Max (observer 1) is on a train car moving with speed v = 2c/3 relative to Mindy
ID: 2281071 • Letter: M
Question
Max (observer 1) is on a train car moving with speed v = 2c/3 relative to Mindy (observer 2). Max measures the positions of the front and rear of the car simultaneously (relative to him) to determine the car's length. He measures the rear at position xrear1 at time trear1, and the front at xfront1 = xrear1 + L1 at time tfront1 = trear1 (the car's length is L1 and Max's measurements are simultaneous in reference frame 1). (a) What is the car's length L2 according to Mindy in reference frame 2? (b) Relative to Mindy, how much time passed between Max's measurements of the car's rear and front positions? Use the Lorentz coordinate transformation to find tfront2 - trear2, where trear2 is the time Mindy sees Max measure the car's rear position and tfront2 the time she sees Max measure the car's front position.Explanation / Answer
a)
dx = L1
dt = 0
L2 = dx'
L2 = gamma (dx - v dt)
L2 = (1/(1 - (v/c)^2)^0.5) (dx - v dt)
L2 = (1/(1 - (2/3)y2)y0.5) * (L1)
L2 = 1.34 L1
b)
dt' = gamma (dt - v dx/c^2)
dt' = (1/(1 - (v/c)^2)^0.5) * (0 - (2/3) L1/c)
dt' = (1/(1 - (2/3)y2)y0.5) * ((-2/3) L1/c)
dt' = -0.894 (L1/c)