ASTR 1010 – Homework Assignment 6 – Spring 2009

Question 1 – Use (1 – (v/c)²)^1/2 with v = 10 m/s. If you’re calculator is normal, it won’t have enough significant digits to give an answer other than 1.00000000. In other words, at 10 m/s, the change from 1 produced by the function is not measurable. With v = 1000 m/s, you also get 1.00000000. Only when v gets to be 1000000 m/s, does your calculator become accurate enough to give a value that is not 1.00000000 but 0.999994444 .

Question 2 – For this problem, v/c = 0.6 and t_stationary = 100 seconds.

t_moving = t_stationary(1 – (v/c)²)^1/2 = 80 seconds

For v/c = 0.99, t_moving = 14.1 seconds

Question 3. – Use the results from problem 1: at 10 m/s, the bar’s shortening is undistinguishable, so its length is 10.0 cm, at 1000000 m/s, the moving bar is 9.99994 m in length.

Question 4. – Postulate 1: The results of physics experiments should be the same for all frames moving at constant velocity with respect to each other. Postulate 2: The speed of light is the fastest speed at which anything can propagate and is independent of the velocity of the various frames. The second postulate is odd because it is the only thing that doesn’t change its speed as viewed from different frames.

Question 5. – For the first part of this problem, v/c = 0.6, so the proton’s mass increases to 2.09 x 10^-27 kg. For v/c = 0.99, the proton’s mass increases to 1.18 x 10^-26 kg. For v/c = 0.9999, the proton’s mass increases to 1.18 x 10^-25 kg.