) is pre-given in the question information = (CB), (A). Part B is calculated using the number of years they traveled as their ages is increasing relatively to the spaceships.

Right.

 

[omer10000]

Alright Doc al, it seems that what we started with is what we ended with, albeit now it's much more pellucid (clear - nice word right!). To summarize what has happened in this thread:

1) Part A and Part B triplet information was rearranged and caused a misunderstanding in the interpretation of data (and it was easily overlooked that answer to Part B was already included in question information).

This was solved by making both sets of information consistent. Part A and Part B are now as follows:

A- T= 20 years, v=0.4
B- T= 10 years, v=0.8
C- T= 10 years, v=0.4

∴ Part A does in fact = A B C
Part B = (BC), (A) ... BC = CB; they are the same​

2) Δt' is relative to spaceship.

∴Δt' = 0.96s​

Thank you for all you help Doc al, any final comments?

 

[Doc Al]

I'd say you got it just right.