Chapter 28. Relativity

Problem 2.

v_A = 0.75 c and v_B = 0.94 c

the proper time interval is the same for both A and B: Deltat0_A=Deltat0_B

if Deltat_A=37h is the time interval measured by the observer moving at a speed relative to Earth v_A then

Deltat_A sqrt[1-.75^2] = Deltat_B sqrt[1-.94^2]

then Deltat_B = 72h

Problem 5.

proper time: Deltat_0 = 2 pi sqrt(m/k)

period of oscillation for the other observer:

Delta_t = 2 pi sqrt(m/k) / sqrt[1-(v/c)^2] = 2.28s

Problem 12.

L=1800m, W = 1500m

L0 = L/sqrt[1-(v/c)^2] = 3400m

W0=W

Problem 14.

the dilated distance is x = x0 sqrt[1-(v/c)^2]

and y=y0, then

tan theta = y/x = y / x0 sqrt(1-.73^2) = tan 30 / 0.683

theta = 40.2

Problem 27.

KE = mc^2 [ 1/sqrt(1-v^2/c^2) - 1] = 5 10^-13 J

Problem 39.

a. p = 5.1 10^15 kg m /s

b. p = 9.7 x 10^15 kg m /s