Relativity - Mastering Physics There are three (large) images. Each one correspo
ID: 1301221 • Letter: R
Question
Relativity - Mastering Physics
There are three (large) images. Each one correspond to a differing question. Please, answer them correctly and in order.
THANKS
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1.
"
Five identical quintuplets leave earth when they reach the age of 21, in the year 2121. Each quintuplet 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.
The graph below (Figure 1) shows the value of the term 1?v2/c2???????? as a function of velocity."
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Explanation / Answer
Special Relativity states that time is measured according to the relative velocity of the reference frame it is measured in. To calculate how time much time elapses on earth for a given time on the spaceship we use the equation:
T_earth = t_spaceship / sqrt(1-v^2/c^2)
To tidy up the equations the symbol g (which should be written using a Greek letter gamma but I don't know how to use Greek letters on here) is often defined as:
g = 1/(sqrt(1-v^2/c^2)
we can then write the time dilation equation as:
T_earth = t_spaceship * g
for a speed of 0.2c v/c is just 0.2 so:
g = 1/(sqrt(1-0.2^2)
= 1.02
similarly for the other speeds so:
speed gamma
0.2 1.02
0.4 1.09
0.8 1.67
We can now use these gamma values to calculate the time as measured on earth.
so A is gone for 10*1.67 years = 16.7 years
B for 5 * 1.02 = 5.1 years
C for 20 * 1.09 = 21.8 years
D for 10 * 1.09 = 10.9 years
E for 20 * 1.67 = 33.4 years
Since they left at the same time, the order from largest year of return to smallest is therefore:
E for 20 * 1.67 = 33.4 years
C for 20 * 1.09 = 21.8 years
A for 10 * 1.67 = 16.7 years
D for 10 * 1.09 = 10.9 years
B for 5 * 1.02 = 5.1 years