PC1144 Homework 1

Qi Ji (A0167793L)

3rd Feb 2021

(a)

Let event 1 be lamp A turning on and event 2 for lamp B. Let frame F be the moving along the rod, at velocity V away from frame F that is stationary with respect to O.

(b)

Start from the frame F where rod 1 is at rest and the other is moving at speed V. We want to find a frame F moving at velocity u away from rod 1 such that V=Vu1uc2V and V=u, this will make both rods have the same length. Solving for u, we have u=c2v(121v2c2) reject the other quadratic solution since that will make uc.

(c)

Total energy twice as rest energy, this means γmc2=2mc2γ=2.

Solving 12=1β2 we have u=32c.