HW7%20solutions

# HW7%20solutions - Homework 7 solutions Physics 204 evening...

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Homework 7 solutions Physics 204 evening summer 2008 1. REASONING The distance between earth and the center of the galaxy is the proper length L 0 , because it is the distance measured by an observer who is at rest relative to the earth and the center of the galaxy. A person on board the spaceship is moving with respect to them and measures a contracted length L that is related to the proper length by () 22 0 1/ LL vc =− . The contracted distance is also equal to the product of the spaceship’s speed v the time interval measured by a person on board the spaceship. This time interval is the proper time interval Δ t 0 because the person on board the spaceship measures the beginning and ending events (the times when the trip starts and ends) at the same location relative to a coordinate system fixed to the spaceship. Thus, the contracted distance is also L = v Δ t 0 . By setting the two expressions for L equal to each other, we can find the how long the trip will take according to a clock on board the spaceship. SOLUTION Setting 0 equal to L = v Δ t 0 and solving for the proper time interval Δ t 0 gives 0 0 15 2 27 8 9.47 10 m 23 500 ly 1ly 0.9970 1yr 1 1822yr 3.16 10 s 0.9970 3.00 10 m/s Δ= ⎛⎞ × ⎜⎟ ⎡⎤ ⎝⎠ ⎢⎥ × × ⎣⎦ L tv c v c c = 2. REASONING Assume that traveler A moves at a speed of v A = 0.59 c and traveler B moves at a speed of v B = 0.83 c , both speeds being with respect to the earth. Each traveler is moving with respect to the earth and the distant star, so each measures a contracted length L A or L B for the distance traveled. However, an observer on earth is at rest with respect to the earth and the distant star (which is assumed to be stationary with respect to the earth), so he or she would measure the proper length L 0 . For each traveler the contracted length is given by the length-contraction equation as stated in Equation 28.2: AB A0 B0 1 and 1 vv cc It is important to note that the proper length L 0 is the same in each application of the length-contraction equation. Thus, we can combine the two equations and eliminate it.

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HW7%20solutions - Homework 7 solutions Physics 204 evening...

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