1. At what fraction of the speed of light must you travel for your apparent mass
ID: 1973589 • Letter: 1
Question
1. At what fraction of the speed of light must you travel for your apparent mass to be twice your rest mass?
2. You are traveling at 99% the speed of light. As you approach a meter stick, what would you perceive its length (in centimeters) to be?
3. You observe a spaceship coming towards you at a high rate of speed. A clock on board the spaceship appears to be running about 2.5 times slower than your clock. How fast is the spaceship going relative to you?
4. What value would you measure for the speed of the light (in miles/second) coming from the moving object in question 3?
Explanation / Answer
(1) M = M0 / sqrt { 1 - (v/c)^2 } M/M0 = 2 sqrt { 1 - (v/c)^2 } = 1/2 1 - (v/c)^2 = 1/4 (v/c)^2 = 3/4 v/c = (1/2) sqrt(3) v/c = 0.866025403784438646763723170752936 Note that... v/c = sin(60 degrees) M0/M = cos(60 degrees) So another way to do the problem, given M/M0, is... v/c = sin{ ArcCos[ M0/M ] } (2) gamma = 1/(1-v^2/c^2)^0.5 = 7.08 The meter stick would look shorter as you zoomed by it, by a factor of gamma. So L' = L/gamma = 14.1 cm t = gamma*t' -> gamma = 2.5 in the case of the clocks. 2.5 = 1/(1-v^2/c^2)^0.5 -> v = 0.917 (3) t'=(t-xv/c^2)/sqrt(1-v^2/c^2) .9165c (4)The speed of propagation of electromagnetic waves in a vacuum, which is a physical constant equal to exactly 299,792.458 kilometers per second. Also known as electromagnetic constant; velocity of light.
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