Questions 69-71
The velocity of the car in the garage’s rest frame is
A. 0.4c
B. 0.6c
C. 0.8c
D. Greater than c
E. Not determinable from the data given
Length contraction: L = L0/γ
with γ = 1/(1 − v2/c2)½
Given for the car, L0 = 5 m and L = 3 m
γ = L0/L = 5/3 = 1/(1 − v2/c2)½
γ² = 25/9 = 1/(1 − v2/c2)
1 − v²/c² = 9/25
v²/c² = 1 − 9/25 = 16/25
v = 4/5 c = 0.8c
Answer: C
A car of rest length 5 meters passes through a garage rest length 4 meters. Due to the relativistic Lorentz contraction, the car is only 3 meters long in the garage’s rest frame. There are doors on both ends of the garage, which open automatically when the front of the car reaches them and close automatically when the rear passes them. The opening or closing of each door requires a negligible amount of time.
The velocity of the car in the garage’s rest frame is
A. 0.4c
B. 0.6c
C. 0.8c
D. Greater than c
E. Not determinable from the data given
(GR8677 #69)
Solution:
Length contraction: L = L0/γ
with γ = 1/(1 − v2/c2)½
Given for the car, L0 = 5 m and L = 3 m
γ = L0/L = 5/3 = 1/(1 − v2/c2)½
γ² = 25/9 = 1/(1 − v2/c2)
1 − v²/c² = 9/25
v²/c² = 1 − 9/25 = 16/25
v = 4/5 c = 0.8c
Answer: C
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